Noncooperative Counter-threats to Vote Trading

It is demonstrated that whenever the first issue of a vote trade involves pivotal vote switching, vote trades can never be advantageous only for a minority if the members of the majority act individually to attain optimal benefits. Thus, contrary to conventional wisdom, a disorganized majority may be able to protect itself against an organized minority. The argument proceeds as follows. Optimal strategies are defined for each individual in the absence of cooperation. Such strategies are usually termed "sophisticated". A vote trade is then defined as a threat to this initial n-tuple of strategies. "Trade-sophisticated" strategies are then defined for each nontrader assuming that vote traders carry out their threat. Such strategies are noncooperatie and exist for all vote trades. It is shown that trade-sophisticated strategies may restore the sophisticated outcome or may even produce an outcome which a majority likes better. However, trade-sophisticated strategies may produce an outcome that is worse for a majority. In this case, if the first trade issue is pivotal, a member of the minority will also be worse off. Otherwise, the minority may be better off. In this last case, a counter-coalition would seem necessary to prevent a socially perverse result.