Approval voting is also worth considering, where you put a checkmark in the box for any candidate you’d be okay with. Advantage over ranked choice is that communicating the scoring to citizens is simple: “$CANDIDATE received the most checkmarks.” Whereas with ranked voting, the person who gets the most #1’s might not win and that can confuse some citizens.
Approval voting would result in “the okay-est” candidate winning rather than anyone towards an extreme winning in the primaries. Works well when there are a lot of fairly similar milquetoast candidates that split votes, like the Republican primaries of 2015.
> Whereas with ranked voting, the person who gets the most #1’s might not win and that can confuse some citizens.
Not ranked voting, ranked voting is still very broken. Rated voting. Approval voting is a rated voting system.
Score voting: Rate each candidate on a scale of 1 to 10.
Approval voting: Rate each candidate on a scale of 0 or 1.
Score voting (or STAR) is generally better and the argument that people are going to be confused by "that thing they use at the Olympics" is nonsense, but approval voting is fine if you want to silence the complainers while still using something that basically works.
Score voting is just approval voting with an additional permitted tactical error.
In both systems, the correct tactic is to determine the two candidates most likely to win. Then, assign maximum score to whichever of those is better and to everyone preferable to that candidate.
It is never correct to assign a score between the minimum and the maximum, so why allow it in the first place?
> It is never correct to assign a score between the minimum and the maximum, so why allow it in the first place?
Because it is often correct.
Suppose there are candidates A, B and C. Candidates A and B are each polling around 6/10 and candidate C is polling around 4/10, but candidates A and B are quite similar to each other and share a base of support. According to your strategy, A and B are the two most likely to win, so if you prefer A then even though you still prefer B to C you refuse to express your preference and instead assign 10/10 to A and 1/10 to B and C. The voters who prefer candidate B do the same. The result is that A and B end each up at 3.5/10, C ends up at 4/10 and C wins. In other words, you've devolved back into first past the post and caused your least favored candidate to win because of your erroneous strategizing.
By contrast, if you assign 10/10 to A, 5/10 to B and 1/10 to C, you've given A a significant advantage over B without assigning B such a low score that you could deliver the election to C if C defeats A.
In your scenario, I have made a mistake in assessing which two candidates are most likely to win -- because I took vote shares as win probabilities. This is also a mistake, and it is a mistake no matter the voting system or the next step in your strategy.
You're also assuming that everyone axiomatically uses the same strategy as me. If A-voters use your strategy and B-voters use my strategy, then B is straightforwardly favored to win. This results in a prisoner's dilemma, with its well-known Nash equilibrium in favor of defection.
> you've devolved back into first past the post
Correct. The potential for this to happen is one of the drawbacks of rated voting systems. It's also, through a different mechanism, one of the drawbacks of ranked systems. It doesn't mean we shouldn't try, since both alternatives give some ability to hedge against incorrect assessments.
> By contrast, if you assign 10/10 to A, 5/10 to B and 1/10 to C, you've given A a significant advantage over B without assigning B such a low score that you could deliver the election to C if C defeats A.
I can accomplish the same mathematical thing by assigning 10/10 to A, 1/10 to C, and flipping a coin to determine whether to give B 1/10 or 10/10. Both give the same odds of winning to A and B (well, mine gives B slightly higher odds because its average is 5.5 -- but you get the point). The only difference is that your method outsources the randomness to the rest of the electorate, rather than generating it yourself.
> In your scenario, I have made a mistake in assessing which two candidates are most likely to win -- because I took vote shares as win probabilities.
Your problem is that your voting strategy changes which two candidates are most likely to win. If everyone votes their actual preferences then it's A and B. If too many people vote according to your strategy, C becomes a frontrunner.
> You're also assuming that everyone axiomatically uses the same strategy as me.
I'm only assuming that some proportion of voters use the same strategy as you. The higher that proportion is, the more likely it is that C wins instead of A or B. It doesn't have to be 100% of people to cross the threshold into changing the outcome.
> If A-voters use your strategy and B-voters use my strategy, then B is straightforwardly favored to win. This results in a prisoner's dilemma, with its well-known Nash equilibrium in favor of defection.
