Incoherent majorities: the McGarvey problem in judgement aggregation
`Judgement aggregation' is a model of social choice where the space of social alternatives is the set of consistent truth-valuations (`judgements') on a family of logically interconnected propositions. It is well-known that propositionwise majority voting can yield logically inconsistent judgements. In this paper authors show that, for a variety of spaces, propositionwise majority voting can yield any possible judgement. By considering the geometry of sub-polytopes of the Hamming cube, they also estimate the number of voters required to achieve all possible judgements. These results generalize the classic results of \textit{D. C. McGarvey} [Econometrica 21, 608--610 (1953)] and \textit{R. Stearns} [Am. Math. Mon. 66, 761--763 (1959; Zbl 0090.25101)].
scientific article; zbMATH DE number 5964687
scientific article