### Majority decisions when abstention is possible

by Larson and Matteo and Shelah. [LrMaSh:965]

Discrete Math, 2012

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 [Sh:816], but here
we allow each voter to abstain. There are four cases.

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