The capacity of a committee (Q1085023)

It is known that under moderate requirements of strategy-proofness, a committee is in general incapable of choosing by vote if the set of alternatives is too big. This led \textit{B. Peleg} [Int. J. Game Theory 7, 81-94 (1978; Zbl 0391.90007)] to introduce the notion of the capacity of a committee. It is shown here how this number is determined by the combinatorial structure of the committee. The general criteria are quite complex, but they are somewhat simplified by a homogeneity assumption, and they reduce to a simple arithmetical formula for symmetric committees.