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Lumifer comments on A Voting Puzzle, Some Political Science, and a Nerd Failure Mode - Less Wrong
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Nope. Imagine an asymmetric voter distribution (just skewed is enough, we don't have to care about multimodal ones). If you stand at the mode, I'll choose to stand just to the side of you in the direction of the median and I'll get more votes.
There's the possibility that staking out a position too close to the mode (but not close enough to take those votes) will alienate a significant bloc of voters who will punish you by voting for someone else, or not at all. There's a threshold for a lot of voters where it doesn't matter that you're the "best available" candidate - for them it's like being asked to choose between a fatal dose of cyanide and one of arsenic. The fact that you're going to get one or the other is no incentive for complicity.
In reality the median-voter theorem sometimes works, sometimes doesn't work, and sometimes works partially. Reality is complicated and has a lot of extraneous forces and factors which are abstracted away in models. It's easy to construct plausible scenarios where the best strategies would be very very different.
You are right. Thanks for the correction.