At least our opinion polls have better calibrated probability estimates!
But you are correct, though the issue is a bit subtler. For example, Metaculus advertises its track record: in past Metaculus aggregated predictions have been quite good, so it is worthwhile to look at their current predictions, too. However, they don't guarantee that the predictor pool stays stable nor even of equivalently high quality. Their platform is vulnerable to Eternal September.
The other part of answer is: do not underestimate power of the opinion polls. They are very useful, and they are not cheap to conduct either!
The true public opinion is valuable information which is difficult to obtain and access to it was restricted only to those who have the means to obtain it. And many people have an incentive to manipulate people's perception of what it is. How would you know what is the true aggregated common public opinion if you had only old-fashioned media available? You could talk to people you know, but that is only your social bubble, it could be biased. Suppose you watch TV and read newspapers. A reporter goes out and interviews the proverbial "man on the street" -- they are likely to interview several, and make a decision which interview gets airtime or is printed. Or talk show host invites several pundits to discuss what is the expert consensus on some phenomena or another -- they have editorial discretion over who they invite. And so on. You could call Gallup and ask for their rates -- not something everyone can do.
Regarding the degradation of Zelenskyy NO on Polymarket, a lot of these markets behave like options: they have a time value, and in absence of any new meaningful information, the time value falls until it reaches 0.
Good point! Given this time-value-of-options model, does it surprise you that the Zelenskyy NO price fell from 63% to 20% in the first 14 out of the 53 days until expiration?
It does not. I was a decently sized player in helping the odds go from ~60% to 20 or so. The bulk of the move was when market participants realized how inefficient Russian troop movements have been in Northern Ukraine.
Furthermore, the bulk of the shock move was done by one participant (a whale) who's trades move polymarkets substantially.
I see. Sounds like "market participants realized how inefficient Russian troop movements have been" was a bigger factor than "options generally go to 0 due to time value" in this case -- does that seem right to you in explaining what happened in the market?
Appropriately, "Will Kyiv fall by April" has dropped by more than half since March 7 (one week ago), whereas "Will Kyiv fall by June" has fallen only a little since then.
For a more colloquial explanation think of a question which goes "Will [Biden] [be president] by [December 31st]?" Particularly this works for questions when the answer is yes for today and you're asking if it'll change to no.
Every day that passes the odds should go down right? So looking back we could say (as Scott does), "this is decreasing linearly, better frontrun it". However this would be a mistake. More likely than small independent events which 'boost' Biden still being president (for Kyiv this would be small events which are pro-Ukraine) it is the lack of a large event which boosts Russia.
We can also think about a lottery. "Will I win the lottery before x date buying a ticket every day?" This would go down over time and is a much easier to understand and simpler model.
It's dangerous to immediately price in the updates you expect to see based on the trend! The forecasters are behaving as proper Bayesian agents and updating slowly, according to the trickle of evidence. Moreover, waiting makes existing evidence stronger - nobody debunked it, you've seen nothing that contradicts it despite time in which such information could surface.
"This is almost monotonically decreasing. Every day it’s lower than the day before. How suspicious should we be of this? If there were a stock that decreased every day for twenty days, we’d be surprised that investors were constantly overestimating it. At some point on day 10, someone should think “looks like this keeps declining, maybe I should short it”, and that would halt its decline. In efficient markets, there should never be predictable patterns!"
If you plotted a prediction for "will this iodine-131 nucleus have decayed by April 1" you'd also get a roughly linear decline (unless it decayed in which case it would jump up to 100%). Prediction markets are allowed to have "story arcs", so long as the *expected* change is zero.
My father's example was the Peso market. For a long time, investing in Pesos gave you a higher return than investing in dollars, which looks like a failure of efficient markets. Then Mexico devalued the Peso.
Similarly here. The pattern is what you would expect if, every day, there was a high probability of a small piece of evidence in favor of Ukraine and a very low probability of a very large piece of evidence in favor of Russia.
I am not a physicist, but IIRC the readioactive decay is exponentially distributed, i.e. "memory-less". It is of course true then, that you would expect this pattern for the iodine-131, but for a different reason than in the case of the war. The process of iodine-131 decay is Markovian because of its memorylessness (is that a word?) but the process of "who is winning the war in Ukraine" is not (the current state of the war is not enough to tell you less than knowing also the history).
But I was convinced by David's example with the peso and his translation to the war in Ukraine. I think it is a good description of how the market probably behaves and it kind of simplifies the situation to a Markov process where you have two absorbing states (Russia winning vs Ukraine winning in the sense of keeping its independence and Zelensky surviving). The process started somewhere in the middle (closer to the Russian absorbing state...pun intended) and has been moving to the other state since.
With a very high probability the process moves incrementally in the direction of the Ukrainian state and with a low probability it can move abrubtly in the Russian direction (from each state it can move directly to the Russian absorbing state or at least close to it, whereas it can only move incrementally in the opposite direction). The closer it gets to the Ukrainian state, the lower the probability of moving to the Russian state (but it can still jump there quickly if the trainsition does occur).
I guess this model makes sense. It seems that Ukraine is ready to fight for quite a long time provided that Russia does not do something very dramatic to force capitulation (capturing Kiev or something...I am not even sure that killing Zelensky would stop the Ukrainian determination at this point). Slow consistent Russian gains seem less likely, they have loads of problems with logistics, low morale, mounting problems at home (I don't think they would be willing or effectively able to fight until June, incidentally). So with that in mind, the markov model above makes sense.
I just wonder whether my description actually adds anything atop of what David said or whether it is not simply the same thing described in a more complicated way :)
What makes you say the progress of a war is necessarily non-Markovian? I would say good arguments can be given for it being a pretty Markovian process. That doesn't at all mean it's memoryless in the sense that anything at all can happen now, it just means its trajectory is determined mostly by what happened recently (with perhaps some constant bias in one direction or another). That seems rather likely to describe the course of a war, in the sense that what Belligerent A or B does at the start has a big influence on what happens next, and what happens next (and the next set of decisions) have a big influence on the next step, and so forth -- classic Markovian model.
A strongly non-Markovian model would be something a like a self-avoiding random walk, a situation where certain decisions made very early in the conflict have profound and somewhat random influence on things that happen much later. Like a bomb planted at time X that goes off at some unpredictable time X + dX (dX >> 0) and which then has a decisive effect. It's difficult to see how this could readily manifest in human affairs. What would this be? The chance of foreign intervention? Death of some critical leader? It would seem to presuppose a pretty contingent view of the evolution of a war, that "surprising" things out of the distant past could have unpredictably decisive effects on the present -- "unpredictable" in the sense that we could not easily trace their influence through time, A at time t1 caused B at time t2 which caused C at time t3, et cetera, *because* such a chain of influence is exactly what a Markovian process represents, a *non-Markovian* process is one where there are weird "Star Trek transporter" connections by which something far in the past leaps over all intervening events and affects the present all by itself, without going through any causal chain.
I think the discussion of Markovian vs non-Markovian is a bit of a non sequitur. I believe that the relevant property here is being a martingale not a Markov process. Obviously for continuous time (continuous) martingales there is not going to be any period of monotonicity almost surely, but in the case of discrete time, it is easy to see that for any delta > 0 there are martingales such that with probability at least 1 - delta the process is monotonically increasing and remains bounded between 0 and 1.
The martingale property comes immediately from mathematical finance, where a fundamental theorem says that no-arbitrage implies the existence of a measure under which the price is a martingale. Even ignoring the finance part, though, it should be obvious that we expect a (Levy) martingale. If we want the ERM predictor of the indicator of an event (with squared loss) with some information available in a sub-sigma algebra, we just take the conditional expectation. Thus at each time t, we should predict the expectation of the final event conditioned on the information available up to time t. This is just a Levy martingale. Where does the Markovian property enter?
Hmm, I guess you are right. The conditional probability should be a martingale. I guess this is the crucial bit that explains the behaviour.
I was thinking that a harmonic function of a Markov process is a martingale and the probability of ending in an absorption state of the markov process is a harmonic function.
I guess that Carl is right though that the Markov property is not that unreasonable here. What we really have at time t is not just the current state of the war but also all the previous information as well. And the bet is made based on this full information so it should trivially be Markovian.
I do not think it needs to be Markov; there could certainly be path-dependent information and my earlier comment still applies. Even absent the relevance question (I still do not think that it matters one way or the other for this question on the behavior of the process) I do not think that it is obvious that it even should be Markov, even in an efficient market.
I agree that it does not need to be Markov. My comment is rather justifying the model in case it is Markov, but you are correct that it applies more broadly.
You are saying that the reason is A whereas I was saying that it is because of B (and B implies A). You are correct that A is the important thing and there are ways you can arrive at A other than B.
Still, B still seems like quite a reasonable model to me after reflection (after thinking about Carl's comment).
But maybe I am missing a more elegant model which could describe the war that you might have had in mind?
Being a martingale is not synonymous with being Markov either in discrete or continuous time. There are plenty of examples one way or the other.
To give two trivial examples in discrete time, consider a process where X_0 has support of size at least 3 and y_n are independent Rademacher random variables for each n. Let X_n = X_{n-1} + y_n X_0. This is clearly a martingale. It is not Markov though because conditioning on the path (knowing X_0) concentrates the distribution for X_n given the history on two points while not knowing X_0 cannot have this concentration. (It is not hard to extend this example to continuous time by solving an SDE).
For the other way, take any Markov process (X_t) whose distributions conditional on the past are nonatomic and any function f that is subharmonic but not harmonic on the support of the X_t. Then the process given by f(X_t) is going to be a submartingale but not a martingale. This applies both in discrete and continuous time.
Ah I see what you mean. Thanks for the example. It's pretty contrived, however. I think for the real-world processes we are discussing here the distinction is not relevant.
Markov processes and martingales have a close relationship (via harmonic functions, also solutions of "well-behaved" SDEs are Markov processes) but they are indeed not synonymous and neither necessarily implies the other as Adam mentions.
On the other hand a lot of simple examples of martingales are markovian and vice versa (or their functions are, such as the relevant probability above) and a "markov process of the war" I am describing above is still the most intuitive toy model for me.
Exactly! Basically the pattern speaks to how little we know at a "gears level" about how the war is going. Given the right prior distribution I'd expect the prediction to evolve the same way if our only source of new information was a webcam in downtown Kyiv.
It's worse than the iodine-131 example; it's more like "will this iodine nucleus have decayed by April 1" when you don't even know what isotope of iodine you're dealing with.
I'm kind of OK with Metaculus's initial and current numbers, but the linear-ish trend seems off. The first week gave us a *lot* of useful information. First, it told us that the Ukrainian army wasn't going to fold like the Afghan National Army, that the people would back them up, and that Volodymyr Zelenskyy had the right stuff. All of those were in real doubt on 24 February. Second, it told us that this is not your father's Guards Motor Rifle Division we're dealing with, that the Russian Army of 2022 is not the one we were worried was going to overrun the Fulda Gap in 1982 but has severe logistical, organizational, technical, and morale problems. We *sort* of knew that on 24 Feb, but not with high confidence.
