Stable winner set: Difference between revisions
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[[User:Jameson Quinn|Jameson Quinn]] has suggested the terms "sum-stable winner set" and "proportionally-stable winner set" for the stable winner sets under definitions 4.1 and 4.2 respectively.
==Limitations==
A set being in the core is not sufficient for "fairness". This can be seen in the following example<ref>https://www.cs.toronto.edu/~nisarg/papers/priceability.pdf</ref>
[[File:Core.jpg|none|left|Taken from https://www.cs.toronto.edu/~nisarg/papers/priceability.pdf]]
== Droop Version==
If the formula V(S,S′)/n >= K′/K is modified to instead be V(S,S′)/n >= K′/'''(K+1),''' (it may be appropriate to make it only a > rather than an >=, for reasons to be explained below), then this makes stable sets' definition of proportionality become more similar to other definitions of PR that use Droop [[Quota]]s (or more specifically, Hagenbach-Bischoff Quotas) rather than Hare [[Quota]]s, and begins to resemble a Condorcet PR method. <ref>{{Cite web|url=https://arxiv.org/abs/1701.08023|title=The Condorcet Principle for Multiwinner Elections: From Shortlisting to Proportionality|last=|first=|date=|website=|url-status=live|archive-url=|archive-date=|access-date=|quote=A size-k committee is locally stable in an election with n voters if there is no candidate c and no group of more than n/(k+1) voters such that each voter in this group prefers c to each committee member.}}</ref>
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