In this very interesting paper, the authors initiate an analysis of the evolution of groups, clubs or societies where at a number of fixed intervals, the current members of the group elect new members. In order to give some depth to this initial analysis, the authors impose some simplifying assumptions, among them a quota one rule (that any candidate may be admitted as the result of a single vote from a current member), that each player may vote for as many candidates as desired, and that there is a known utility (positive or negative) to each member of each candidate joining the society. The authors assume a finite number of election stages for the society, after which it is dissolved. This finiteness condition allows for a total utility to be assigned to each player for any sequence of membership by subsets of candidates. A further assumption is that no player leaves the society before the final stage. A crucial assumption is that `friendship' (i.e., positive utility) is not transitive. Electing a friend now may be against a player's best long-term interests if that `friend' will then elect enemies of the original player. Hence, the dynamic structure of the multi-stage games allows for the appearance of strategic considerations that would not be relevant in a single-stage game. The authors provide a number of examples illustrating some of these strategic issues under various assumptions, and analyze certain cases in greater depth. For these particular cases, the authors give a characterization of pure-strategy Nash equilibrium outcomes and also give a sufficient condition for the existence of a perfect equilibrium in a pure strategy. An example shows that this condition is not necessary. The authors give criteria for existence of pure strategy perfect equilibria for two stage games and indicate directions for further research.