Voting by Committees with exit
by
Dolors Berga
Universitat de Girona
Coauthors: Gustavo Bergantiños (Universidade de Vigo), Jordi Massó (Universitat Autònoma de Barcelona), Alejandro Neme (Universidad Nacional de San Luís)

Barberà, Sonnenschein, and Zhou (1991) consider a finite set of agents who originally form a club and who have to decide which candidates from a finite set will joint the club. The choice is done by means of a voting rule which associates a set of candidates to any preference profile of the founding members of the club. Barberà, Sonnenschein, and Zhou (1991) analyze this problem without the possibility of exit and they characterize Voting by Committees as the only strategy-proof voting rules whenever agents' preferences are separable.

In this paper we start from their problem and we are interested in introducing two different situations: the exit and the expulsion from the club of some founding members. The idea under exit is the following: imagine that some founder i does not like at all candidate k, however this candidate enters the club. Thus, founder i would prefer leaving rather than staying in the club. Our rule should allow founder i to exit the club after the entrance of k. The underlying idea under expulsion is that some coalition of founders may not like founder i after the entrance of candidate k, so they may want to expel him.

A recent work studying the social decision problem of choosing new members for a club in a dynamic framework is due to Barberà, Maschler, and Shalev (1999). They consider a fixed number of periods, a society and a set of candidates. At the beginning of each period, the society chooses a set of candidates to enter the club using voting by quota 1 (one vote is sufficient for admission). Because of the dynamics, they observe some strategic behavior of agents. In the paper, they characterize all Nash equilibria outcomes using pure strategies and they show Nash equilibria can also be obtained using Nash subgame perfection.

In another recent paper, Granot, Maschler, and Shalev (1999) study a similar dynamic problem of admitting members in a club and introducing the possibility of expulsion of the members in the society. They consider different possibilities to analyze expulsion: either simultaneously, before, or after the admission.

Our paper is different from these two works in two main things: first, we consider the general and standard framework of a social choice function defined on the domain of agents' preferences in order to analize its resistance to manipulations. We do not introduce any explicit dynamism as in Barberà, Maschler, and Shalev (1999). Second, we consider not only the expulsion of actual members of the club (as Granot, Maschler, and Shalev (1999) does), but also the possibility of exit of the founders.

More concretely, our target in this paper is to determine the class of strategy-proof social choice functions in the following three different situations. First, when founders can exit from the club although they can not expel their colleagues. Second, when we allow for both expulsion and voluntary exit. And third, when founders can expel their colleagues although they can not exit voluntarily (that is, there is some kind of slavery in the model).

Date received: April 27, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caez-71.