What Majority Decisions Are Possible Sh816
نویسنده
چکیده
Suppose we are given a family of choice functions on pairs from a given finite set (with at least three elements) closed under permutations of the given set. The set is considered the set of alternatives (say candidates for an office). The question is, what are the choice functions c on pairs of this set of the following form: for some (finite) family of “voters”, each having a preference, i.e., a choice from each pair from the given family, c{x, y} is chosen by the preference of the majority of voters. We give full characterization. Partially supported by the United States-Israel Binational Science Foundation I would like to thank Alice Leonhardt for the beautiful typing. First Typed 03/July/1, first version [Sh:E37] in Jan. 2003 Latest Revision 08/Sept/25 Typeset by AMS-TEX 1
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What Majority Decisions Are Possible with Possible Abstaining
Suppose we are given a family of choice functions on pairs from a given finite set. The set is considered as a set of alternatives (say candidates for an office) and the functions as potential “voters.” The question is, what choice functions agree, on every pair, with the majority of some finite subfamily of the voters? For the problem as stated, a complete characterization was given in Shelah ...
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