Both DFC and DMC make use of the set P of all alternatives that pairwise defeat the alternatives that have greater approval. I would like to define another set which I will call BP consisting of all alternatives that have beat paths to every alternative with greater approval. In other words, alternative A is in BP iff for each alternative X with greater approval than A, there is a beat path from A to X. Of course P is a subset of BP, and BP will always include the entire Smith set, as well as the approval winner, and when the latter is a member of the Smith set, BP will be the Smith set itself. I suggest picking the winning alternative by random ballot from BP, rather than from P when there is serious potential for something like the 49 C 24 B (sincere B>A) 27 A>B scenario. Forest
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