Stability and voting by committees with exit

We study the problem of a society choosing a subset of new members from a finite set of candidates (as in Barberà et al. 1991). However, we explicitly consider the possibility that initial members of the society (founders) may want to leave it if they do not like the resulting new society. We show that, if founders have separable (or additive) preferences, the unique strategy-proof and stable social choice function satisfying founders sovereignty (on the set of candidates) is the one where candidates are chosen unanimously and no founder leaves the society.A previous version of this paper was entitled Voting by Committees with Exit. We are very grateful to the associate editor and two anonymous referees for their detailed suggestions and comments. We also thank Salvador Barberà, Carmen Beviá, Anna Bogomolnaia, Renan Goetz, Matthew Jackson, Howard Petith, Carmelo Rodríguez-Álvarez, James Schummer, and Tayfun Sönmez for their helpful comments and suggestions. The work of D. Berga, G. Bergantiños, and J. Massó is partially supported by Research Grants AGL2001-2333-C02-01, BEC2002–04102-C02-01, and BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología, respectively. The work of A. Neme is partially supported by Research Grant 319502 from the Universidad Nacional de San Luis. The work of D. Berga is also partially supported by Research Grant 9101100 from the Universitat de Girona. The work of G. Bergantiños is also partially supported by Research Grant PGIDT00PXI30001PN from the Xunta de Galicia. The work of J. Massó is also partially supported by Research Grant 2001SGR-00162 and the Barcelona Economics Program of CREA from the Generalitat de Catalunya. The paper was partially written while A. Neme was visiting the UAB under a sabbatical fellowship from the Generalitat de Catalunya.