= 27d567bc2d48d9f40e9ccc20ea370b15)
roystgnr comments on A Voting Puzzle, Some Political Science, and a Nerd Failure Mode - 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 (180)
The first Google hit I found for "plott 1967 majority vote" was a article with 44 reported citations beginning with the claim that Plott had established sufficient conditions for an equilibrium to exist but had then been repeatedly misinterpreted as having established necessary conditions. Is this the case?
Hmm. The article is technically correct but irrelevant. The case where necessity fails relies on three conditions: (1) the number of voters is even (2) the number of voters is small (3) at least one voter has their optimal preferences exactly identical to the proposed equilibrium; not merely 'very close' but exactly. All three (plus some additional, complicated conditions) must hold for Plott's conditions to be sufficient but not necessary.
(2) is obviously not a concern here, for nation-state electorates. (3) is implausible: just introduce a suitably fine-grained continuum of possible policies. If you still have an ideal voter at the equilibrium, it's not fine-grained enough.
On (3), in particular: in general, mainstream economics ignores degenerate cases in utilitarian analysis. That's why the additional conditions are not mentioned: it requires that of a (finite) number of voter ideal points, at least one of them must fall on the equilibrium. But in a multidimensional phase space, the set of equilibrium points is a set of measure zero! Why would you care about that case?
(3) is guaranteed, assuming that a politician running for office will vote for himself.