The well known result that every finite, strictly deterministic game with perfect information has a unique solution unless the utility functions of the players lie in a low dimensional exception space, is generalized to games containing change moves. Two group decision procedures, "voting by successive proposal and veto" and "voting by repeated veto," are analyzed in this context. The first procedure is efficient, anonymous, and neutral for an arbitrary number n of participants and an arbitrary finite set of alternatives, the second only if n @? 3.