That isn't a prisoner's dilemma. A's voters prefer that B win over C and B's voters prefer that A win over C, so they each have the selfish incentive to give their second choice a higher score than their third choice to prevent the worst-case outcome.
> I can accomplish the same mathematical thing by assigning 10/10 to A, 1/10 to C, and flipping a coin to determine whether to give B 1/10 or 10/10.
But then the voting system is receiving less information from you. Requiring your preferences to be expressed statistically increases the error bars for no reason. Also, most people are not going to do that and requiring them to in order to express their preferences is needlessly confusing.
> I'm only assuming that some proportion of voters use the same strategy as you.
My strategy does not change other voters' strategies. Secret ballots prevent this type of coordination. That's my point. The collective strategy of 1/3 of the electorate does change which two candidates are most likely to win, but my individual strategy does not meaningfully do that.
> they each have the selfish incentive to give their second choice a higher score than their third choice to prevent the worst-case outcome.
If a voter values preventing the worst case over achieving the best case, then the optimal strategy is to assign maximum scores to every candidate except the worst case. Hedging by assigning a non-maximal score increases the chance of the worst case compared to that approach, in exactly the same way that it reduces the chance of that compared to assigning a minimal score.
I'll grant that my specific tactic is predicated on a preference for achieving the best outcome rather than avoiding the worst one, but the best tactic for someone who finds avoiding the worst-case to be more important also only requires extreme votes.
> A's voters prefer that B win over C and B's voters prefer that A win over C, so they each have the selfish incentive to give their second choice a higher score than their third choice to prevent the worst-case outcome.
Expressing that preference directly reduces the likelihood of each such voter's preferred outcome, even if a single voter does it. It affects the chance of the worst-case outcome only if voters on both sides of the A/B division do it. The secret ballot prevents any kind of enforced coordination. This is exactly a prisoner's dilemma.
> Requiring your preferences to be expressed statistically increases the error bars for no reason.
You don't know the exact score each candidate will end up with absent your vote -- if you did, you could analytically determine a single-vote strategy that gives the best available outcome. Since you don't know that, your choice of an intermediate score is a statistical expression. It's just expressed in terms of the uncertainty in what the rest of the electorate is doing, not in terms of a coin flip. It does not meaningfully increase the error bars (in a large election -- say, >1k voters) because the former uncertainty quickly dwarfs the latter.
> My strategy does not change other voters' strategies.
of course it does. this is basic game theory. but the point is, at some level of iterating on what other voters will do, you arrive at an effectively static "wave function" of possibilities, so you can behave as if you have constant fixed win probabilities for the other candidates, and vote accordingly.
> My strategy does not change other voters' strategies.
It does when you describe it to them and convince or force them to use it, e.g. by removing their ability to score the candidate on a scale.
And it does because you are part of the electorate, situated the same as the others, so the strategy you devise should be the one that yields the result you want given that similarly situated people will reach the same conclusion:
Special note for the critics of superrationality: Your vote isn't going to change the outcome, so according to classical game theory you should stay home instead of wasting your time doing something that doesn't matter. Therefore, voting at all is an exercise of superrationality. If you're not willing to use it in your voting strategy then you shouldn't use it in deciding whether to vote to begin with and so you should either use a superrational voting strategy or you should stay home.
> If a voter values preventing the worst case over achieving the best case, then the optimal strategy is to assign maximum scores to every candidate except the worst case.
You're not thinking probabilistically.
Suppose there are two plausible final election outcomes where your vote matters:
Option 1, candidate A is at 4.99/10, candidate B is at 5/10, candidate C is at 4/10.
Option 2, candidate A is at 4/10, candidate B is at 4.99/10, candidate C is at 5/10.
If it's option 1 and you assigned 10/10 to candidate B, your preferred candidate loses. If it's option 2 your preferred candidate can't win and if you assign 1/10 to candidate B, your least preferred candidate wins.
But if you assign 10/10 to candidate A and 5/10 to candidate B then in option 1 that could still be enough to see candidate A win, and in option 2 it could still be enough to see candidate C lose.
