Abstract
Following the results of Nakamura (1979) and Muto (1984), we derive, for a given proper voting game G, the upper bound on the size of the space of alternatives, which guarantees that the core constitutes a von Neumann-Morgenstern solution for any profile of voter's preferences. In particular, we show that if the space of alternatives consists of more than two elements, then, in general, the core is not a von Neumann-Morgenstern solution.
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