Algorithmic Asset Voting: Difference between revisions
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The use of the [[KP transform]] on rated ballots and then converting those Approval ballots to ranked ballots allows voters to submit, for example, a rated ballot A5 B4 C3, and have it treated either as 0.2 votes A>B, 0.2 votes B>C, and 0.4 votes A>C (score for preferred candidate minus score for less preferred candidate divided by max score yields the number of votes in each matchup) or 1 vote A>B, 1 vote B>C, 1 vote A>C.
Note that in a pairwise match-up between two winner sets, a third winner set can actually emerge as the winner. This is because some voters may prefer some candidates from one set and some from the other. For example, in a matchup between a set with only the majority's preferred candidates and another set with mostly candidates with almost no support, but one candidate whom a quota prefer, the final winner will actually be a new winner set where most of the candidates are the majority's preferred candidates and the final candidate is the quota's preferred candidate. Example: <blockquote>5-winner election:
51: Party A candidates
20: Party B candidates
20: Party C
9: split between random candidates, call them D, E, F, G
Winner set (5 A’s) vs. (B, D, E, F, G)
I’d argue that the winning winner set of the pairwise matchup here is actually (4 A’s, B). The B voters have enough votes to force B to be one of the top 5 candidates in a iterated cumulative voting election or an Asset negotiation, and no voters can force an improvement from their perspective from there.
Edit: To be clear no improvement based on the candidates in either set is possible. If we take (4 A’s, B) and compare it to all remaining candidates, it’s clear the C voters can force 1 C to be among the top 5 as well, and that would be the equilibrium outcome, so the final Condorcet PR winner set is 3-1-1 A-B-C.<ref>https://forum.electionscience.org/t/monroe-pr-doesnt-work-properly/528/9?u=assetvotingadvocacy</ref></blockquote>
== The multi-winner Smith Set and Smith-efficient cycle resolution ==
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