Stable winner set: Difference between revisions
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It can be argued that even though {C, D} doesn't include any voter's 1st choice candidate, whereas {A,B} includes a 1st choice candidate of every voter, {C,D} is a better solution because it maximizes all voters' satisfaction with the overall set of winners. In essence, 1 point of utility is lost when comparing a voter's favorite candidate in each set but 9 points are gained for their 2nd-favorite candidate in each set. This form of analysis has been done with Condorcet PR methods before, though not while also discussing cardinal utility:<blockquote>Lifting preferences from candidates to committees is achieved through what we call ''f''-preferences. A given voter has an ''f''-preference for one possible committee ''A'' over another, ''B'', if the voter prefers ''A'' to ''B'' when considering in each committee '''only''' the ''f'' candidates most preferred by that voter. For example, a voter has a 1-preference for committee ''A'' over committee ''B'' if the voter's favorite candidate in committee ''A'' is preferred by that voter over the voter's favorite candidate in committee ''B''. The voter has a 2-preference for committee ''A'' over committee ''B'' if the two favorite candidates on committee 1 are preferred over the two favorite candidates on committee ''B''.<ref name=":0">https://civs.cs.cornell.edu/proportional.html</ref></blockquote>Note that under the "voter prefers the set with more of their highest-preferred candidates" definition, {A,B} would be the stable set here. This definition makes stable sets appear to become more analogous to a Smith-efficient Condorcet PR method, such as [[Schulze STV]].
(It is possible to create various hybrids of the two definitions. One example is a voter being considered to prefer a set that offers them slightly less utility so long as it has a certain additional number of more-preferred candidates in it. So between one set where a voter gets their favorite candidate and 10 utility and another set where the voter gets their 2nd and 3rd favorite candidates and 11 utility, the former set could be considered preferred if the definition of "strictly prefer" added at least 1 or more points of utility to the voter's preference for the former set because it had a more-preferred candidate, the favorite, in it.)
=== Example in which definition of "strictly prefers" matters===
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== Droop Version==
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