YouTuber "Physics for the Birds" on Voting
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@jack-waugh This seems to be a very abstract proof of something that doesn't even seem to be true - an ordinal voting system can't be continuous, respect anonymity and unanimity. At the end of the video he asks about an election (using FPTP) used to elect a pizza topping. He says he personally thinks the most likely condition to fail is continuity. He personally thinks? I mean, does it? I'd say that by any reasonable definition of continuity, FPTP doesn't fail. You don't get any weird jumps in the result after changing one vote, like you might do in a Condorcet method if e.g. a cycle suddenly appears or gets broken. You wouldn't get any discontinuities in the Borda count either.
Edit - Just looking at the comments, people are talking about how any change in a vote is a discrete jump so it's not continuous in that respect, but that much is obvious from the start.