## 04 November 2008

### Vote!

Scott Aaronson points out that the probability of your vote changing the results of the election scales like N-1/2, where N is the number of people. But the amount of change your vote creates, if it tips the election, scales like N. So the expected amount of change you will cause, by voting, scales like N1/2. That's a big number, so you should vote. If you live in a big country, you should vote more, although that's irrelevant; if any other country is voting today, the US media has ensured that I don't know that.

Of course, N1/2 seems a bit high, and it comes from modeling people as flips of a fair coin; Aaronson points out that under a more realistic prior (due to Andrew Gelman), the expected probability that your vote flips the election is N-1, so the expected amount of change your vote causes doesn't depend on the size of the country.

I won't "officially endorse" anybody. But one of the candidates in the present election trained as a lawyer, taught in a law school for a while, and likes to compare himself to a certain Senator from Illinois. That senator, in order to equip himself to understand the law better, studied Euclid. Being a mathematician, I think this is pretty cool. Who I'm voting for is left as an exercise for the reader.

CarlBrannen said...

If the election is so close that it is decided by just a few votes, then it should be clear that the two candidates are approximately equally acceptable.

Anonymous said...

That is not necessarily true. Let's say we had 100 voters and 51 preferred candidate A but thought candidate B was acceptable. The other 49 voters thought candidate A was unacceptable and thought B was acceptable (therefore voted for B). Now A would win 51-49, but 100% of the voters thought candidate B was acceptable while only 51% thought candidate A was.

CarlBrannen said...

"Acceptable" by my definition means that no group is so upset with the results of the election that they start a war over it.

In the US, about 98% of presidential elections are "acceptable", at least so far.

Kea said...

That wasn't close.

Joseph said...

If you want an intellectual President, you should remember that if the Republicans had done a little better in the 1998 elections, Professor Newt Gingrich would be finishing his second term.

Can I move to a different timeline?