Stable winner set: Difference between revisions
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B is the Score/Utilitarian winner and is stable under Hare but not Droop.
If all sets are blocked by at least one other set, it may still be possible to come up with the smallest set of sets that aren't blocked by any other sets, and consider this the core. This is analogous to the Schwartz Set.
Also, stable sets can have this "quota" computed based solely on voters who have preferences between any pair of sets that are being compared, so that in a 2-winner Approval Voting election with 67 A 33 B 10 C, the quota when looking at matchups between sets including either or both A and B is only computed off of at most the 100 voters that have preferences between them, rather than all 110. This would fix some but not all of the issues with this definition.
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Using Droop Quotas and this "only voters with preferences between the relevant sets are used to compute the quota" trick makes stable sets become a Smith-efficient Condorcet method in the single-winner case. However, use of the [[KP transform]] (most simply thought of as: convert scores into fractional approval ballots) appears to prevent this, and make stable sets include degree of preference.<ref>[https://forum.electionscience.org/t/the-concept-of-a-stable-winner-set/553/26?u=assetvotingadvocacy https://forum.electionscience.org/t/the-concept-of-a-stable-winner-set/553/26]</ref>
Interestingly, the two varying modes of deciding which set a voter prefers in each pairwise matchup (evaluate a voter's preference between sets as based either on, first whether they have a more-preferred candidate in one set and then second more of their more-preferred candidates in that set, or as being based on which set gives more utility), as well as the discussion over whether to use Droop Quotas vs. Hare Quotas within the formula, has already been
==Further Reading==
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