= 27d567bc2d48d9f40e9ccc20ea370b15)
Sniffnoy comments on Democracy and rationality - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (47)
I'll certainly have more content that addresses these questions as the post develops. For now, I'll simply respond to your misunderstanding about Arrow. The problem is not that there will always be an a posteori pivotal voter, but that (to satisfy the other criteria) there must be an a priori dictator. In other words, you would get the same election result by literally throwing away all ballots but one without ever looking at them. This is clearly not democracy.
This is kind of late and not exactly on point, but I wanted to add in two points about Arrow's Theorem that I hope will help clarify things somewhat.
There is a generalization of Arrow's Theorem to the case where the set of voters may be infinite. In this more general case, the conclusion of the theorem (where here I'm considering the premises to be IIA and unanimity) is not that there must be a dictator, but rather that the voting system is given by an ultrafilter on the set of voters. That is to say, there exists an ultrafilter U on the set of voters such that the candidate elected is precisely the candidate such that the set of people voting for that candidate is large with respect to U. The fact that if there are only finitely many voters there must be a dictator then follows as any ultrafilter on a finite set is principal.
In a nephew/niece comment, homunq mentions sortition (select a voter at random to be dictator) as an example. I don't think this is correct? That is to say, Arrow's Theorem only applies to deterministic voting systems, and "dictatorship" refers to having a pre-specified dictator. There may be a generalization to nondeterministic systems for all I know, but if so, I don't think it's normally considered part of the theorem per se, and I don't think sortition is normally considered an example of dictatorship.