Is there any difference between ways of counting Borda?
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I've heard of three different ways to count Borda-like ballots
- "each one receives n – 1 points for a first preference, n – 2 for a second, and so on"
- "As Borda proposed the system, each candidate received one more point for each ballot cast than in tournament-style counting, eg. 4-3-2-1 instead of 3-2-1-0"
- Sum up the rankings themselves and elect the candidate with the lowest sum
I've always assumed these are exactly equivalent, and will always elect the same candidate with a given set of ballots, but I want to make sure I'm not missing something. Are they the same even in cases where incomplete rankings are allowed, and in cases where equal rankings are allowed?
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Well, it partly depends on what you do with equal ranks or incomplete ballots. If an unranked candidate is scored as 0 then a 4-3-2-1 system would be different from 3-2-1-0. But if it's done in a more sensible way, they would be equivalent.