Game Theory Of Michigan Muslims

When do you vote for a worse candidate to punish a better one?

(this post was written before the election, but nothing in it changes based on the result)

Mentioned before: a group of Muslims in Michigan are backing Trump because they’re mad at the Biden/Harris administration for supporting Israel. They understand that Trump supports Israel even more. They just worry that if they always vote straight Democrat like every other minority group, the Democrats have no incentive to listen to them. They hope that if they elect Trump, even if he doesn’t listen to them, then the Democrats will work harder to woo them next time around.

What do we make of this?

On the one hand, it makes sense that admitting “I am forced to vote for you, whether you address my concerns or not” wouldn’t be a great bargaining tactic, and that they would look for something else.

On the other hand, it doesn’t seem great to actually elect someone who you hate and who will work as hard as he can to thwart your policy priorities. Imagine if every group tried this, and we ended up with gun owners and evangelicals voting Harris and Muslims and trans people voting Trump. It would be ridiculous. Is there some sort of middle ground?

My reasoning after thinking this over a bit: it seems wrong for the Muslims to vote Trump, because then Trump is left actively better off by his decision to be so hostile to the Muslims that they’re not even interested in convincing him (and so use him as a foil to affect the still-convince-able Kamala). It seems like the equilibrium there is for more candidates to become 100% hostile to Muslims, since this leaves them unextortable and liable to benefit from the Muslims’ attempt to extort their opponents. So whatever strategy the Muslims choose, it should end with Kamala better off than Trump.

How do you preserve ability to bargain with Kamala while continuing to treat her better? You could try to add a stochastic element to your vote. Maybe you roll a dice and vote Kamala for 1-4, and Trump for 5-6. Then you tell Kamala that you’ll vote for her with certainty (rather than only 66% chance) if she does what you want in Palestine. Maybe you could generalize this: figure out what percent of your ideal policy platform Trump gives you, what percent Kamala gives you, and vote with a frequency equal to the ratio of those percentages (eg if Kamala gives you twice as much as Trump, then you vote for Kamala with 66% probability). Then you adjust your frequency up or down as candidates grant your demands.

I was very pleased with this elegant solution, but here’s a counterargument: isn’t this just throwing away your voting power? Telling Kamala “You better give me what I want or else I’ll vote for Trump with 1/3 probability” seems like a strictly less compelling threat than “You better give me what I want or I’ll vote for Trump”. In fact, you could imagine the former as being identical to the latter, only voiced by a coalition one-third the size. Why would you voluntarily decrease your power to that of a coalition one-third your size?

In retrospect, maybe I’m erring by using intuitions I got from Eliezer Yudkowksy’s decision theory work, intended for bargaining with literally-galaxy-brained superintelligences who might respond with things like “Sorry, I’ve already pre-committed to rejecting all offers that would seem like extortion to omniscient entities negotiating from behind a veil of ignorance, and if you think about it carefully you’ll realize that this is fair enough that your own set of galaxy-brained logically-perfect pre-commitments don’t require you to retaliate against me for doing this”. This is a good strategy if you can pull it off, and it forces you to pay a two-thirds tax to place yourself in a bin of slightly-higher-cooperativeness. But Kamala Harris probably hasn’t done this, maybe hasn’t even done any instinctual thing which cashes out to the equivalence of this, and maybe doesn’t respond differently to the outright extortion of “do what I want or I’ll vote Trump” or the massaged-to-fit-a-series-of-fair-precommitments offer of “do what I want or I’ll vote Trump with 33% probability”. In fact, IIUC Kamala hasn’t shown any inkling that these people exist at all (which could itself be a powerful game theoretic strategy!)

I asked Eliezer to see if I was understanding his position right. He said:

So, first of all, if you want a sensible analysis of this, you're gonna have to use logical decision theory instead of causal decision theory, or something that ends up equivalent to LDT by talking about a CDT agent who wants a "good reputation" meaning they always behave like LDT. Worse than that, you're going to have to jump ahead to using folk theorems of LDT that seem like they ought to be proven someday but which we currently lack the representational framework to prove. If you use conventional classical academically standard causal decision theory, there's no notion of "fairness", there is just accepting an offer of $1 in the Ultimatum Game being called "rational", and so Harris should offer Muslims policy the bare minimum better than Trump and Muslims should accept it. This is almost directly isomorphic to the Ultimatum Game, on which the classic causal decision theory answer is "offer $1 and accept $1, for this alone is Rational".