So most of the fall-off should I think have occurred in the first week, ruling out most of the "Shock and Awe prevails" scenarios. Rather like, if I hand you one of the seven major isotopes of iodine picked at random, there's a good chance that it's one of the ones with a half-life of hours to a few days, definitely not going to last a month. But a week later, you pretty much know that you're dealing with one of the longer-lived isotopes and maybe the actually-stable one.
Now I want to spreadsheet up a forecast of the decay of a random iodine atom in one month, conditional on it having lasted N days already.
Unless I'm mistaken, you can easily compute this by hand: Let $T$ be April 1, $t$ be the time of the first occurrence of decay, $p_s=\mathbb P(t\leq T\mid t>s)$ be the probability of decay by time $T$, conditional on no decay up to time $s<T$, $A_i$ be the event that we're looking at an iodine nucleus with half-life $a_i$ for $i=1,\dots,n$.
Then we have $p_s = \sum_{i=1}^n\mathbb P(A_i\mid t>s)\mathbb P(\text{Exp}(a_i)\leq T-s) = \frac{\sum_{i=1}^n e^{-{s\over a_i}}(1-e^{-{T-s\over a_i}})}{\sum_{i=1}^n e^{-{s\over a_i}}}$.
Intuitively, due to the exponentially decaying tails of exponential distributions, once we observe no decay after 2h we can almost certainly rule out half-times of <1h (provided there is an alternative hypothesis, like the possibility of another particle with half-time >2h). Once the contribution from a particle with longer half-time becomes dominant, linear decay seems reasonable.
For the record, I was primarily interested in how much this particular toy model would deviate from a linear function and would not use this for actual predictions.
(Apologies for the lack of formatting, I couldn't find a way to properly display links/equations on here.)
to answer the question, no i don't think that drop is strange. over that two weeks, we saw the results and new information adjusted quickly, then it should slowly decline as the deadline approaches.
Sorry, I'm probably just reading the graph badly, but what period in 2/28 are you thinking of as the "adjusted quickly" period, and what period is the "slowly decline" period? (The graph that Scott posted of the metaculus aggregation over time seems to move pretty smoothly from 2/28 to now; I don't see an obvious "adjusted quickly" period.)
The way I interpret and see the chart, it had some relatively old value Feb 28-Mar5, then steep drop to new lower value, then slow decay from there. This may not be the case, but the main point of my comment is to describe the behavior after that Mar5 drop. The comment from House Always Wins illustrates that point perhaps more articulately.
Ah, thinking of 3/5-3/6 as being a quick adjustment, and the resulting slide from 40% to 14% in the 8 days of the remaining 26 seems helpful. I still wouldn't have guessed that 2/3 of the probability mass "should" lie in the first 1/3 of days, so it does seems like there's more information being incorporated than just "probability decreases with each day closer to the April deadline that Kiev hasn't fallen".
The slowness of Russia in the early phases of seizing Kyiv suggests a slowness of their attack in the later phases. The distribution of "how long it takes Russia to get its troops to Kyiv," "how long does it take Russia to start shelling Kyiv with artillery," "how long does it take Ukrainian resistance to break down," "how long does it takes to seize the first raion," "how long does it take to seize the second raion," etc, are not going to be uncorrelated, even if they don't all have the same distribution.
A prediction market for next week’s Powerball numbers makes no sense as that is an unknowable thing. Similarly how Putin, Zelinskyy, Biden, Sholtz, random software problems that accidentally send a Russian Cruise Missile to Warsaw all interact to influence the future is just as unknowable as the future state of the balls bouncing around at lottery HG.
A prediction market for next week's Powerball numbers should have every combination priced at around ~0.000000342229781%. The balls bouncing around have a huge number of unknowable interactions, so it's hopeless to form predictions based on predicting every step of the process. But, like with the Powerball *results*, it's possible to estimate what the distribution of *outcomes* might be, even if it's hopeless to predict every footfall of every soldier.
It isn't *just as* unknowable as Powerball, even if it's quite unknowable. All those men you named have stated their intentions and have a history of behaviors in situations of varying degrees of similarity. Human behavior can be predictable to some extent. Degrees of confidence exist.
That’s true if you’re predicting the outcome of general events. The life insurance market works great at predicting how likely you are to die in the next 10 or 20 years. It’s predicting specific events that I’m not sure about.
For example - Tesla wants to take out $100 billion in life insurance to protect itself from Elon commuting suicide or other mwise ending his life prematurely. How much value is the life expectancy of the set of all 50 year old males in the US?
It provides a good base rate, which you can adjust upwards or downwards based on Elon Musk's particular characteristics (e.g. is he depressed, does he drink and drive, does he do dangerous drugs, etc).
Superforecasting, by Philip E. Tetlock, covers the specifics of how those who make these kind of "one-off" predictions accurately manage to do so. Unfortunately, it's sufficiently long and detailed in its coverage that there are few money quotes, though somebody reproduced the "Ten Commandments" from the appendix here: https://www.lesswrong.com/posts/dvYeSKDRd68GcrWoe/ten-commandments-for-aspiring-superforecasters
Define "Musk-like scenarios"? If you mean scenarios which rely on complex, multivariable human decision making similar to the ongoing war in Ukraine, you can just go to https://www.metaculus.com/questions/track-record/ and look at Geopolitics; Metaculus gets significantly above monkey levels, though I don't know how it compares to braindead heuristics like "the next five years will be identical to the previous five years".
If you mean literally predicting when specific people die, that's not a very common thing to see on prediction markets, probably because of the moral hazard.
A prediction market for next week's Powerball numbers is perfectly legitimate - the correct probability to assign to any number would be 1 / 1 million (or whatever the actual Powerball odds are). The only reason people wouldn't use such a market is that it would be so obvious that nobody would bet against the 1 / 1 million number.
What's the correct odds (ie the equivalent of saying "1 / 1 million") for Russia taking Kyiv this month? I'm not sure, but it's probably a different number than the correct odds for Russia taking Mariupol this month, and it's fair to speculate on both sets of odds.
The fact that we can't get certainty is fine, all prediction markets are asking you for is a probability. You probably have opinions on this probability already - 99% would seem unreasonably high, 0.1% unreasonably low.
People definitionally bet on Powerball numbers at worse than their actual odds of winning. So in principle there should be people available to bet that the odds of a given combo are higher than they actually are based on gamblers' fallacies or magical thinking.
No one is saying that you could use a prediction market to predict the exact winning numbers. They are saying that the prediction market will give an accurate PROBABILITY for a given set of numbers.
That is, if you ask a prediction market "will all 20 of these dice come up as 6s?" the market will say "with probability 1/6^20", which is the best possible answer given the available information.
To a hypothetical person who doesn't know how to calculate that probability for themself, that would be useful information.
That hypothetical person would have to be significantly dumber than average, since the market merely presents the conventional wisdom. So the question might be: why would a prediction market be useful to someone *other than* the unusually clueless?
I mean, the stock market tells me what the conventional wisdom is on the future earnings of Tesla, and that would be useful if I had never heard of the company. Gee, maybe buying Tesla stock makes more sense than putting my money under the mattress.
But if that does not describe me -- if I know as much as the average schmo -- what useful information can I extract from the present price of TSLA? Pretty much zip. If I buy when the price is high, and sell when the price is low -- i.e. I follow the conventional wisdom the market summarizes -- I will never make money. The *only* way the information can be practically useful is if I have *more* information than the average schmo, e.g. I am insider (or just smarter than everybody else) and I happen to know the conventional wisdom greatly under- or overvalues Tesla. In that case I can use the current market value to know when to bet against the market and win.
I guess I'll add that it is nearly definitionally not possible for my extra insight to dominate the market, so that the market reflects my extra knowledge. The market isn't exactly a one-man-one-vote democracy, but it's also not super duper different from that. Except in the rare circumstances that I am staggeringly rich *as well as* unusually well informed, my influence on the market (even as I make a killing) is not going to be enough to shift the conventional wisdom.
Obviously, the information from the market won't help you **at beating the market**.
If you know something the market doesn't, you can make money, and in the process make the market more informed. If the market knows something you don't, then you can learn something, and use that information ELSEWHERE in your life.
You might even be able to do both of those things on a single question, if you and the market know *different* information. ("I don't know how the market decided on a price of X, but I have inside information I'm sure the market hasn't taken into account, so I can guess the *direction* of its error.")
But for any given bit of info, you can either learn it from the market OR use it to make money from the market, not both. Markets are not perpetual motion machines.
(And even if you were going to try to use the market's information to play the market, "buy high, sell low" would be a profound misunderstanding of what the market is telling you. If you had an option to buy or sell at a fixed price of $X (regardless of what price the market is currently trading at), then looking at the market price could tell you whether you should exercise that fixed-price option. But if you're talking about buying or selling **at the market price**, then a high price is NOT a recommendation to buy--it indicates the value is high, but THE COST IS ALSO HIGH, so they cancel out!)
Sure, but those things are only true pretty far out on the statistical tail. I have to know *a lot* more than the market, because I need to know enough to know I'm better informed than the market. Given the epistemic bias of the rational actor against thinking he knows something special -- he's dead right and millions of others are dead wrong -- it would take a very well informed person to rationally conclude he can safely bet against the market. Similarily, it takes an unusually poorly-informed person to realize the market knows much more than he does, since the market doesn't have any special qualifications -- it's made up of average people. How badly informed do I have to be on any subject to conclude reliably that the averae schmo on the street knows much more than me? Pretty badly.
So in both cases *as a prediction tool* the market is only useful for a small demographic at either extreme. That wouldn't justify its existence, since it would be ipso facto useless for the great bulk of its participants. Why would anyone willingly participate in a market the main positive effect of which is to make unusual people who are not you better off? Nobody's that altruistic.
People *do* participate in "prediction markets," e.g. every time they go to the track and place a bet on the horses. The existence of the odds -- or indeed the market in general -- benefits only the people who know nothing at all about horses, who can avoid putting their money on the 100-1 long-shot, and the people who know *everything* about horses, who can *put* their money on the 100-1 long shot that they happen to know is going to win for some obscure reason or other. The rest of the people participate not because they seriously expect to come out ahead, financially (unless they're idiots), but because people generally get a thrill out of betting on stuff for some weird psychological reason. (Perhaps because by strategic forgetting of our losses we can feel smart about our wins.)
Yes, I agree, if I have a fixed option the market can tell me whether to exercise it. Under what consideration could I have something like that in a prediction market? I am not following how this would work in, say, a prediction market on the Ukrainian war. How could I come into possession of such an option, in a natural way? If you have a specific example in mind, it would help me understand what you mean.
