03 November 2008

A thought on expectation

Political campaigns should not campaign in such a way as to maximize their expected number of votes. Rather, they should campaign in such a way as to maximize their probability of winning.

Early in a campaign, these are pretty much the same thing, because one doesn't know how things are going to play out; late in a campaign they diverge. The candidate that's behind in the polls should, perhaps, start doing things that are, in expectation, Bad Ideas. If there were something that McCain could do that had a 1% chance of swinging 10% of the vote to him in the next 24 hours, and a 99% chance of scaring all the voters away, he should do it. (For example, let's say McCain turns out to secretly be an extraterrestrial; we probably don't want to be ruled by extraterrestrials, but who knows, we might change our mind? Of course, I'm being deliberately silly here.)

This is somewhat analogous to what happens in sports; strategies change late in a game. In the early innings of a baseball game you play, basically, in such a way as to maximize the difference between the expectation of your number of runs and your opponents' number of runs. In the late innings, when you have a better idea of how many runs you need, you change your strategies. See, for example, the bottom of the ninth inning of Game 3 of the World Series; tie game, bases loaded, nobody out. The Rays bring in one of their outfielders to create a fifth infielder; the idea is essentially that they want to maximize the probability of the Phillies scoring zero runs, and if the ball gets into the outfield a run is scoring anyway. (As it turns out, the Phillies won that game -- on a hit in the infield.) Of course, nobody saw that because it happened at two in the morning. Things are different when you're playing for one run.

Basically, what's happening as I write this is that Obama is running out the clock. (Yes, baseball doesn't have a clock. But Obama's a basketball player, so I think he'd like this metaphor.)

What politics and sports have in common, of course, is that there's a huge difference between second place and first place. If you're a company of some sort, does it matter if you sell 1% more or 1% less than your competitor? Not really, although it might have meaning for your pride. But if you're a politician, 1% of the vote makes a big difference.

1 comment:

Efrique said...

I sometimes give some heuristics to do with tactics in board games and hobby card games:

(i) Early in the game, maximize expectation of whatever it is that counts toward winning

(ii) In the endgame, maximize win probability

(iii) in between, if you're ahead, minimize variance at a given expectation, and if you're behind, maximize variance at a given expectation - this best applies when there's plenty of moves (enough that the distribution of your prospective position in the endgame can be fully described in terms of mean and variance - i.e. that the CLT "kicks in").

(iv) continuing on from (iii), there's a tradeoff between expectation and variance. If you're ahead, you will be prepared to give up a little expectation in order to get a substantial reduction in variance (to an extent that overall makes it more likely you remain in front by the end), and if you're behind, you will be prepared to give up a little expectation to get a substantial increase in variance (to an extent that makes it more likely that you will be in a position to have the best win probability at the end - which for many games means "nearly caught up by the end"). The degree to which you're willing to trade expectation for more or less variance starts near zero and generally gets larger as you approach the endgame. [But in any case, as soon as you can, switch to the probability calculations in (ii)]