With that said: Consider the obviously better nonstandard solution to the Ultimatum Game of "accept $5, accept $4 with probability 5/6 minus epsilon, accept $3 with probability 5/7 minus 2*epsilon", etc. Formally, this would look something like, "Calculate what you think is your fair share, here the Shapley value of $5, and then agree to trade with a probability that is a function of the offer, such that your opponent's expected gains fall off monotonically but slowly as they offer you less than a fair value." The goal here is not to punish a greedy opponent, but to minimize losses in the case that people have legit disagreements about what's fair. (If you're part of a partially exploitable population and the opponent is trying to test exploiting you, then things get more complicated so let's leave that aside for now.) The analogy here would be that Muslims think Harris is not offering them a fair share of the value of their vote in anti-Israel policies. Offering more anti-Israel policies would cost Harris with other voters, though.

Let's spitball that a fair share of anti-Israel policy is a level of anti-Israelism where Harris loses half as many other marginal voters, as she gains in Muslim voters voting for her. (Maybe more sensible is "loses half as much in victory probability, as she gains from Muslims voting for her", which for small amounts of votes and the popular vote would be the same thing, but is not at all the same thing given the Electoral College.) Then if Harris offers less than this, Muslims could collectively decide to vote with a probability where Harris gains, eg, twice as much in voting win probability from Muslims, as Harris spent by alienating other voters with more anti-Israel policies than Trump has. Voting for Trump on the surface of things makes no sense, but maybe the Muslims want to demonstrate that they are in fact willing to vote and get out the vote. In this case, they could arrange for paired Harris and Trump votes (by region) to cancel each other out while still showing their strongest voting record.

None of this is a rigorous answer. First of all, because nobody has actually derived the LDT Ultimatum solution from first principles. (Bearing in mind that, eg, CDT does not even derive Nash equilibria from first principles, because there's an unjustified step where you have to assume the other player has already decided to play Nash equilibria, before you first decide to play Nash equilibria, and in CDT this is an infinite recursion, while LDT can derive it from first principles. So we are not assuming any more in LDT than CDT assumes in order to derive Nash equilibria.) Second, because we're not trying to put Muslim gains and Harris gains into a common currency, just evaluating everything from Harris's viewpoint on gains and losses. But it beats the CDT analysis by miles, I'd say.

Once you do have a notion of what is fair, you can then try to define what is a "threat" relative to that. Muslims voting for Trump in a nonpaired way looks like a threat because it is not in the interest of Muslims to do that if Harris is not responsive to it, so it would be only Harris's own behavior-pattern which would ever incentivize Muslims to hurt her more than they would if Harris was a rock, so Harris ought not to adopt that behavior pattern and then Muslims ought not to do it. This is the sort of concept that is not theoretically solid and which created the longest Discord thread in the history of Project Lawful when people started to define exactly what constituted a "threat". But in this case of "We will do something that clearly hurts us, and also hurts you, relative to what we would both do if we weren't coordinating at all and had never heard of each other, unless you do this thing we want", that seems pretty clearly a threat.

With that said, of course, threats can make good decision-theoretic sense when you are dealing with another agent that is bad at decision theory. Anybody who tries offering you $1 on the Ultimatum Game is probably also a sort of agent that will offer you $10 in the Ultimatum Game if you set up a doomsday nuke that goes off otherwise.

I appreciated the comparison to the Ultimatum Game. This is a classic game theory experiment where:

1. There is $10 at play

2. Player A proposes a potential split of the $10 pot to Player B.

3. Without any negotiation, Player B either accepts the offer (in which case the money is distributed according to the offer) or rejects (in which case nobody gets any money).

This is sometimes considered paradoxical, because the “rational” answer is for Player A to propose $9.99 for himself and $0.01 to B, and for B to accept (because getting $0.01 by accepting is better than getting 0 by refusing). B’s acceptance retroactively justifies A’s offer as rational (since it leaves A with $9.99, instead of the lesser amount he would get by splitting the pot fairly). But when you test this in real life, most Player A’s offer about $5, and most Player B’s accept only when the offer is $5 or close to it (ie if offered $0.01, they would prefer to screw everything and get $0 in order to “punish” Player A). Part of Eliezer’s work has been trying to formalize a justification of why the real-world pattern is more rational than the supposedly-”rational” solution of offering $0.01 which never works.