Couldn't this market effective simulate a decentralized lottery? Instead of buying an actual $2 powerball ticket with a 1/1 million chance to win a million dollars, someone buys a $2 share on a specific number. Enough people enjoy the tiny chance of winning a huge amount of money that they're willing to do this for real lottery tickets even with negative expected value. Then all it needs is a bunch of rational actors with enough money to provide liquidity in exchange for profiting from the irrational choices of the gamblers, who would probably end up running automated programs that arbitrage any discrepancy between the current market and the mathematical odds. The total amount of money in the system would vary, but in expectation the return for winning should be approximately the reciprocal of the odds for winning, minus any losses from irrational behavior, which are profited by the arbiters.
This seems like it would end up remarkably similar to a regular lottery, except instead of the lottery provider making tons of money from the expected value discrepancy, multiple potential liquidity providers would compete, driving the profit margins down and creating a lottery that was more fair towards the gamblers.
Depends on whether the purpose is to have fun gambling, or actually predict stuff in a reliable way. If the latter, then the necessary underlying assumption is that the future is already determined -- the die is already cast, and it's just a question of discerning which side will face up before it actually happens, like predicting the path of a thrown rock in a vacuum from its initial position and velocity.
We can fudge it a little bit by saying it has to be predictable only in a statistical sense, like ordinary statistical mechanics, or quantum mechanics, e.g. whether *this* time we get nuclear war is unknowable, but we can say with certainty that the odds are 2.633%. That doesn't really change anything, because the predictability still requires perfectly deterministic underlying dynamics -- no chaos, no random events.
Is it possible that 'story arcs' in prediction markets come because most people have far heavier priors on other people's assessment and judgement, than they do on events in reality itself?
Maybe most people, even those using prediction markets, have a real low prior on something like 'prediction markets are totally wrong here' ? I have far more experience with 'prediction markets being general correct' than i do with forecasting military outcomes.
Do we assume that the mother is already taking prenatal vitamins before these recommendations are given? My guess is yes or else folate/iodine/etc will top the list. This matters for things like vitamin D (already in the prenatal pill, so I guess you mean extra D on top of that) and the vitamin A variants (vitamin A is in the prenatal pill, and too much of it is actively harmful, which I assume is why you list these specific lutein/zeaxanthin variants instead of a generic A pill).
"One possibility is that, by a crazy coincidence, every day some new independent event happened that thwarted Russia and made Ukraine’s chances look better. Twenty dice rolls in a row came up natural 20s for Ukraine. Seems unlikely."
That's more or less exactly what's happened. It's not unlikely at all, it's how we experience the world.
On day 1, Ukraine was still standing.
On day 2, Ukraine was still standing.
On day 3, Ukraine was still standing.
etc etc etc
These are all new information! On any given day N, different things might happen, we don't know. We have to wait and observe. Simply drawing a linear extrapolation through the first few days would be lunacy.
Also, labeling these as "natural 20s" is a huge overstatement of what we know about the underlying distribution. We have very little information on which to base an estimate of "Can Ukraine defend against an attack by the Russian army?", and I offer as evidence the fact that this post exists, we're having this conversation, etc etc. So it *may* be that Ukraine is on a hot streak and rolling 20s, or it may be that the outcomes we see are right in the middle of the distribution because it happens that Ukraine is a better match for Russia than some (many? most? idk!) people thought.
I agree, perhaps the market is approximating a “no info environment”. Suppose I arrange to watch a movie at 3pm with a friend. My friend tells me he will try to get there on the early side, but when I arrive he isn’t there. Now how does the probability of him arriving in time for the movie update every minute? I know literally nothing about his progress save the passage of time. I think it looks quite a bit like the Kiev market.
I was thinking about this problem recently while writing code for estimating the speed of a spinning wheel from a pulse train. It's tricky even if you have an estimate from previous pulses.
Consider a bus stop, where expect the bus to arrive every 10 minutes. Up until 10 minutes, you can estimate time remaining based on your original estimate. But now the bus is late, so what do you do?
One way to do it is to assume the bus is always about to arrive. At 11 minutes your new estimate is that buses arrive every 11 minutes. And so on. When the bus finally arrives, your prediction will be correct.
This seems to result in a smoother graph when the speed of the spinning wheel is slowing down. Adding elapsed time to the estimated period results in the frequency decaying like 1/x.
Sometimes, though, the bus will arrive early, and then you need to revise your estimate up.
This is sort of like saying the Lindy effect applies Ukrainian resistance.
But what bounds can we put on this? I would expect that cities under siege (completely surrounded) can't hold out forever. On the other hand, people say the Russian Army has logistical limits on how long they can continue the invasion.
Who has time on their side? The theory of protracted war is apparently that the Ukrainians win by surviving. Perhaps the markets believe this? Or maybe that's just the structure of this bet, since it has a deadline.
Kiev is not completely surrounded, so that changes your calculus a bit. The Russians have not been able to cut off access to the city from the south, and haven't made much progress in that direction over the past few days at least.
I'm thinking that one of the worst things about surviving a nuclear war would be finding yourself in a society organized and dominated by the kind of people who optimize their lives around surviving a nuclear war.
The vast majority of survivors would be people who survived by some combination of coincidence and general competence, no matter how (if) it happens the vast majority of survivors will not be nuclear preppers.
"Preppers are horrible people even if they're right" is enough of a trope in post-apocalyptic fiction that I've become suspicious of it. It reads like status gaming by the big winners of current society (which produces very different values and constraints that they've in turn optimized for) against their outgroup. Selfish, suspicious anti-authority types with unpopular beliefs are exactly the people I'd want to side with in a post-apocalyptic environment.
Preppers are people who are irrational, but happened to be right by pure coincidence. The fact that they are right doesn't change the likelihood of them being irrational.
If we were invaded by aliens who could be stopped by wearing literal tin foil hats, I'd expect the survivors to be even worse.
This past month has really brought back the '80s, when "is nuclear armageddon more or less likely this week?" was a perfectly normal topic for news discussion.
> If there were a stock that decreased every day for twenty days, we’d be surprised that investors were constantly overestimating it. At some point on day 10, someone should think “looks like this keeps declining, maybe I should short it”, and that would halt its decline. In efficient markets, there should never be predictable patterns!
Most high-growth tech stocks have been in secular decline since November (see eg NFLX, COIN, DASH, PTON, U, etc), so if you really believe this, you should go pick up those obvious $100 bills just laying on the ground :)
Ha ha yes that's why I always buy stock when the price is increasing and sell when the price is decreasing, which makes perfect sense except gosh darn it I seem to have less and less money every year...
No no. When price is decreasing, you don't sell (you are already too late to cash in). When price is increasing, you don't sell (you are too early to cash in).
Question from the audience? Let me repeat that everyone hears it. Gentleman here in the studio asked, "When do you buy"? The answer is, whenever you have sufficient funds, or at random intervals, sir.
This is the strategy that allowed us, BUY'N'HODL Inc, to finance our fancy interstellar home, the Axiom. We will return to planet Earth after it has been sufficiently cleaned.
Another explanation for the slow decline in Ukraine predictions:
This might happen if people are thinking something along the lines of "Russia will not capture Kiev by April unless they do something to turn things around before then". If so, then every day that Russia fails to turn things around provides a bit more evidence that Russia will not capture Kiev. This doesn't violate conservation of expected evidence or the efficient market hypothesis, because every day there is some small chance that Russia WILL turn things around and the odds will swing substantially in the other direction.
I'm kind of echoing what's been said before in the comments, but I'm really not sure why the monotonically decreasing pattern is odd. A stock shouldn't decline over time, but a stock is also in theory an infinite prediction (there's no time expiry). A prediction with a specific deadline is quite different.
Suppose your mental model is something like "there is a 1% chance Kiev will fall on any given day". With 30 days until April, you'd predict about a 74% chance of Kiev not falling (.99 ^ 30). With 15 days left, conditional on it not falling yet, you're up to about an 86% chance. Your base rate probability of Kiev falling doesn't have to change (it's still 1% on any given day), but the decreasing time to expiry changes your odds of the actual contract resolving one way or the other.
I basically agree with this take. Every day Russia fails to make progress in taking Kyiv is a day closer to the deadline. They might still be making progress, but so far it's too slow for them to make an April 1st deadline. I think their best bet is in surrounding the city and starving out the defenders, but that'll take a couple of weeks even after they've surrounded the city, which they're still far from doing.
I think that the other thing is that people have been expecting the Russian army to figure out its organizational problems but they haven't done that yet. The longer they fail to do that, the more it looks like they won't be able to do it. Which means the war will be continue to be slow-going and costly for them.
I think the key here is that the evidence has mostly been of the following form:
"the Russians haven't moved very far, and they've already been invading for X days"
That's evidence that becomes monotonically stronger as X increases but there's no sharp cutoff point where it qualitatively changes in character. It's quite different from the updates you would get from crucial pivotal events (agreeing to ship a more advanced SAM system, the fall of a city, losing a key skirmish etc) but I also think it's extremely relevant evidence.
For instance, if we think one of the two situations is likely to be a correct description of the situation, we could reasonably believe that every day without solid Russian progress is evidence towards option 2 and update accordingly.
Scenario 1) Russian forces are fundamentally powerful enough to take Ukraine but take time to deploy effectively
Scenario 2) Russian forces are not powerful enough to take Ukraine
Every day X ticks one higher, and the P(evidence| scenario 2) becomes higher and P(evidence|scenario 1) becomes lower meaning a larger update but incremental update towards scenario 2.
Even now, it's still possible that the Russians are gradually getting into position and will still prevail, but the alternative story where their logistics, morale, tactical awareness etc are too constraining to achieve their objectives has become a lot more plausible.
Yes, this was a weird objection to me. The monotonically decreasing with time in the absense of major new developments seemed the obviously correct reaction.
Zvi has very similar behavior in his Covid predictions. For example, before the recent Hong Kong surge, as time went on with no (apparent) changes in China's case load, he gradually incremented up the likelihood that they would successfully contain the disease. Then, something major happened (the Hong Kong spike and various smaller outbreaks) and he dramatically reduced the likelihood.
(This was a comment made by the real Enopoletus Harding on Metaculus.)
I thought of leaving here due to my disagreements with the moderation here, but since Scott has mentioned me on his blog (I can't comment there since I'm banned for extremist posts), I will continue to make predictions here. Needless to say, the chances of Russia taking Kiev go down each day there is no advance. I personally don't think it makes sense to update very rapidly, since, for all I know, the Russians may have been using the past two weeks to prepare some lightning assault -not something that's likely, certainly, but the chances of that are too high to simply exclude off the bat. Maybe I should update more rapidly -I've been underperforming the community when evaluated at all times. But knowing when to update and having good starting positions are not easy skills to learn.
I've also created an account on Manifold Markets, I expect my predictions to be better there (I have a habit of putting the vast majority of my money on a few markets I can easily win in):
No, I'm not trolling. Wrong, maybe. It's happened before. I had 10% chance of a Russian invasion for way too long, but I obviously changed that as the evidence became more clear.
