Anti-Climacus

WEAK NASH EQUILIBRIA IN FIRST-PAST-THE-POST ELECTORAL SYSTEMS:

Okay, so, more of this McCain as a centrist candidate stuff. Sigh. Brendan discusses some here. Another thing that's occurred to me about this discussion:

There's a finding in game theory that you can get weak Nash equilibria for three-party (generally parliamentary) systems with a left, centrist, and right party: they're weak NE given that each party makes the best move given the moves the other sides make (rather than real mutual best responses). But this finding generally has two problems:

1. The parties, to get this result, have to be ideology-blind, that is, they have to move to wherever puts them in an NE, regardless of what stance that would require them to take. Even if you think McCain is "more centrist" than whomever the (as yet unchosen) republican and democrat will be, he's very, very unlikely to be in the dead center of the voting public.

2. Even if he was, he'd still lose. Consider it generally true that each party can claim 35-40% of the voting public as ID'd supporters or strong leaners: placing them on a spectrum (from 0-1, left to right), the Ds land at .35 and the Rs land at .65, and more or less evenly split the vote between them and McCain (at .5)*. So the Democrats get the .35 to their left plus half the .15 between them and McCain; the same for the Republicans, which makes for a final result of 42.5% of the vote going to each of the "extremist" parties and 15% for the "centrist" McCain. As you might suspect, this finding is quite robust, so the parties would have to be rather extreme before McCain can even get close to a plurality.

In other words, there's no reason to think a centrist candidate can win just because they're in the middle. McCain would have to peel off a lot more than just the independents or moderates to win, and affinities for Party ID being what they are, that's unlikely to happen.

*this is dependent on symmetric one-peaked preferences, except that McCain gets the same vote share no matter how preferences are distributed (so long as they're single-peaked)