### What majority decisions are possible

by Shelah. [Sh:816]

Discrete Math, 2009

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 bold 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,
bold c {x,y} is chosen by the preference of the majority of
voters. We give full characterization.

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