Talk:Ranked voting: Difference between revisions

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I would strongly advise us to remove this bit. It's confusing and mostly incorrect. Cardinal ballots are fundamentally different from ranked ballots, and interval scales are not the same thing as a ranking. Mathematically, cardinal ballots contain more information than ranked ballots and cannot be treated as subsets: the opposite is mathematically true ''under the assumption of transitivity''. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] is correct when they state both are subsets of a more general type of ballot which does pairwise comparisons. One can see cardinal ballots as marginals of such pairwise rating ballots, and ordinal ballots as a further discarding of information from cardinal ballots (again, if you assume transitivity). [[User:lucasvb|lucasvb]] ([[User_talk:lucasvb|talk]]} 14:14, 19 July 2020 (UTC)

: I agree that both ranked and Score ballots are subsets of the [[rated pairwise preference ballot]]. But further, an argument can be made that a Score ballot is equivalent to multiple fractional ranked ballots, though I don't have an issue with removing the piece you're against. Consider that a Score ballot A:5 B:4 C:3, on a scale of 0 to 5, is equivalent to 0.6 ABC Approval ballots (i.e. a Score ballot of A:3 B:3 C:3), 0.2 AB ballots, and 0.2 A ballots (see [[KP transform]]). And obviously, Approval ballots are ranked ballots where the approved candidates are ranked 1st, and the other candidates ranked last. So in some sense, ranked ballots really are a superset of Score ballots, when we make room for fractional ballots. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 16:00, 19 July 2020 (UTC)

== Conflation of ballot type and tabulation type ==