There are three voters trying to elect a leader. If any one of them is elected leader, that person gets utility 1, and the other two get utility 0. However, there is also a third anarchy option where they have no leader. Anarchy is bad. Each person gets ε utility where 0<ε<13. Anarchy is the Condorcet winner, and thus maximal lotteries will choose anarchy with probability 1. This is dumb. Everyone would prefer to just randomly pick between the three candidates, which is what maximal lottery-lotteries does.
Whoa whoa whoa. This isn’t guaranteed. 0 utility is really bad! Like, if the winner gets to just torture me and my loved ones to death, I don’t want that to happen! I’d prefer anarchy than submitting to that with a 2/3rd probability! Part of the point of the election is that it should mean, ‘this kinda sucks, but I’ll get another chance to have my candidate win next time’. Any voting outcome which is worse than the alternative of ‘must fight an underdog rebellion’ should be expected to turn into an underdog rebellion. Underdog rebellion is worse for the group than anarchy (equal footing, no established leader), but still better than no utility at all. Or did you mean ‘gets 0 utility’ to mean a perfectly neutral state where things are neither positive or negative? That’s a very different and not to-my-mind default meaning.
It seems like an important feature of democracy that winners are in some sense partial, the condition is temporary and intended to have largely reversible effects where possible. This isn’t always the case, like Candidate A committing the country to a war that the other candidates wouldn’t have, but in many cases it is. If the laws passed by one regime are, in practice, found to be intolerable by a large minority, then reversing those laws will become a party ticket in the subsequent campaign.
Here’s another thought. Maybe voting method is less important than campaigning rules by a large margin. Maybe if campaigns were structured in such a way that important information about the relative competence and biases of the proposed candidates were exposed, the voting method would become mostly irrelevant. Forcing all the candidates to undergo public trials of their ability to do legislative decision making in realistic simulations, and then simply summarizing and publicizing their scores seems to me that it could do more to get better candidates elected. If a particular group thought they wanted candidate A, but then saw that actually candidate B’s decisions regularly resulted in much better outcomes for them in the simulations as well as for B’s base (because the world isn’t zero sum, and better decisions can be the tide which floats all boats)… Seems like the shift in favor of B would likely outweigh subtleties of voting methods around edge cases. If I had to pick between candidate-simulation-trials plus a random choice of voting method between <theoretically perfect method> / ranked choice / approval voting, or not have candidate-simulation-trials and be sure to get to use <theoretically perfect voting method>, I’d strongly prefer the option with simulation trials.
Whoa whoa whoa. This isn’t guaranteed. 0 utility is really bad! Like, if the winner gets to just torture me and my loved ones to death, I don’t want that to happen! I’d prefer anarchy than submitting to that with a 2/3rd probability! Part of the point of the election is that it should mean, ‘this kinda sucks, but I’ll get another chance to have my candidate win next time’. Any voting outcome which is worse than the alternative of ‘must fight an underdog rebellion’ should be expected to turn into an underdog rebellion. Underdog rebellion is worse for the group than anarchy (equal footing, no established leader), but still better than no utility at all. Or did you mean ‘gets 0 utility’ to mean a perfectly neutral state where things are neither positive or negative? That’s a very different and not to-my-mind default meaning.
It seems like an important feature of democracy that winners are in some sense partial, the condition is temporary and intended to have largely reversible effects where possible. This isn’t always the case, like Candidate A committing the country to a war that the other candidates wouldn’t have, but in many cases it is. If the laws passed by one regime are, in practice, found to be intolerable by a large minority, then reversing those laws will become a party ticket in the subsequent campaign.
Here’s another thought. Maybe voting method is less important than campaigning rules by a large margin. Maybe if campaigns were structured in such a way that important information about the relative competence and biases of the proposed candidates were exposed, the voting method would become mostly irrelevant. Forcing all the candidates to undergo public trials of their ability to do legislative decision making in realistic simulations, and then simply summarizing and publicizing their scores seems to me that it could do more to get better candidates elected. If a particular group thought they wanted candidate A, but then saw that actually candidate B’s decisions regularly resulted in much better outcomes for them in the simulations as well as for B’s base (because the world isn’t zero sum, and better decisions can be the tide which floats all boats)… Seems like the shift in favor of B would likely outweigh subtleties of voting methods around edge cases. If I had to pick between candidate-simulation-trials plus a random choice of voting method between <theoretically perfect method> / ranked choice / approval voting, or not have candidate-simulation-trials and be sure to get to use <theoretically perfect voting method>, I’d strongly prefer the option with simulation trials.