Moreover, the score allows you to express how concerned you are about each outcome. If you're pretty okay with candidate B but have a moderate preference for candidate A then you can give candidate B 7/10. If candidate B is almost as bad as candidate C you can give candidate B 3/10. It allows you to hedge: How much advantage for candidate A are you willing to give up to reduce the chances of candidate C? You seem to be assuming that the only possible answers are "all of it" or "none of it", but there are other options.
> Expressing that preference directly reduces the likelihood of each such voter's preferred outcome, even if a single voter does it. It affects the chance of the worst-case outcome only if voters on both sides of the A/B division do it.
If affects the chance of the worst-case outcome in all cases because it increases candidate C's chance against candidate B, and you don't know what the other voters are going to do. If candidate A has less support than expected due to inaccurate polling then it turns into a race between B and C regardless of whether B's supporters give A 1/10 or 5.5/10. Meanwhile you assigning a lower score to B is reducing B's chances against C regardless of why the race turns out to be between B and C.
> This is exactly a prisoner's dilemma.
No it isn't. In a prisoner's dilemma, defection is to your advantage regardless of what the other person does. In this case, if the other party defects -- and sometimes even if they don't -- then your defection harms you, because their defection (or something else) put candidate A behind candidate C. Then it's not clear if your support for candidate A will allow them to defeat candidate C, but if it isn't, your defection in assigning the lowest possible score to candidate B would cause candidate C to defeat candidate B, which is to your own disadvantage.
> Since you don't know that, your choice of an intermediate score is a statistical expression.
It has less information content. If you roll a D10 and then assign 10/10 to candidate B if it's above a 6 and 1/10 if it isn't, the voting system only gets a single bit of information from you, whereas assigning the equivalent score gives it >3 bits of information. That only matters if the election is very close, but it always only matters if the election is very close.
In 2024 there were dozens of state legislative races decided by fewer than 100 votes:
> It does when you describe it to them and convince or force them to use it, e.g. by removing their ability to score the candidate on a scale.
This is essentially the argument that it's good to allow other people to make tactical errors, because it gives more power to those who do not make such errors. Or, perhaps, that I should take an approach that reduces the power of my vote on the basis that others might copy me. Frankly, I philosophically reject both of these.
Look, I buy superrationality from an ethical perspective. I favor the Kantian imperative as a framework (among others) for assessing ethical questions, and it's basically the same concept as superrationality.
Superrationality is not, however, a reasonable way to make practical decisions about scarce resources. The reason is because it essentially ignores the problem of perverse incentives. In practical situations, one must deal with perverse incentives. My voting does not create a perverse incentive for anyone else, and in fact it only benefits me (by signaling that I do vote, so my vote is worth competing for).
> Suppose there are two plausible final election outcomes where your vote matters:
You are claiming that I'm not thinking probabilistically, but first off: you're providing an overly specific scenario rather than a probabilistic one. Second, your own overly specific scenario does not even work. If the extra 4 points that I give to B (over the "preferred outcome" strategy) is enough to result in B defeating C in scenario 2, it is also enough to result in A defeating B in scenario 1. A winning isn't an option in either of these cases, even if there is some dataset about the world that makes this set of outcomes plausible.
Maybe try thinking about it this way: In score voting, points are summed and nonrivalrous. So, a point is a point -- regardless of how many other points you gave to that candidate. Why, then, are you choosing 5/10 for B, specifically? What, analytically, leads you to that choice? If you're trying to prevent a C victory as your most important value, why not choose 6/10? 7? And so on. If you find it more important to cause an A victory, why not choose 4/10? A point is a point, no matter how many other points the candidate got from the same voter.
> In a prisoner's dilemma, defection is to your advantage regardless of what the other person does.
There are formulations of the prisoner's dilemma in which a double defection is worse for both parties than a single defection is for the losing party. But it's clear that this terminology is more confusing than helpful, so I'm OK abandoning it.
> Then it's not clear if your support for candidate A will allow them to defeat candidate C, but if it isn't, your defection in assigning the lowest possible score to candidate B would cause candidate C to defeat candidate B, which is to your own disadvantage.
Crucially, this is equally true for every other score I can assign to B less than the maximum. This reasoning does not argue for a vibe-based score assignment, it argues for giving the maximum score to both A and B. By assigning a lower score to either, I have already accepted some risk.
> It has less information content.