Ukraine is going to lose in the end. Maybe only after most cities are destroyed, but they cannot win. Then they will be ruled by russian marionettes & dictat in the foreseeable future. The dictat will be harder and longer, in particular on the West-ukrainians, the more blood the Russians have to spill to conquer the country. The only alternative is for the ukrainians to cut their losses some way, but so far that seems unlikely. I'm writing this because the endgame is what matters. Making "predictions" about which week Kyiv and other cities fall is a teenager-way of thinking and acting about a real-life war. It is of very marginal importance which week it will happen, and such speculations are also rather distasteful. Grow up.
The big questions rely on and derive from the little questions. The most accurate way to make large predictions is to break them down into many smaller subpredictions for which we can derive some reference class. Or, to borrow Jesus's phrasing, "Whoever can be trusted with very little can also be trusted with much."
The longer Kyiv holds out, the more time there is for some major event to change the entire equation. A general collapse in one of the two armies, for example. Of for another major power to get directly involved, for another. The math might currently be in Russia's favor (actually it's not that clear; it depends on what the casualty numbers are really like,) but there's still time for major events to upset matters.
It's also important to understand that it's not just the "endgame" in Ukraine that matters. This war affects most of the world at the moment, and whether Ukraine continues to fight matters a lot to what the other powers involved should do about it. For example, if Ukraine can be expected to hold out for another few months or a year, then Putin needs to worry about supply and domestic issues so it affects him greatly. It also affects the kind of aid it makes sense for the EU and NATO to send to Ukraine. It also affects what countries that used to depend on Ukrainian grain will have to do to deal with their own crisises. So yes, this matters.
"Teenager"? It seems like you can make real money betting against the people you disagree with. There are lots of adults who making a living on speculative markets.
My mental model for the progress of this war is essentially as a race - damage to Ukrainian civilians and military may push Ukraine to concede a disadvantageous peace, and damage to Russian military and economy may push Russia to concede a disadvantageous peace; both of these damages are progressing at varying speeds, and the question is which one of these "progress bars" will reach a breaking point first.
And I strongly disagree with your assumption - I don't see how Russia can force *that* kind of peace even if their military operation completely succeeds now. If Russia conquers or destroys all the major cities and installs a puppet government, that does not enable Russia to rule over Ukraine - the populace will not agree to that, not even in the eastern Russian-speaking areas like Kharkiv, not after what has been done in the war. And Russia can not afford enough manpower to enforce proper control, that would require something like 500k permanent garrison there; so Russia will have to leave and their marionette regime falls right afterwards (as after USSR-Afghanistan). I mean, pacifying and controlling a hostile country is really, really hard; it has not gone well for USA recently despite immense resources, and even for the quite effective Stalin-NKVD apparatus it took many, many years after WW2 to suppress guerilla warfare in Eastern Europe - and those people and Taliban didn't have external support/arms supply from all the wealthy countries, like Ukrainian guerillas would have in case of a Russian conquest. So as Russia can't plausibly hold Ukraine, they would have to concede to something more reasonable (e.g. recognition of Crimea + DNR/LNR, perhaps a bit more land, but Ukraine government remaining in place) even in the case of an overwhelming victory - which itself is far from certain.
In my opinion the main part of the war has not started yet - the Ukrainian strategy apparently was to trade space for time, preparing for the actual fighting in taking over the large cities, which is going to be difficult for the attacker, and where the war would be decided. So far Russia is only assaulting the relatively small Mariupol (Kherson and Melitopol are many times smaller than that), not even trying to make serious progress in Kharkiv or Kyiv. We can see how much men and time it took Russia to take Grozny; it seems plausible to consider that Kyiv - which is much larger and has much more resourced defenders - will take at least as much.
Im skeptical of the "russia will never submit Ukraine". Didn't they do it with Chechnya pretty succesfully? Seems like they could pull it off at least on a portion of Ukraine.
Chechnya is much smaller, but Ukraine doesn't have much in the way of mountains.
Chechnya is a very relevant example of how they were very much *not* able to do it "pretty successfully". They tried to enforce submission for many years and failed, and they succeeded only with a combination of keeping excessive military garrison (at levels which Russia can't afford at the larger scale of Ukraine) plus effectively buying off the local leaders and population with excessive subsidies (again, at levels which Russia can't afford at the larger scale of Ukraine) and political concessions.
The Chechen resistance did not end with surrender and submission, the current result is "an understanding" where formally Kremlin gets a victory, territorial integrity and declarative submission, but in practice devolves severe autonomy and large monetary "tribute" to Chechnya. Kadyrov is not like other regional leaders which are at the mercy of Moscow, he is independently powerful, with his own army (that is not accountable to Russian hierarchy), and is effectively an ally of convenience to Putin personally and has a lot of de-facto autonomy from the rest of Russian authorities - there are all kinds of incidents with Kadyrov's people in violent conflict with other Russia region's court system and police system, and having de facto immunity for that. I don't have a specific English source in mind, but if you're interested about this aspect, I would recommend you to read about how Kadyrov came to power, all of that process was quite interesting.
I don't know any - it's relatively recent, most written information is in Russian with little analysis from the western part, and I doubt if the authorities would allow to publish an analytical book like that in Russia (and IIRC both threats and actual violence has been applied both to local Chechens and expats commenting on Kadyrovs regime). However, I just stumbled upon a quite extensive summary in English in Twitter-thread form - https://twitter.com/kamilkazani/status/1497612331953577991
I'm not sure if your claim is "I'm so obviously right that it's useless for people to try to predict things" or "the things you're predicting are too small scale to matter".
I disagree with the first because the people who say the first have a worse-than-average track record of being right, and I disagree with the second because big things are made up of small things. I bet there are a lot of Ukrainian generals who would like to know in what month Kiev will/won't fall right now, and would change a lot of what they're doing if they knew.
But also - realistically everything that's happening on prediction markets now is capacity-building / proof-of-concept. The more we establish a record for prediction markets on small things, the more likely we'll have them ready and established when we need to use them for big things.
(the Arb report I linked finds that forecasters beat epidemiologists and models in predicting the spread of COVID-19 and its effects on interventions - seems potentially useful)
I would like to go on record that I find that poster's attitude distasteful AND I disagree with his object-level prediction about the end-result of the Ukraine war.
However, upon reflection, he may be on to something, and I don't think your answer addresses that something. A more sophisticated, steelmanned version of the sentiment he expresses would go as follows:
It should be, of course, uncontroversial that every little data point brings us closer to a correct big picture view. However, it does not follow that a *prediction market* about every little single data point gives us more information. Realistically, prediction markets about little things will be extremely correlated with each other, influenced much more strongly by the overarching big picture sentiment looming above them than by any actual new information directly related to the question they're trying to answer. (And even if one of them is actually pricing in some important niche knowledge, we have no way of teasing that knowledge out from the single probability number that the prediction market produces.)
In other words, in a flow of information from primary data to their increasingly more processed derivatives, prediction markets about small things may actually be further down the line than the big picture view, with the big picture view having already absorbed the relevant information from the primary small-thing datapoints. The corollary to this would be that predictions about small things should not, and probably do not, reflexively influence the big picture view. This is an important, non-trivial point that, honestly, I find likely to be correct.
I'm actually trending towards thinking that Russia is not likely to win unless China props them up. At this point it's looking like a long, long grind and I don't know how long Russia can sustain that with the way their economy is going.
this is an example of definitions being really important - as the definition of 'win' is the key factor here. And where prediction markets on those various definitions of 'win' are highly valuable
Perhaps the best outcome for Russia is a 'loss' in Ukraine.
A Russian 'win' leaves Russia maintaining a very large military force in the country for years. Possibly decades. A never ending money and resource pit. This was true from the moment it become clear that Ukrainians were not hoping to become part of Russia.
Especially in a scenario where Russia trades their withdrawal for significant sanction relief. But even in a scenario without that, I think Russia withdrawing would give some portion of parties participating in sanctions the cover they need to slowly back away.
Why do you think they cannot win? Russia is about three and a half times the size of Ukraine in population, which is an advantage but may not be enough to balance the facts that Ukraine is on the defensive, that the Russian military appears to be very poor and Ukraine's military pretty good. Russia is richer than Ukraine, which in most contexts would be important, but Ukraine is being supplied by NATO countries that are much richer than Russia.
It's hard to be sure but it looks as though, despite its size, Russia has a very limited number of trained soldiers, many, possibly most, of whom have already been committed to the invasion. So I think one plausible outcome is that the Russian military ends up unable to advance further, possibly unable to hold what it is currently occupying. They can kill a substantial number of Ukrainians, but not a substantial fraction of the population, and at the cost of further losses of men and material.
"Ukraine is going to lose in the end. Maybe only after most cities are destroyed, but they cannot win."
Your confidence in the ability of the Russian army to sustain its morale and current operational tempo indefinitely, is I think unjustifiably high. The best unclassified sources I can find suggests that the Russian army has already lost 10-20% of its *total* effective combat strength in this campaign. That can be reconstituted, but not in real time. And Putin isn't going to run his army down to literally zero combat effectiveness.
The 30% of forecasts where Russia hasn't even taken three major cities by June, those are the ones where Ukraine probably wins. And, yeah, maybe promises to recognize Crimea as part of Russia to dissuade Puting from spite-nuking Kyiv, but that's still a win for Ukraine.
"Russia will probably win" is a reasonable forecast. "Ukraine *can't* win", is not.
At least our opinion polls have better calibrated probability estimates!
But you are correct, though the issue is a bit subtler. For example, Metaculus advertises its track record: in past Metaculus aggregated predictions have been quite good, so it is worthwhile to look at their current predictions, too. However, they don't guarantee that the predictor pool stays stable nor even of equivalently high quality. Their platform is vulnerable to Eternal September.
The other part of answer is: do not underestimate power of the opinion polls. They are very useful, and they are not cheap to conduct either!
The true public opinion is valuable information which is difficult to obtain and access to it was restricted only to those who have the means to obtain it. And many people have an incentive to manipulate people's perception of what it is. How would you know what is the true aggregated common public opinion if you had only old-fashioned media available? You could talk to people you know, but that is only your social bubble, it could be biased. Suppose you watch TV and read newspapers. A reporter goes out and interviews the proverbial "man on the street" -- they are likely to interview several, and make a decision which interview gets airtime or is printed. Or talk show host invites several pundits to discuss what is the expert consensus on some phenomena or another -- they have editorial discretion over who they invite. And so on. You could call Gallup and ask for their rates -- not something everyone can do.
Regarding the degradation of Zelenskyy NO on Polymarket, a lot of these markets behave like options: they have a time value, and in absence of any new meaningful information, the time value falls until it reaches 0.
Good point! Given this time-value-of-options model, does it surprise you that the Zelenskyy NO price fell from 63% to 20% in the first 14 out of the 53 days until expiration?
It does not. I was a decently sized player in helping the odds go from ~60% to 20 or so. The bulk of the move was when market participants realized how inefficient Russian troop movements have been in Northern Ukraine.
Furthermore, the bulk of the shock move was done by one participant (a whale) who's trades move polymarkets substantially.
I see. Sounds like "market participants realized how inefficient Russian troop movements have been" was a bigger factor than "options generally go to 0 due to time value" in this case -- does that seem right to you in explaining what happened in the market?