Eliezer’s insight is that the Michigan Muslims’ dilemma follows this same logic. Suppose we abstract away the pro-Israel voters into part of Kamala’s utility function (she wants to support Israel, and we leave it unsaid that this is because she wants to woo pro-Israel voters). Now Kamala’s job is to “make an offer” which divides the “pot” (her ability to distribute goodies if she becomes President) between the Muslims’ utility function and her own. And it’s the Muslims’ job to either accept the offer (by voting for her) or reject it (by abstaining, or voting against). It’s naive-rational for the Muslims to always vote for Kamala, because they always get a better outcome than if they voted for Trump - but only in the same way it’s naive-rational for Player B to always take $0.01 offers, because at least he gets $0.01. If the Muslims are smart, they’ll add in some term for punishing Kamala if her offer is offensively low - which is what the real Muslims are doing now

What is a “fair offer” in this ultimatum game? It seems like she should offer to split the gains from getting the Muslim vote in half, keeping half for herself and giving half to the Muslims. I think this is what Eliezer means by "Let's spitball that a fair share of anti-Israel policy is a level of anti-Israelism where Harris loses half ... as much in victory probability [from other voters leaving her] as she gains from Muslims voting for her."

(does this make sense? In the real world, she’s simultaneously negotiating a deal with Jews and other pro-Israel voters on the other side. She can’t keep half the gain from both sides, because there is no personal gain, we’re assuming Kamala herself doesn’t care about the Middle East and is just trying to please various voting blocs. I think once we instantiate the Jews as equally coherent actors, this start to just look like landing somewhere in the middle on Israel, weighted by the relative size of both sides’ coalitions and how much they would vote for her for other reasons, and neither side is incentivized to threaten her further because they know she knows she’d lose more votes by giving in than by standing firm. But I admit I’m having trouble thinking about this part.)

So I think this is the right move if everyone involved is a superintelligence and has already made all commitments they would make if they were omniscient and had infinite time to think about the problem. What about in the real world?

The more I think about this, the more I think it’s also the right move in the real world. Kamala might not know the word “pre-committment”, but I think she’s smart enough to know that if she gives one interest group special treatment for conspicuously betraying her, then every interest group will conspicuously betray her the very next moment. So if she’s smart, she’ll do nothing (or even punish them by veering further anti-Israel?) and they’ll be stuck both having no voice in the Democratic Party and having a higher chance of Republicans taking power.

(wait, is this right? A Kamala whose interests were aligned with the long-term interests of the Democrats would do this, but Kamala may not care about anything past this one election. So maybe she should give into them at the last second, just long enough before the election that nobody else has a chance to organize a similar campaign? I think this would work in theory, but fail in practice because it would make her look weak.)

In fact, we could think of this not as the Muslims defecting against Kamala, but as them defecting against the Democratic coalition. Every part of the Democratic coalition would like to defect in a way that prioritizes their pet issue and screws over every other part of the coalition. The Democrats succeed as a party (and beat the Republicans) insofar as the coalition members stay strong and don’t do this. Maybe Kamala’s actual response should be something like “here are the usual levers for influencing Democratic Party policy, like voting in the primary, you lost, and you are trying to re-litigate a completed political process because you don’t like the result, in the same way we condemn Donald Trump for doing.”

Maybe there’s no such thing as “captive voting blocs” who are so clearly destined to vote for the Democrats that the party leadership ignores their priorities. Teachers unions always vote Democrat, and it’s hard to imagine them defecting and voting Republican, but the Democrats seem to work hard to satisfy them anyway. Maybe we should think of teachers unions’ ability to influence Democratic policy as not at all based on the plausibility of them threatening to vote Republican; maybe the Democrats factor in and reward them for their loyalty in a way that exactly compensates for the clout they lose for not being on the fence, meaning there’s no benefit to them making a big show of maybe breaking for Trump.

In this case, the advantage of the Muslims voting for Trump isn’t that they’re showing their willingness to defect, it’s that they’re organizing. As the Marxists always say, organized political blocs can get more concessions than unorganized political blocs. Partly this is out of an implied threat of doing what the Muslims are doing now - switching en masse in a coordinated way - but among savvy political operators, nobody ever has to come anywhere close to making this threat and it’s taboo to try. The organizers just gently remind the candidates that they’re organized, the candidates give them some level of handouts proportional to their power, and everyone stays friendly.

So my best guess is that most normal political groups probably approximate the correct decision theory, the Muslims are defecting from this in a way that’s probably going to get them taken less seriously, and what they should do instead is organize (like they’re doing now) without the explicit threat, then accept that they’re probably getting the most that normal coalition politics decrees they should be offered.

I still wish I had a better idea of when to protest-vote (not in the sense of third party, but in the sense of voting for a plausibly-electable worse politician to punish a better politician who you think has strayed). California elections are often a choice between a corrupt and incompetent Democrat and a Republican with policies that I don’t like. One of the few checks that voters have on the Democrats’ corruption and incompetence levels is to threaten to vote Republican. Is there some level of Democratic corruption at which I should vote Republican to “punish” the incumbent even if I think the Republican would be a worse leader overall? I’m not sure, and currently lean towards no, but I can’t say it doesn’t tempt me.