[gxyryosd] Identical candidates

A simple one-dimensional political model predicts that a candidate should choose a platform at the median voter of the political spectrum. If not, he or she will lose to another candidate closer to the median, if each voter chooses the candidate closer to them on the one dimension.

This should result in candidates with nearly identical platforms running against each other, as humorously depicted on an episode of Futurama ("A Head in the Polls").

But clearly this has not happened. Why?

One way to measure how different the voters perceive the candidates to be is to ask, how much would you need to be paid, as a proportion of your wealth, to vote for the other candidate?

The assumption of a one-dimensional political spectrum may be wrong.

Another possibility, vaguely, is that there exists a irreconcilable deep ideological divide in this country. This is troubling: we have already fought one civil war over that kind of divide.

Arrow's Theorem rears its ugly head when there is a lot of heterogeneity in individual preferences. Our social choice function might make some terrible choices.