Comment by amalcon 7 months ago
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?
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.
just look at the VSE figures.
> 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.
yeah this is all explained here. score voting is even better than approval voting, obviously.
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.
http://scorevoting.net/RVstrat6
https://www.rangevoting.org/ShExpRes
> It is never correct to assign a score between the minimum and the maximum, so why allow it in the first place?
it would help you to spend at least 30 seconds researching a complex field like voting methods before asking a deeply misguided question like this.
> 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.