Appropriately, "Will Kyiv fall by April" has dropped by more than half since March 7 (one week ago), whereas "Will Kyiv fall by June" has fallen only a little since then.
Excellent description
Does anyone remember Intrade? Very similar dynamics occurred regularly in many of its markets.
This 100%.
For a more colloquial explanation think of a question which goes "Will [Biden] [be president] by [December 31st]?" Particularly this works for questions when the answer is yes for today and you're asking if it'll change to no.
Every day that passes the odds should go down right? So looking back we could say (as Scott does), "this is decreasing linearly, better frontrun it". However this would be a mistake. More likely than small independent events which 'boost' Biden still being president (for Kyiv this would be small events which are pro-Ukraine) it is the lack of a large event which boosts Russia.
We can also think about a lottery. "Will I win the lottery before x date buying a ticket every day?" This would go down over time and is a much easier to understand and simpler model.
It's dangerous to immediately price in the updates you expect to see based on the trend! The forecasters are behaving as proper Bayesian agents and updating slowly, according to the trickle of evidence. Moreover, waiting makes existing evidence stronger - nobody debunked it, you've seen nothing that contradicts it despite time in which such information could surface.
"This is almost monotonically decreasing. Every day it’s lower than the day before. How suspicious should we be of this? If there were a stock that decreased every day for twenty days, we’d be surprised that investors were constantly overestimating it. At some point on day 10, someone should think “looks like this keeps declining, maybe I should short it”, and that would halt its decline. In efficient markets, there should never be predictable patterns!"
If you plotted a prediction for "will this iodine-131 nucleus have decayed by April 1" you'd also get a roughly linear decline (unless it decayed in which case it would jump up to 100%). Prediction markets are allowed to have "story arcs", so long as the *expected* change is zero.
My father's example was the Peso market. For a long time, investing in Pesos gave you a higher return than investing in dollars, which looks like a failure of efficient markets. Then Mexico devalued the Peso.
Similarly here. The pattern is what you would expect if, every day, there was a high probability of a small piece of evidence in favor of Ukraine and a very low probability of a very large piece of evidence in favor of Russia.
I am not a physicist, but IIRC the readioactive decay is exponentially distributed, i.e. "memory-less". It is of course true then, that you would expect this pattern for the iodine-131, but for a different reason than in the case of the war. The process of iodine-131 decay is Markovian because of its memorylessness (is that a word?) but the process of "who is winning the war in Ukraine" is not (the current state of the war is not enough to tell you less than knowing also the history).
But I was convinced by David's example with the peso and his translation to the war in Ukraine. I think it is a good description of how the market probably behaves and it kind of simplifies the situation to a Markov process where you have two absorbing states (Russia winning vs Ukraine winning in the sense of keeping its independence and Zelensky surviving). The process started somewhere in the middle (closer to the Russian absorbing state...pun intended) and has been moving to the other state since.
With a very high probability the process moves incrementally in the direction of the Ukrainian state and with a low probability it can move abrubtly in the Russian direction (from each state it can move directly to the Russian absorbing state or at least close to it, whereas it can only move incrementally in the opposite direction). The closer it gets to the Ukrainian state, the lower the probability of moving to the Russian state (but it can still jump there quickly if the trainsition does occur).
I guess this model makes sense. It seems that Ukraine is ready to fight for quite a long time provided that Russia does not do something very dramatic to force capitulation (capturing Kiev or something...I am not even sure that killing Zelensky would stop the Ukrainian determination at this point). Slow consistent Russian gains seem less likely, they have loads of problems with logistics, low morale, mounting problems at home (I don't think they would be willing or effectively able to fight until June, incidentally). So with that in mind, the markov model above makes sense.
I just wonder whether my description actually adds anything atop of what David said or whether it is not simply the same thing described in a more complicated way :)
What makes you say the progress of a war is necessarily non-Markovian? I would say good arguments can be given for it being a pretty Markovian process. That doesn't at all mean it's memoryless in the sense that anything at all can happen now, it just means its trajectory is determined mostly by what happened recently (with perhaps some constant bias in one direction or another). That seems rather likely to describe the course of a war, in the sense that what Belligerent A or B does at the start has a big influence on what happens next, and what happens next (and the next set of decisions) have a big influence on the next step, and so forth -- classic Markovian model.
A strongly non-Markovian model would be something a like a self-avoiding random walk, a situation where certain decisions made very early in the conflict have profound and somewhat random influence on things that happen much later. Like a bomb planted at time X that goes off at some unpredictable time X + dX (dX >> 0) and which then has a decisive effect. It's difficult to see how this could readily manifest in human affairs. What would this be? The chance of foreign intervention? Death of some critical leader? It would seem to presuppose a pretty contingent view of the evolution of a war, that "surprising" things out of the distant past could have unpredictably decisive effects on the present -- "unpredictable" in the sense that we could not easily trace their influence through time, A at time t1 caused B at time t2 which caused C at time t3, et cetera, *because* such a chain of influence is exactly what a Markovian process represents, a *non-Markovian* process is one where there are weird "Star Trek transporter" connections by which something far in the past leaps over all intervening events and affects the present all by itself, without going through any causal chain.
I think the discussion of Markovian vs non-Markovian is a bit of a non sequitur. I believe that the relevant property here is being a martingale not a Markov process. Obviously for continuous time (continuous) martingales there is not going to be any period of monotonicity almost surely, but in the case of discrete time, it is easy to see that for any delta > 0 there are martingales such that with probability at least 1 - delta the process is monotonically increasing and remains bounded between 0 and 1.
The martingale property comes immediately from mathematical finance, where a fundamental theorem says that no-arbitrage implies the existence of a measure under which the price is a martingale. Even ignoring the finance part, though, it should be obvious that we expect a (Levy) martingale. If we want the ERM predictor of the indicator of an event (with squared loss) with some information available in a sub-sigma algebra, we just take the conditional expectation. Thus at each time t, we should predict the expectation of the final event conditioned on the information available up to time t. This is just a Levy martingale. Where does the Markovian property enter?
Hmm, I guess you are right. The conditional probability should be a martingale. I guess this is the crucial bit that explains the behaviour.
I was thinking that a harmonic function of a Markov process is a martingale and the probability of ending in an absorption state of the markov process is a harmonic function.
I guess that Carl is right though that the Markov property is not that unreasonable here. What we really have at time t is not just the current state of the war but also all the previous information as well. And the bet is made based on this full information so it should trivially be Markovian.
I do not think it needs to be Markov; there could certainly be path-dependent information and my earlier comment still applies. Even absent the relevance question (I still do not think that it matters one way or the other for this question on the behavior of the process) I do not think that it is obvious that it even should be Markov, even in an efficient market.
I agree that it does not need to be Markov. My comment is rather justifying the model in case it is Markov, but you are correct that it applies more broadly.
You are saying that the reason is A whereas I was saying that it is because of B (and B implies A). You are correct that A is the important thing and there are ways you can arrive at A other than B.
Still, B still seems like quite a reasonable model to me after reflection (after thinking about Carl's comment).
But maybe I am missing a more elegant model which could describe the war that you might have had in mind?
Not sure what your objection is. A martingale *is* a Markov process.
Being a martingale is not synonymous with being Markov either in discrete or continuous time. There are plenty of examples one way or the other.
To give two trivial examples in discrete time, consider a process where X_0 has support of size at least 3 and y_n are independent Rademacher random variables for each n. Let X_n = X_{n-1} + y_n X_0. This is clearly a martingale. It is not Markov though because conditioning on the path (knowing X_0) concentrates the distribution for X_n given the history on two points while not knowing X_0 cannot have this concentration. (It is not hard to extend this example to continuous time by solving an SDE).
For the other way, take any Markov process (X_t) whose distributions conditional on the past are nonatomic and any function f that is subharmonic but not harmonic on the support of the X_t. Then the process given by f(X_t) is going to be a submartingale but not a martingale. This applies both in discrete and continuous time.
[Edited to add example]
Ah I see what you mean. Thanks for the example. It's pretty contrived, however. I think for the real-world processes we are discussing here the distinction is not relevant.
Markov processes and martingales have a close relationship (via harmonic functions, also solutions of "well-behaved" SDEs are Markov processes) but they are indeed not synonymous and neither necessarily implies the other as Adam mentions.
On the other hand a lot of simple examples of martingales are markovian and vice versa (or their functions are, such as the relevant probability above) and a "markov process of the war" I am describing above is still the most intuitive toy model for me.
I agree with you. and I am scientist I need some other statistical algorithms with ten pages of proofs or something IMHO.
Exactly! Basically the pattern speaks to how little we know at a "gears level" about how the war is going. Given the right prior distribution I'd expect the prediction to evolve the same way if our only source of new information was a webcam in downtown Kyiv.
It's worse than the iodine-131 example; it's more like "will this iodine nucleus have decayed by April 1" when you don't even know what isotope of iodine you're dealing with.
I'm kind of OK with Metaculus's initial and current numbers, but the linear-ish trend seems off. The first week gave us a *lot* of useful information. First, it told us that the Ukrainian army wasn't going to fold like the Afghan National Army, that the people would back them up, and that Volodymyr Zelenskyy had the right stuff. All of those were in real doubt on 24 February. Second, it told us that this is not your father's Guards Motor Rifle Division we're dealing with, that the Russian Army of 2022 is not the one we were worried was going to overrun the Fulda Gap in 1982 but has severe logistical, organizational, technical, and morale problems. We *sort* of knew that on 24 Feb, but not with high confidence.
So most of the fall-off should I think have occurred in the first week, ruling out most of the "Shock and Awe prevails" scenarios. Rather like, if I hand you one of the seven major isotopes of iodine picked at random, there's a good chance that it's one of the ones with a half-life of hours to a few days, definitely not going to last a month. But a week later, you pretty much know that you're dealing with one of the longer-lived isotopes and maybe the actually-stable one.
Now I want to spreadsheet up a forecast of the decay of a random iodine atom in one month, conditional on it having lasted N days already.
Unless I'm mistaken, you can easily compute this by hand: Let $T$ be April 1, $t$ be the time of the first occurrence of decay, $p_s=\mathbb P(t\leq T\mid t>s)$ be the probability of decay by time $T$, conditional on no decay up to time $s<T$, $A_i$ be the event that we're looking at an iodine nucleus with half-life $a_i$ for $i=1,\dots,n$.
Then we have $p_s = \sum_{i=1}^n\mathbb P(A_i\mid t>s)\mathbb P(\text{Exp}(a_i)\leq T-s) = \frac{\sum_{i=1}^n e^{-{s\over a_i}}(1-e^{-{T-s\over a_i}})}{\sum_{i=1}^n e^{-{s\over a_i}}}$.
