Stable voting procedures for committees in economic environments

A strong representation of a committee, formalized as a simple game, on a c onvex and closed set of alternatives is a game form with the members of the committee as players such that (i) the winning coalitions of the simple ga me are exactly those coalitions, which can get any given alternative indepe ndent of the strategies of the complement, and (ii) for any profile of cont inuous and convex preferences, the resulting game has a strong Nash equilib rium. In the paper, it is investigated whether committees have representati ons on convex and compact subsets of R-m. This is shown to be the case if t here are vetoers; for committees with no vetoers the existence of strong re presentations depends on the structure of the alternative set as well as on that of the committee (its Nakamura- number). Thus, if A is strictly conve x, compact, and has smooth boundary, then no committee can have a strong re presentation on A. On the other hand, if A has non-smooth boundary, represe ntations may exist depending on the Nakamura-number (if it is at least 7). (C) 2001 Elsevier Science B.V. All rights reserved.