What majority decisions are possible with possible abstaining

Details What majority decisions are possible with possible abstaining What majority decisions are possible with possible abstaining

2010-03-14

arxiv.org/abs/1003.2756v1

Mathematics

Combinatorics

23 pages

Scientific paper

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 \citet{shelah2009mdp}, but here we allow each voter to abstain. There are four cases.

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