The Median Voter Theorem says that, given some reasonable assumptions, the candidate closest to the beliefs of the median voter will win. So if candidates are rational, they'll all end up at the same place on a one-dimensional political spectrum: the exact center.

Here's a simple argument for why this should be true: suppose the Democrats wisely choose a centrist platform, but the Republicans foolishly veer far-right:

https://www.astralcodexten.com/p/secrets-of-the-median-voter-theorem