Less information on the ballot, yes, but it has the same effect on the outcome. Let's exclude cases where my vote is irrelevant. I have ten options, and nine of them are potential numbers of additional points that a candidate needs to win. Each of those numbers are roughly equally likely, because they are the least significant bits (least significant bits in stochastic processes tend to approximate a uniform distribution).
If I give 1 point, the candidate wins 0/9 times. If I give 10 points, the candidate wins 9/9 times. If I give 5 points, the candidate wins if the number of additional points needed is 2-5 (1 would make my vote irrelevant), and loses if it's 6-10. So, the effect on the outcome is the same as if I gave 10 points 4/9 times.
The only reason this would meaningfully increase the variance is if a large fraction of people in a small election were doing this, too small for the central limit theorem to work its magic but enough people doing it to exceed the difference in fixed preferences.
> This is essentially the argument that it's good to allow other people to make tactical errors, because it gives more power to those who do not make such errors.
You keep describing it as a tactical error to use a strategy that amounts to hedging. There are legitimate non-mistake reasons to do that.
> Or, perhaps, that I should take an approach that reduces the power of my vote on the basis that others might copy me.
You're not trying to get them to copy you, you're trying to devise a strategy that maximizes your advantage in the event that other people in exactly the same situation as you come to the same conclusion. In other words, knowing that people using the same reasoning as you will copy you, what reasoning do you choose to use?
> The reason is because it essentially ignores the problem of perverse incentives.
It isn't ignoring the problem, it's describing a solution to it: Enlightened self-interest.
Or to consider it another way, think of it as iterated prisoner's dilemma. You sure you want to make "defect" your first move when the aggregate outcome will be public and there will be future elections?
> My voting does not create a perverse incentive for anyone else, and in fact it only benefits me (by signaling that I do vote, so my vote is worth competing for).
Voting is a perverse incentive for you. It takes time to cast a vote, the chances of it determining the outcome are entirely negligible and so is any notion that the candidates will know, much less change their behavior, based on whether you as an individual cast a vote. It's why so many people stay home, and everyone who doesn't is spending their own time to do otherwise because they altruistically prefer that the system work than that they save the time it takes them to do something that yields no personal benefit.
> You are claiming that I'm not thinking probabilistically, but first off: you're providing an overly specific scenario rather than a probabilistic one. Second, your own overly specific scenario does not even work. If the extra 4 points that I give to B (over the "preferred outcome" strategy) is enough to result in B defeating C in scenario 2, it is also enough to result in A defeating B in scenario 1.
You're ignoring the probabilistic part. It's not scenario 1 and scenario 2 at the same time. You don't know if it's scenario 1 or scenario 2, that's the thing that's indeterminate, and you have to fill out your ballot not knowing that. Then if you assign 10/10 instead of 5/10 to candidate B and it turns out to be scenario 1, you've given the election to B over A. But if you assign 1/10 instead of 5/10 to candidate B and it turns out to be scenario 2, you've given the election to C over B. Neither of those are in your interest, so you have the personal incentive to reduce their probabilities by assigning candidate B a score in the middle of the range.
> If you're trying to prevent a C victory as your most important value, why not choose 6/10? 7? And so on.
Because that's a trade off. There is no single "most important value". You want both for A to score higher than B and for B to score higher than C. Assigning a lower score to B makes one of the things you want more likely and the other one less likely. If you judge them to be equally important and equally probable then you should assign B a score in the middle to hedge your bets. If you judge one to be more important or more likely then you should weight the score in proportion to how much of your vote you're willing to spend to make one possibility more likely at the expense of the other. Assigning the maximal or minimal score assumes that you prioritize one thing entirely at the expense of the other. It's putting all of your eggs in one basket.
> Crucially, this is equally true for every other score I can assign to B less than the maximum.
Except that you're trading each of those increments against the probability of the other thing you want.
> The only reason this would meaningfully increase the variance is if a large fraction of people in a small election were doing this, too small for the central limit theorem to work its magic but enough people doing it to exceed the difference in fixed preferences.
But why would you admit even this deficiency just to avoid allowing yourself to specify a score instead?
