Comment by AnthonyMouse

> 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?