Plugging in some made-up values, e.g. only two different types of iodine atoms, one with half-life shorter and one longer than the time horizon of interest ("shock and awe prevails" vs "Ukraine strong", respectively), we actually get [something linear-ish with a bit of a kink](https://www.wolframalpha.com/input?i=plot+%28e%5E%28-s%2Fa%29%281-e%5E%28-%28T-s%29%2Fa%29%29+%2B+e%5E%28-s%2Fb%29%281-e%5E%28-%28T-s%29%2Fb%29%29%29%2F%28e%5E%28-s%2Fa%29%2Be%5E%28-s%2Fb%29%29+for+T%3D10%2Ca%3D1%2Cb%3D20+from+s%3D0+to+s%3D10).
Intuitively, due to the exponentially decaying tails of exponential distributions, once we observe no decay after 2h we can almost certainly rule out half-times of <1h (provided there is an alternative hypothesis, like the possibility of another particle with half-time >2h). Once the contribution from a particle with longer half-time becomes dominant, linear decay seems reasonable.
For the record, I was primarily interested in how much this particular toy model would deviate from a linear function and would not use this for actual predictions.
(Apologies for the lack of formatting, I couldn't find a way to properly display links/equations on here.)
Shouldn't the fall of Kiev by April decrease with each day closer to the April deadline that it hasn't fallen? It doesn't seem that strange to me
Does it seem strange to you that it fell from 69% to 14% in the first 14 out of 53 days before the deadline?
April 1 is 17 days away, and the forecast graph only goes back to feb 28, 14 days ago, so 31 days total. I don't know where your 53 comes from.
to answer the question, no i don't think that drop is strange. over that two weeks, we saw the results and new information adjusted quickly, then it should slowly decline as the deadline approaches.
Sorry, I'm probably just reading the graph badly, but what period in 2/28 are you thinking of as the "adjusted quickly" period, and what period is the "slowly decline" period? (The graph that Scott posted of the metaculus aggregation over time seems to move pretty smoothly from 2/28 to now; I don't see an obvious "adjusted quickly" period.)
The way I interpret and see the chart, it had some relatively old value Feb 28-Mar5, then steep drop to new lower value, then slow decay from there. This may not be the case, but the main point of my comment is to describe the behavior after that Mar5 drop. The comment from House Always Wins illustrates that point perhaps more articulately.
Ah, thinking of 3/5-3/6 as being a quick adjustment, and the resulting slide from 40% to 14% in the 8 days of the remaining 26 seems helpful. I still wouldn't have guessed that 2/3 of the probability mass "should" lie in the first 1/3 of days, so it does seems like there's more information being incorporated than just "probability decreases with each day closer to the April deadline that Kiev hasn't fallen".
Oh, I mixed up the deadline on the Zelenskyy polymarket market with the Kiev metaculus market. Should have said:
"Does it seem strange to you that it fell from 69% to 14% in the first 14 out of 32 days before the deadline?"
The slowness of Russia in the early phases of seizing Kyiv suggests a slowness of their attack in the later phases. The distribution of "how long it takes Russia to get its troops to Kyiv," "how long does it take Russia to start shelling Kyiv with artillery," "how long does it take Ukrainian resistance to break down," "how long does it takes to seize the first raion," "how long does it take to seize the second raion," etc, are not going to be uncorrelated, even if they don't all have the same distribution.
A prediction market for next week’s Powerball numbers makes no sense as that is an unknowable thing. Similarly how Putin, Zelinskyy, Biden, Sholtz, random software problems that accidentally send a Russian Cruise Missile to Warsaw all interact to influence the future is just as unknowable as the future state of the balls bouncing around at lottery HG.
What am I missing?
A prediction market for next week's Powerball numbers should have every combination priced at around ~0.000000342229781%. The balls bouncing around have a huge number of unknowable interactions, so it's hopeless to form predictions based on predicting every step of the process. But, like with the Powerball *results*, it's possible to estimate what the distribution of *outcomes* might be, even if it's hopeless to predict every footfall of every soldier.
How is the prediction market doing better than our general knowledge of statistics?
If our general knowledge of statistics is the best we can do, then a prediction market should represent that.
It isn't *just as* unknowable as Powerball, even if it's quite unknowable. All those men you named have stated their intentions and have a history of behaviors in situations of varying degrees of similarity. Human behavior can be predictable to some extent. Degrees of confidence exist.
That’s true if you’re predicting the outcome of general events. The life insurance market works great at predicting how likely you are to die in the next 10 or 20 years. It’s predicting specific events that I’m not sure about.
For example - Tesla wants to take out $100 billion in life insurance to protect itself from Elon commuting suicide or other mwise ending his life prematurely. How much value is the life expectancy of the set of all 50 year old males in the US?
It provides a good base rate, which you can adjust upwards or downwards based on Elon Musk's particular characteristics (e.g. is he depressed, does he drink and drive, does he do dangerous drugs, etc).
Superforecasting, by Philip E. Tetlock, covers the specifics of how those who make these kind of "one-off" predictions accurately manage to do so. Unfortunately, it's sufficiently long and detailed in its coverage that there are few money quotes, though somebody reproduced the "Ten Commandments" from the appendix here: https://www.lesswrong.com/posts/dvYeSKDRd68GcrWoe/ten-commandments-for-aspiring-superforecasters
Do we have data that says prediction markets of Musk like scenarios are more accurate than general life insurance underwriting?
Define "Musk-like scenarios"? If you mean scenarios which rely on complex, multivariable human decision making similar to the ongoing war in Ukraine, you can just go to https://www.metaculus.com/questions/track-record/ and look at Geopolitics; Metaculus gets significantly above monkey levels, though I don't know how it compares to braindead heuristics like "the next five years will be identical to the previous five years".
If you mean literally predicting when specific people die, that's not a very common thing to see on prediction markets, probably because of the moral hazard.
A prediction market for next week's Powerball numbers is perfectly legitimate - the correct probability to assign to any number would be 1 / 1 million (or whatever the actual Powerball odds are). The only reason people wouldn't use such a market is that it would be so obvious that nobody would bet against the 1 / 1 million number.
What's the correct odds (ie the equivalent of saying "1 / 1 million") for Russia taking Kyiv this month? I'm not sure, but it's probably a different number than the correct odds for Russia taking Mariupol this month, and it's fair to speculate on both sets of odds.
The fact that we can't get certainty is fine, all prediction markets are asking you for is a probability. You probably have opinions on this probability already - 99% would seem unreasonably high, 0.1% unreasonably low.
Does that answer your question?
The odds of winning any lottery, for anybody, is 50%. It’s 50-50. You either do or you don’t.
That explains why half of all lottery players win.
Wait.
People definitionally bet on Powerball numbers at worse than their actual odds of winning. So in principle there should be people available to bet that the odds of a given combo are higher than they actually are based on gamblers' fallacies or magical thinking.
How would a powerball prediction market work in practice? I’m taking legitimate to mean it would work to determine the outcome.
No one is saying that you could use a prediction market to predict the exact winning numbers. They are saying that the prediction market will give an accurate PROBABILITY for a given set of numbers.
That is, if you ask a prediction market "will all 20 of these dice come up as 6s?" the market will say "with probability 1/6^20", which is the best possible answer given the available information.
To a hypothetical person who doesn't know how to calculate that probability for themself, that would be useful information.
That hypothetical person would have to be significantly dumber than average, since the market merely presents the conventional wisdom. So the question might be: why would a prediction market be useful to someone *other than* the unusually clueless?
I mean, the stock market tells me what the conventional wisdom is on the future earnings of Tesla, and that would be useful if I had never heard of the company. Gee, maybe buying Tesla stock makes more sense than putting my money under the mattress.
But if that does not describe me -- if I know as much as the average schmo -- what useful information can I extract from the present price of TSLA? Pretty much zip. If I buy when the price is high, and sell when the price is low -- i.e. I follow the conventional wisdom the market summarizes -- I will never make money. The *only* way the information can be practically useful is if I have *more* information than the average schmo, e.g. I am insider (or just smarter than everybody else) and I happen to know the conventional wisdom greatly under- or overvalues Tesla. In that case I can use the current market value to know when to bet against the market and win.
I guess I'll add that it is nearly definitionally not possible for my extra insight to dominate the market, so that the market reflects my extra knowledge. The market isn't exactly a one-man-one-vote democracy, but it's also not super duper different from that. Except in the rare circumstances that I am staggeringly rich *as well as* unusually well informed, my influence on the market (even as I make a killing) is not going to be enough to shift the conventional wisdom.
Obviously, the information from the market won't help you **at beating the market**.
If you know something the market doesn't, you can make money, and in the process make the market more informed. If the market knows something you don't, then you can learn something, and use that information ELSEWHERE in your life.
You might even be able to do both of those things on a single question, if you and the market know *different* information. ("I don't know how the market decided on a price of X, but I have inside information I'm sure the market hasn't taken into account, so I can guess the *direction* of its error.")
But for any given bit of info, you can either learn it from the market OR use it to make money from the market, not both. Markets are not perpetual motion machines.
(And even if you were going to try to use the market's information to play the market, "buy high, sell low" would be a profound misunderstanding of what the market is telling you. If you had an option to buy or sell at a fixed price of $X (regardless of what price the market is currently trading at), then looking at the market price could tell you whether you should exercise that fixed-price option. But if you're talking about buying or selling **at the market price**, then a high price is NOT a recommendation to buy--it indicates the value is high, but THE COST IS ALSO HIGH, so they cancel out!)
Sure, but those things are only true pretty far out on the statistical tail. I have to know *a lot* more than the market, because I need to know enough to know I'm better informed than the market. Given the epistemic bias of the rational actor against thinking he knows something special -- he's dead right and millions of others are dead wrong -- it would take a very well informed person to rationally conclude he can safely bet against the market. Similarily, it takes an unusually poorly-informed person to realize the market knows much more than he does, since the market doesn't have any special qualifications -- it's made up of average people. How badly informed do I have to be on any subject to conclude reliably that the averae schmo on the street knows much more than me? Pretty badly.
So in both cases *as a prediction tool* the market is only useful for a small demographic at either extreme. That wouldn't justify its existence, since it would be ipso facto useless for the great bulk of its participants. Why would anyone willingly participate in a market the main positive effect of which is to make unusual people who are not you better off? Nobody's that altruistic.
People *do* participate in "prediction markets," e.g. every time they go to the track and place a bet on the horses. The existence of the odds -- or indeed the market in general -- benefits only the people who know nothing at all about horses, who can avoid putting their money on the 100-1 long-shot, and the people who know *everything* about horses, who can *put* their money on the 100-1 long shot that they happen to know is going to win for some obscure reason or other. The rest of the people participate not because they seriously expect to come out ahead, financially (unless they're idiots), but because people generally get a thrill out of betting on stuff for some weird psychological reason. (Perhaps because by strategic forgetting of our losses we can feel smart about our wins.)
Yes, I agree, if I have a fixed option the market can tell me whether to exercise it. Under what consideration could I have something like that in a prediction market? I am not following how this would work in, say, a prediction market on the Ukrainian war. How could I come into possession of such an option, in a natural way? If you have a specific example in mind, it would help me understand what you mean.
