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dimension10 comments on A Voting Puzzle, Some Political Science, and a Nerd Failure Mode - Less Wrong
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There's a solution I always thought of since young, that is instead of letting voters vote for a single candidate of their choice, let them assign each candidate a score and the representation will be defined by the total score of a party's candidates.
Perhaps it would be better to let voters rank the candidates instead, and assign each rank a well-defined score, if directly assigning a score is to arbitrary.
If, off the top of your head, you thought of a solution to a problem that's existed for hundreds of years and had lots of smart people look at it, it probably was thought up by someone else already and found wanting.
Ranking is subject to Arrow's impossibility theorem.
Having voters assign candidates a score is still covered by the Gibbert-Satterthwaite theorem.
According to Warren "Range Voting" Smith, Gibbard-Satterthwaite only applies when what voters provide is a ranking rather than a scoring.
[EDITED to put the link on a slightly better choice of words.]
Yeah, sorry, I don't know what I was thinking.