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. We 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, we also estimate the number of voters required to achieve all possible judgements. These results generalize the classic results of McGarvey (1953) and Stearns (1959).
|Date of creation:||10 May 2010|
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- Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
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