This post does not prove Maximal Lottery Lotteries exist. Instead, it redefines MLL to be equivalent to the Nash bargaining solution (in a way that is obscured by using the same language as the MLL proposal), and then claims that under the new definition MLL exist (because the Nash bargaining solution exists).
I like Nash bargaining, and I don’t like majoritarianism, but the MLL proposal is supposed to be a steelman of majoritarianism, and Nash bargaining is not only not MLL, but it is not even majoritarian. (If a majority of voters have the same favorite candidate, this is not sufficient to make this candidate win in the Nash bargaining solution.)
Dang. I wasn’t entirely sure whether you were firm on the definition of lottery-lottery dominance or if that was more speculative. I guess I wasn’t clear that MLLs were specifically meant to be “majoritarianism but better”? Given that you meant for it to be, this post sure doesn’t prove that they exist. You’re absolutely right that you can cook up electorates where the majority-favored candidate isn’t the Nash bargaining/Geometric MLL favored candidate.
This post does not prove Maximal Lottery Lotteries exist. Instead, it redefines MLL to be equivalent to the Nash bargaining solution (in a way that is obscured by using the same language as the MLL proposal), and then claims that under the new definition MLL exist (because the Nash bargaining solution exists).
I like Nash bargaining, and I don’t like majoritarianism, but the MLL proposal is supposed to be a steelman of majoritarianism, and Nash bargaining is not only not MLL, but it is not even majoritarian. (If a majority of voters have the same favorite candidate, this is not sufficient to make this candidate win in the Nash bargaining solution.)
Dang. I wasn’t entirely sure whether you were firm on the definition of lottery-lottery dominance or if that was more speculative. I guess I wasn’t clear that MLLs were specifically meant to be “majoritarianism but better”? Given that you meant for it to be, this post sure doesn’t prove that they exist. You’re absolutely right that you can cook up electorates where the majority-favored candidate isn’t the Nash bargaining/Geometric MLL favored candidate.