Chris Smith
Jul 10, 2023

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That was a statement about a particular model of voters. You're right that Condorcet winners are unlikely "the closer it approaches impartial culture", but the IC model is not a realistic one.

It turns out that Condorcet winners remain very likely in all of the spatial models I considered: they appear with probability approaching 100% (with increasing number of voters) in uniform and single-Gaussian models, but the MoG models I ultimately settled on reduce that to about 97%. Without either adopting artificial and unrealistic assumptions like IC or dramatically reducing the number of voters, I don't ever see a really significant chance of lacking a Condorcet winner, though.

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Chris Smith
Chris Smith

Written by Chris Smith

Software engineer, volunteer K-12 math and computer science teacher, author of the CodeWorld platform, amateur ring theorist, and Haskell enthusiast.

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