Power of Voters and Domain of Preferences Where Voting by Committees Is Strategy-Proof

Abstract We study the preference domain where voting by committees of Barbera et al. (S. Barbera, H. Sonnenschein, and L. Zhou, Voting by committees, Econometrica 59 (1991), 595-609) is strategy-proof in an extended model. "Cross-shaped" preference is a generalization of separable preference of Barbera et al. We show that if a scheme of voting by committees without a dummy voter is strategy-proof on some rich domain, then any preference of a voter is cross-shaped on some set. The width of such set depends on his power. As a corollary, we have that the cross-shaped domain is the maximal one where voting by committees is strategy-proof except for "extreme" cases. Journal of Economic Literature Classification Numbers: C72, D71.