Also, what benefit is being achieved by forcing ordinary voters to choose their vote using random number generation instead of simply allowing them to write down the number they would have used as the threshold?
> It isn't ignoring the problem, it's describing a solution to it: Enlightened self-interest.
"Everybody just does the right thing" is not a solution you can implement in the real world.
> You keep describing it as a tactical error to use a strategy that amounts to hedging.
Maybe this is the source of the confusion: an intermediate score is not an optimal way to hedge. A hedge is a decision that offsets potential losses in the event of a bad outcome. No vote configuration on a single question can do that. It can, in some cases, reduce the chance of a bad outcome. In the best case, it does so by also reducing the chance of a good outcome (in favor of a moderate outcome). But crucually, each point affects each outcome in the same way as each other point.
So, by what rational reason am I choosing an intermediate value? Why would I prefer (in a contrived example, but all cases are linear) a 20% chance of both the good outcome and the bad outcome over both a 25% chance and a 15% chance? Moving from 4 points to 5 always does the same thing as moving from 5 to 6. It's linear, so the local maxima and minima are at the ends.
> There is no single "most important value".
You are making a linear probabilistic trade-off between two values. One of them must be more important than the other in order for any score assignment to be better than any other. Either being more important than the other will drive the score to one extreme.
> But why would you admit even this deficiency just to avoid allowing yourself to specify a score instead?
It's not something I want people to actually do. It's a reduction ad absurdum. Your approach does the same thing as a random approach, so - barring deception reasons - it must be a mistake.
2. a lot of people will do it REGARDLESS of whether it's rational, just like people donate to charity. so YOU as a rational self-interested voter BENEFIT by using a voting method which allows you to receive utility donations from those altruistic voters, however irrational they may be. and that leads to a greater NET utility, because voting isn't a zero sum game.
https://www.rangevoting.org/ShExpRes
again, it would really help you to just spend a few minutes reading elementary voting theory before going off on such a wild misguided tangent like this.
> 1. of course it is, if you're not mathematically savvy.
I don't think that says what you're claiming it does. If you actually look at the simulation linked from there (which I do take some issues with, but those are irrelevant to the point):
- Scaled sincerity, the one that gets their claimed 91% effectiveness, is actually one of the more mathematically complicated strategies to execute.
- Maxing + sincerity, the version of "mildly-optimized sincerity" that is least complicated to execute (and thus the one most likely to be executed intuitively), is among the least effective in large elections.
- Mean-based thresholding -- the closest approximation of my proposed strategies here, consistently outperforms all sincere-derived approaches in elections of 10+ participants. It is also simpler to execute than scaled sincerity.
> and that leads to a greater NET utility
This is not accounting for the reduced utility of increasing the complexity of the voting system, or of weakening the secret ballot by allowing more information content on it.
The latter is the real argument against score voting that I don't think has a counter. I haven't brought it up yet, because it's a lot less convincing if you believe that optimal individual strategy in score voting performs much better than optimal individual strategy in approval voting. But you, in particular, don't seem to believe that. So...
Score voting puts more information on the ballot than any other system, for an only marginal improvement over approval voting (which puts the second-least, after single vote). Putting more information on the ballot is bad, because it allows votes to be dis-aggregated. Attack description:
- Alice instructs Bob to fill out the ballot in a specific way. That specific way includes minor random perturbations of scores that are unlikely to influence the election result, but are likely to make Bob's ballot unique. E.g. selecting a random score for a candidate with a very low chance of victory, fully randomizing a question that Alice does not care about, or (worst case) adding or subtracting 1-5 percent from scores of relevant candidates.
- Alice observes the vote counting, and notes if Bob's ballot was observed.
- Alice rewards or punishes Bob accordingly
The value of the secret ballot is very high. I suggest that it is greater than any increase in utility achievable in the delta between score voting and approval voting.
tactical error is GOOD, because it donates more utility to society than that non-strategic voter loses. AND for a lot of not-so-math-savvy voters, an honest score ballot is actually a better vote than a botched attempt to use strategic approval thresholds.
Approval voting would result in “the okay-est” candidate winning rather than anyone towards an extreme winning in the primaries. Works well when there are a lot of fairly similar milquetoast candidates that split votes, like the Republican primaries of 2015.