Stable winner set: Difference between revisions
→Example in which definition of "strictly prefers" matters: more complete.
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Under the above definition 4.1. of V(S,S'), the winner set {B, B, B, B, B} is strictly preferred by all voters over any other set of size 5 or less, so it is the unique stable winner set.
Under the above definition 4.2. of V(S,S'), the winner set {B, B, B, B, B} is not stable. For instance, the set {A, A, A} blocks it (or any other set without at least three As), because the first group of voters — over 3/5 of all voters — prefers {A, A, A} over any 3 candidates from {B, B, B, B, B}. Similarly, any set without at least one B is blocked by {B} because of the second group of voters. Thus, the only stable sets under this definition are {A, A, A, A, C}, {A, A, A, B, C}, and {A, A, A, C, C}.
Under the above definition 4.3. of V(S,S'), the situation is the same as for definition 4.2. (These definitions might still differ in more-complex situations. Since definition 4.3. has stronger criteria for "strictly prefer", the set of stable winner sets under 4.2. will be a non-strict subset of that for 4.3.)
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