A note on balancedness and nonemptiness of the core in voting games (Q1123825)

\textit{J. Greenberg}'s result [Econometrica 47, 627-636 (1979; Zbl 0423.90007)] on the non-emptiness of the core of a majority game in \({\mathbb{R}}^ m\) is generalized to arbitrary voting games. More recently \textit{J. Greenberg} and \textit{Sh. Weber} [Int. J. Game Theory 13, 65-68 (1984; Zbl 0537.90004)] have shown that the majority game is balanced. In this paper, the author shows that this result cannot be generalized to arbitrary voting games.