Stability and voting by committees with exit

Abstract

We consider the problem of a society whose members have to choose an alternative from a given set of them. After knowing the chosen one, members may reconsider their membership to the society either by staying or by exiting it. In turn, and as a consequence of the exit of some of its members, other members might now find undesirable to belong to the society as well. We analyze the voting behavior of these members who take into account the effect of their votes not only on the chosen alternative, but also on the final composition of the society.