Couldn't this market effective simulate a decentralized lottery? Instead of buying an actual $2 powerball ticket with a 1/1 million chance to win a million dollars, someone buys a $2 share on a specific number. Enough people enjoy the tiny chance of winning a huge amount of money that they're willing to do this for real lottery tickets even with negative expected value. Then all it needs is a bunch of rational actors with enough money to provide liquidity in exchange for profiting from the irrational choices of the gamblers, who would probably end up running automated programs that arbitrage any discrepancy between the current market and the mathematical odds. The total amount of money in the system would vary, but in expectation the return for winning should be approximately the reciprocal of the odds for winning, minus any losses from irrational behavior, which are profited by the arbiters.
This seems like it would end up remarkably similar to a regular lottery, except instead of the lottery provider making tons of money from the expected value discrepancy, multiple potential liquidity providers would compete, driving the profit margins down and creating a lottery that was more fair towards the gamblers.
Depends on whether the purpose is to have fun gambling, or actually predict stuff in a reliable way. If the latter, then the necessary underlying assumption is that the future is already determined -- the die is already cast, and it's just a question of discerning which side will face up before it actually happens, like predicting the path of a thrown rock in a vacuum from its initial position and velocity.
We can fudge it a little bit by saying it has to be predictable only in a statistical sense, like ordinary statistical mechanics, or quantum mechanics, e.g. whether *this* time we get nuclear war is unknowable, but we can say with certainty that the odds are 2.633%. That doesn't really change anything, because the predictability still requires perfectly deterministic underlying dynamics -- no chaos, no random events.
Is it possible that 'story arcs' in prediction markets come because most people have far heavier priors on other people's assessment and judgement, than they do on events in reality itself?
Maybe most people, even those using prediction markets, have a real low prior on something like 'prediction markets are totally wrong here' ? I have far more experience with 'prediction markets being general correct' than i do with forecasting military outcomes.
For 5., the Biodeterminist's Guide to Parenting, #5 reads "Supplement with nicotinamide mononucleotide (for fathers)"
Should we assume that #s 2, 3, 7, 4, 10, all of them really, apply to the mother prior to birth? Subsequent to birth? The baby?
Yes, all the others are about the mother when pregnant.
Do we assume that the mother is already taking prenatal vitamins before these recommendations are given? My guess is yes or else folate/iodine/etc will top the list. This matters for things like vitamin D (already in the prenatal pill, so I guess you mean extra D on top of that) and the vitamin A variants (vitamin A is in the prenatal pill, and too much of it is actively harmful, which I assume is why you list these specific lutein/zeaxanthin variants instead of a generic A pill).
"One possibility is that, by a crazy coincidence, every day some new independent event happened that thwarted Russia and made Ukraine’s chances look better. Twenty dice rolls in a row came up natural 20s for Ukraine. Seems unlikely."
That's more or less exactly what's happened. It's not unlikely at all, it's how we experience the world.
On day 1, Ukraine was still standing.
On day 2, Ukraine was still standing.
On day 3, Ukraine was still standing.
etc etc etc
These are all new information! On any given day N, different things might happen, we don't know. We have to wait and observe. Simply drawing a linear extrapolation through the first few days would be lunacy.
Also, labeling these as "natural 20s" is a huge overstatement of what we know about the underlying distribution. We have very little information on which to base an estimate of "Can Ukraine defend against an attack by the Russian army?", and I offer as evidence the fact that this post exists, we're having this conversation, etc etc. So it *may* be that Ukraine is on a hot streak and rolling 20s, or it may be that the outcomes we see are right in the middle of the distribution because it happens that Ukraine is a better match for Russia than some (many? most? idk!) people thought.
I agree, perhaps the market is approximating a “no info environment”. Suppose I arrange to watch a movie at 3pm with a friend. My friend tells me he will try to get there on the early side, but when I arrive he isn’t there. Now how does the probability of him arriving in time for the movie update every minute? I know literally nothing about his progress save the passage of time. I think it looks quite a bit like the Kiev market.
I agree. See also the thread on House Always Wins' comment above
I was thinking about this problem recently while writing code for estimating the speed of a spinning wheel from a pulse train. It's tricky even if you have an estimate from previous pulses.
Consider a bus stop, where expect the bus to arrive every 10 minutes. Up until 10 minutes, you can estimate time remaining based on your original estimate. But now the bus is late, so what do you do?
One way to do it is to assume the bus is always about to arrive. At 11 minutes your new estimate is that buses arrive every 11 minutes. And so on. When the bus finally arrives, your prediction will be correct.
This seems to result in a smoother graph when the speed of the spinning wheel is slowing down. Adding elapsed time to the estimated period results in the frequency decaying like 1/x.
Sometimes, though, the bus will arrive early, and then you need to revise your estimate up.
This is sort of like saying the Lindy effect applies Ukrainian resistance.
But what bounds can we put on this? I would expect that cities under siege (completely surrounded) can't hold out forever. On the other hand, people say the Russian Army has logistical limits on how long they can continue the invasion.
Who has time on their side? The theory of protracted war is apparently that the Ukrainians win by surviving. Perhaps the markets believe this? Or maybe that's just the structure of this bet, since it has a deadline.
Kiev is not completely surrounded, so that changes your calculus a bit. The Russians have not been able to cut off access to the city from the south, and haven't made much progress in that direction over the past few days at least.
I'm thinking that one of the worst things about surviving a nuclear war would be finding yourself in a society organized and dominated by the kind of people who optimize their lives around surviving a nuclear war.
The vast majority of survivors would be people who survived by some combination of coincidence and general competence, no matter how (if) it happens the vast majority of survivors will not be nuclear preppers.
"vast majority" does not equal "organized and dominated by"
we already live in a disease-surviving, war-surviving hellhole (:
"Preppers are horrible people even if they're right" is enough of a trope in post-apocalyptic fiction that I've become suspicious of it. It reads like status gaming by the big winners of current society (which produces very different values and constraints that they've in turn optimized for) against their outgroup. Selfish, suspicious anti-authority types with unpopular beliefs are exactly the people I'd want to side with in a post-apocalyptic environment.
I've had to interact with too many people like that in real life, you see.
But if they're selfish, why would *they* want to side with you?
Preppers are people who are irrational, but happened to be right by pure coincidence. The fact that they are right doesn't change the likelihood of them being irrational.
If we were invaded by aliens who could be stopped by wearing literal tin foil hats, I'd expect the survivors to be even worse.
This past month has really brought back the '80s, when "is nuclear armageddon more or less likely this week?" was a perfectly normal topic for news discussion.
Not to mention all the Jimmy Carter comparisons
> If there were a stock that decreased every day for twenty days, we’d be surprised that investors were constantly overestimating it. At some point on day 10, someone should think “looks like this keeps declining, maybe I should short it”, and that would halt its decline. In efficient markets, there should never be predictable patterns!
Most high-growth tech stocks have been in secular decline since November (see eg NFLX, COIN, DASH, PTON, U, etc), so if you really believe this, you should go pick up those obvious $100 bills just laying on the ground :)
Ha ha yes that's why I always buy stock when the price is increasing and sell when the price is decreasing, which makes perfect sense except gosh darn it I seem to have less and less money every year...
The efficient market hypothesis appreciates your sacrifice!
No no. When price is decreasing, you don't sell (you are already too late to cash in). When price is increasing, you don't sell (you are too early to cash in).
Question from the audience? Let me repeat that everyone hears it. Gentleman here in the studio asked, "When do you buy"? The answer is, whenever you have sufficient funds, or at random intervals, sir.
This is the strategy that allowed us, BUY'N'HODL Inc, to finance our fancy interstellar home, the Axiom. We will return to planet Earth after it has been sufficiently cleaned.
Another explanation for the slow decline in Ukraine predictions:
This might happen if people are thinking something along the lines of "Russia will not capture Kiev by April unless they do something to turn things around before then". If so, then every day that Russia fails to turn things around provides a bit more evidence that Russia will not capture Kiev. This doesn't violate conservation of expected evidence or the efficient market hypothesis, because every day there is some small chance that Russia WILL turn things around and the odds will swing substantially in the other direction.
Yep, this seems to be the consensus answer to the mystery (several other threads discuss it too).
Nice handle, by the way.
I'm kind of echoing what's been said before in the comments, but I'm really not sure why the monotonically decreasing pattern is odd. A stock shouldn't decline over time, but a stock is also in theory an infinite prediction (there's no time expiry). A prediction with a specific deadline is quite different.
Suppose your mental model is something like "there is a 1% chance Kiev will fall on any given day". With 30 days until April, you'd predict about a 74% chance of Kiev not falling (.99 ^ 30). With 15 days left, conditional on it not falling yet, you're up to about an 86% chance. Your base rate probability of Kiev falling doesn't have to change (it's still 1% on any given day), but the decreasing time to expiry changes your odds of the actual contract resolving one way or the other.
I basically agree with this take. Every day Russia fails to make progress in taking Kyiv is a day closer to the deadline. They might still be making progress, but so far it's too slow for them to make an April 1st deadline. I think their best bet is in surrounding the city and starving out the defenders, but that'll take a couple of weeks even after they've surrounded the city, which they're still far from doing.
I think that the other thing is that people have been expecting the Russian army to figure out its organizational problems but they haven't done that yet. The longer they fail to do that, the more it looks like they won't be able to do it. Which means the war will be continue to be slow-going and costly for them.
I think the key here is that the evidence has mostly been of the following form:
"the Russians haven't moved very far, and they've already been invading for X days"
That's evidence that becomes monotonically stronger as X increases but there's no sharp cutoff point where it qualitatively changes in character. It's quite different from the updates you would get from crucial pivotal events (agreeing to ship a more advanced SAM system, the fall of a city, losing a key skirmish etc) but I also think it's extremely relevant evidence.
For instance, if we think one of the two situations is likely to be a correct description of the situation, we could reasonably believe that every day without solid Russian progress is evidence towards option 2 and update accordingly.
Scenario 1) Russian forces are fundamentally powerful enough to take Ukraine but take time to deploy effectively
Scenario 2) Russian forces are not powerful enough to take Ukraine
Every day X ticks one higher, and the P(evidence| scenario 2) becomes higher and P(evidence|scenario 1) becomes lower meaning a larger update but incremental update towards scenario 2.
Even now, it's still possible that the Russians are gradually getting into position and will still prevail, but the alternative story where their logistics, morale, tactical awareness etc are too constraining to achieve their objectives has become a lot more plausible.
Yes, this was a weird objection to me. The monotonically decreasing with time in the absense of major new developments seemed the obviously correct reaction.
Zvi has very similar behavior in his Covid predictions. For example, before the recent Hong Kong surge, as time went on with no (apparent) changes in China's case load, he gradually incremented up the likelihood that they would successfully contain the disease. Then, something major happened (the Hong Kong spike and various smaller outbreaks) and he dramatically reduced the likelihood.
(This was a comment made by the real Enopoletus Harding on Metaculus.)
