Stable winner set: Difference between revisions
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#The definition of V(X,Y) must be such that, if Y is a subset of X, V(X, Y) must be 0. That is to say: it does not make sense for voters to want to "block" a winner set because of how much they like a set of candidates who all won.
#The term "strictly prefer" can have various meanings:
##In the simplest model, voters have a certain quantity of "utility" for each candidate, and they strictly prefer set X over Y iff the sum of their utility for X is greater than the sum of their
##Another possible model is to restrict direct comparison to winner sets of the same size. Thus, when comparing sets of different sizes, we use the rule: a voter strictly prefers set X of size x over a set Y of size y, where x≤y, iff: there is no set Z of size y, where X⊆Z⊆X∪Y, such that they strictly prefer Z over Y. Using the same "utility sum" model as above, this would be equivalent to: they strictly prefer X over Y iff they strictly prefer X over any size-x subset of Y. For instance, they'd prefer the two "Greek" winners {Γ, Δ} over the three "Latin" winners {A, B, C} iff they prefer the two Greeks over any two of the Latins.
##Another possible variation is "voters strictly prefer a winner set iff they receive more of their preferred candidates, counting from the top."
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