User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
User:BetterVotingAdvocacy/Big page of ideas (view source)
Revision as of 20:04, 24 June 2020
, 4 years ago→Rated pairwise preference ballot
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It is possible to treat every pairwise matchup as being a [[Score voting]] match-up where the voter can score both candidates on a scale. In this sense, the traditional pairwise preference idea of a voter giving one vote to their preferred candidate in a match-up is akin to them giving the max score to that candidate, and a min score to the other candidate. This may make it easier to think about the rated support and pairwise support that are both allowed with the [[rated pairwise preference ballot]].
==== Transitivity ====
Though the most important transitivity requirements for rated pairwise are likely the ones based on margins (if 1st choice is 4 points better than 2nd choice, then they must be at least 4 points better than 3rd choice, etc.), it's also possible to require transitivity of score for a candidate across matchups i.e. if 1st choice was a 3 against the 2nd choice's 2, they can't then become a 2 against 3rd choice, even if 3rd choice would be scored at 1 or lower (which preserves the minimum transitive margin of 3-2=1 point).
Regarding transitivity, there are two ways it can be formulated. If a voter votes A>B at a 30% margin and B>C at 40%:
* The strongest matchup in the A>B>C chain is 40%, so the margin of A>C must be at least 40%.
* The matchups from A to C in A>B>C add up to 30%+40%=70%. So therefore, A>C must be at least 70%.
The justification for the first type of transitivity can be seen as follows: if the voter had indicated no preference between A and B, then logically A should have the same margin against every other candidate that B has against those candidates. Therefore, if B>C is 40%, then A>C has to be at least 40%. And since the voter evaluated A as being better than B, this can only strengthen this logic.
The justification for the second type of transitivity (which is based on Score voting) can be seen colloquially: if the voter indicates they "somewhat" prefer A to B, and "strongly" prefer B to C, then it'd seem that they ought to "very strongly" prefer A to C.
The use of the rated pairwise ballot may increase the likelihood of a transitive result (i.e. having a Condorcet winner) relative to the use of a ranked ballot in Condorcet methods.
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