I thought of leaving here due to my disagreements with the moderation here, but since Scott has mentioned me on his blog (I can't comment there since I'm banned for extremist posts), I will continue to make predictions here. Needless to say, the chances of Russia taking Kiev go down each day there is no advance. I personally don't think it makes sense to update very rapidly, since, for all I know, the Russians may have been using the past two weeks to prepare some lightning assault -not something that's likely, certainly, but the chances of that are too high to simply exclude off the bat. Maybe I should update more rapidly -I've been underperforming the community when evaluated at all times. But knowing when to update and having good starting positions are not easy skills to learn.
I've also created an account on Manifold Markets, I expect my predictions to be better there (I have a habit of putting the vast majority of my money on a few markets I can easily win in):
https://manifold.markets/EnopoletusHarding
No, I'm not trolling. Wrong, maybe. It's happened before. I had 10% chance of a Russian invasion for way too long, but I obviously changed that as the evidence became more clear.
Remind me what your disagreement with the moderation here was?
(asking because I thought it was that I banned you, but you're here, so I must be misremembering)
Supposedly, "here" is Metaculus, not ACX. https://www.metaculus.com/accounts/profile/118219/
More seriously: "is EHarding a troll" is an excellent example of a question not suitable to a prediction market.
That doesn't quite work. NotEH says the comment was on Metaculus, and says EH was banned on Scott's blog, which is here.
It does not seem implausible to me that Harding would also have disagreements with the Metaculus moderation.
This is correct, he is referring to the Metaculus moderation
Ukraine is going to lose in the end. Maybe only after most cities are destroyed, but they cannot win. Then they will be ruled by russian marionettes & dictat in the foreseeable future. The dictat will be harder and longer, in particular on the West-ukrainians, the more blood the Russians have to spill to conquer the country. The only alternative is for the ukrainians to cut their losses some way, but so far that seems unlikely. I'm writing this because the endgame is what matters. Making "predictions" about which week Kyiv and other cities fall is a teenager-way of thinking and acting about a real-life war. It is of very marginal importance which week it will happen, and such speculations are also rather distasteful. Grow up.
The big questions rely on and derive from the little questions. The most accurate way to make large predictions is to break them down into many smaller subpredictions for which we can derive some reference class. Or, to borrow Jesus's phrasing, "Whoever can be trusted with very little can also be trusted with much."
The longer Kyiv holds out, the more time there is for some major event to change the entire equation. A general collapse in one of the two armies, for example. Of for another major power to get directly involved, for another. The math might currently be in Russia's favor (actually it's not that clear; it depends on what the casualty numbers are really like,) but there's still time for major events to upset matters.
It's also important to understand that it's not just the "endgame" in Ukraine that matters. This war affects most of the world at the moment, and whether Ukraine continues to fight matters a lot to what the other powers involved should do about it. For example, if Ukraine can be expected to hold out for another few months or a year, then Putin needs to worry about supply and domestic issues so it affects him greatly. It also affects the kind of aid it makes sense for the EU and NATO to send to Ukraine. It also affects what countries that used to depend on Ukrainian grain will have to do to deal with their own crisises. So yes, this matters.
"Teenager"? It seems like you can make real money betting against the people you disagree with. There are lots of adults who making a living on speculative markets.
My mental model for the progress of this war is essentially as a race - damage to Ukrainian civilians and military may push Ukraine to concede a disadvantageous peace, and damage to Russian military and economy may push Russia to concede a disadvantageous peace; both of these damages are progressing at varying speeds, and the question is which one of these "progress bars" will reach a breaking point first.
And I strongly disagree with your assumption - I don't see how Russia can force *that* kind of peace even if their military operation completely succeeds now. If Russia conquers or destroys all the major cities and installs a puppet government, that does not enable Russia to rule over Ukraine - the populace will not agree to that, not even in the eastern Russian-speaking areas like Kharkiv, not after what has been done in the war. And Russia can not afford enough manpower to enforce proper control, that would require something like 500k permanent garrison there; so Russia will have to leave and their marionette regime falls right afterwards (as after USSR-Afghanistan). I mean, pacifying and controlling a hostile country is really, really hard; it has not gone well for USA recently despite immense resources, and even for the quite effective Stalin-NKVD apparatus it took many, many years after WW2 to suppress guerilla warfare in Eastern Europe - and those people and Taliban didn't have external support/arms supply from all the wealthy countries, like Ukrainian guerillas would have in case of a Russian conquest. So as Russia can't plausibly hold Ukraine, they would have to concede to something more reasonable (e.g. recognition of Crimea + DNR/LNR, perhaps a bit more land, but Ukraine government remaining in place) even in the case of an overwhelming victory - which itself is far from certain.
In my opinion the main part of the war has not started yet - the Ukrainian strategy apparently was to trade space for time, preparing for the actual fighting in taking over the large cities, which is going to be difficult for the attacker, and where the war would be decided. So far Russia is only assaulting the relatively small Mariupol (Kherson and Melitopol are many times smaller than that), not even trying to make serious progress in Kharkiv or Kyiv. We can see how much men and time it took Russia to take Grozny; it seems plausible to consider that Kyiv - which is much larger and has much more resourced defenders - will take at least as much.
Im skeptical of the "russia will never submit Ukraine". Didn't they do it with Chechnya pretty succesfully? Seems like they could pull it off at least on a portion of Ukraine.
Chechnya is much smaller, but Ukraine doesn't have much in the way of mountains.
Chechnya is a very relevant example of how they were very much *not* able to do it "pretty successfully". They tried to enforce submission for many years and failed, and they succeeded only with a combination of keeping excessive military garrison (at levels which Russia can't afford at the larger scale of Ukraine) plus effectively buying off the local leaders and population with excessive subsidies (again, at levels which Russia can't afford at the larger scale of Ukraine) and political concessions.
The Chechen resistance did not end with surrender and submission, the current result is "an understanding" where formally Kremlin gets a victory, territorial integrity and declarative submission, but in practice devolves severe autonomy and large monetary "tribute" to Chechnya. Kadyrov is not like other regional leaders which are at the mercy of Moscow, he is independently powerful, with his own army (that is not accountable to Russian hierarchy), and is effectively an ally of convenience to Putin personally and has a lot of de-facto autonomy from the rest of Russian authorities - there are all kinds of incidents with Kadyrov's people in violent conflict with other Russia region's court system and police system, and having de facto immunity for that. I don't have a specific English source in mind, but if you're interested about this aspect, I would recommend you to read about how Kadyrov came to power, all of that process was quite interesting.
Thanks, I will further look into this. Any reliable books on the subject?
I don't know any - it's relatively recent, most written information is in Russian with little analysis from the western part, and I doubt if the authorities would allow to publish an analytical book like that in Russia (and IIRC both threats and actual violence has been applied both to local Chechens and expats commenting on Kadyrovs regime). However, I just stumbled upon a quite extensive summary in English in Twitter-thread form - https://twitter.com/kamilkazani/status/1497612331953577991
I'm not sure if your claim is "I'm so obviously right that it's useless for people to try to predict things" or "the things you're predicting are too small scale to matter".
I disagree with the first because the people who say the first have a worse-than-average track record of being right, and I disagree with the second because big things are made up of small things. I bet there are a lot of Ukrainian generals who would like to know in what month Kiev will/won't fall right now, and would change a lot of what they're doing if they knew.
But also - realistically everything that's happening on prediction markets now is capacity-building / proof-of-concept. The more we establish a record for prediction markets on small things, the more likely we'll have them ready and established when we need to use them for big things.
(the Arb report I linked finds that forecasters beat epidemiologists and models in predicting the spread of COVID-19 and its effects on interventions - seems potentially useful)
I would like to go on record that I find that poster's attitude distasteful AND I disagree with his object-level prediction about the end-result of the Ukraine war.
However, upon reflection, he may be on to something, and I don't think your answer addresses that something. A more sophisticated, steelmanned version of the sentiment he expresses would go as follows:
It should be, of course, uncontroversial that every little data point brings us closer to a correct big picture view. However, it does not follow that a *prediction market* about every little single data point gives us more information. Realistically, prediction markets about little things will be extremely correlated with each other, influenced much more strongly by the overarching big picture sentiment looming above them than by any actual new information directly related to the question they're trying to answer. (And even if one of them is actually pricing in some important niche knowledge, we have no way of teasing that knowledge out from the single probability number that the prediction market produces.)
In other words, in a flow of information from primary data to their increasingly more processed derivatives, prediction markets about small things may actually be further down the line than the big picture view, with the big picture view having already absorbed the relevant information from the primary small-thing datapoints. The corollary to this would be that predictions about small things should not, and probably do not, reflexively influence the big picture view. This is an important, non-trivial point that, honestly, I find likely to be correct.
> they cannot win
It is not very likely or likely, but it remains possible (Putin gets overthrown or something).
Making claims like that is a perfect example why tools like prediction markets can be useful.
I'm actually trending towards thinking that Russia is not likely to win unless China props them up. At this point it's looking like a long, long grind and I don't know how long Russia can sustain that with the way their economy is going.
this is an example of definitions being really important - as the definition of 'win' is the key factor here. And where prediction markets on those various definitions of 'win' are highly valuable
Perhaps the best outcome for Russia is a 'loss' in Ukraine.
A Russian 'win' leaves Russia maintaining a very large military force in the country for years. Possibly decades. A never ending money and resource pit. This was true from the moment it become clear that Ukrainians were not hoping to become part of Russia.
Especially in a scenario where Russia trades their withdrawal for significant sanction relief. But even in a scenario without that, I think Russia withdrawing would give some portion of parties participating in sanctions the cover they need to slowly back away.
Why do you think they cannot win? Russia is about three and a half times the size of Ukraine in population, which is an advantage but may not be enough to balance the facts that Ukraine is on the defensive, that the Russian military appears to be very poor and Ukraine's military pretty good. Russia is richer than Ukraine, which in most contexts would be important, but Ukraine is being supplied by NATO countries that are much richer than Russia.
It's hard to be sure but it looks as though, despite its size, Russia has a very limited number of trained soldiers, many, possibly most, of whom have already been committed to the invasion. So I think one plausible outcome is that the Russian military ends up unable to advance further, possibly unable to hold what it is currently occupying. They can kill a substantial number of Ukrainians, but not a substantial fraction of the population, and at the cost of further losses of men and material.
"Ukraine is going to lose in the end. Maybe only after most cities are destroyed, but they cannot win."
Your confidence in the ability of the Russian army to sustain its morale and current operational tempo indefinitely, is I think unjustifiably high. The best unclassified sources I can find suggests that the Russian army has already lost 10-20% of its *total* effective combat strength in this campaign. That can be reconstituted, but not in real time. And Putin isn't going to run his army down to literally zero combat effectiveness.
The 30% of forecasts where Russia hasn't even taken three major cities by June, those are the ones where Ukraine probably wins. And, yeah, maybe promises to recognize Crimea as part of Russia to dissuade Puting from spite-nuking Kyiv, but that's still a win for Ukraine.
"Russia will probably win" is a reasonable forecast. "Ukraine *can't* win", is not.