Vote trading in a legislative context: An analysis of cooperative and noncooperative strategic voting

By way of conclusion we shall discuss the significance of our results for understanding legislative voting strategy. First, Theorem 1 establishes the minimal conditions for a set of sophisticated strategies to be vulnerable to a set of voters. It was argued that due to the form of this vulnerability some type of binding agreement is needed among the required set of voters to ensure that self-interested defections do not occur. This agreement consists of a plan by two or more voters to vote differently on two or more issues, assuming that other voters continue to use their sophisticated strategies. Such an agreement is defined as a vote trade, which in turn is clearly identified as a cooperative type of legislative voting strategy. Theorem 2 is our first result concerning the ability of individuals to restrict vote trading without themselves trading votes. It may be argued that due to the number of issues involved and their temporal proximity in the order of voting, 2-way consecutive trades might be expected to occur somewhat more frequently in the legislative process than trades that are more complex. If so, our result for all such trades that are minority-supported is quite important. What it establishes is that such trades will never occur if each individual who doesn't support this trade simply votes differently from the vote traders on the first issue of the trade. As indicated by our discussion of Figure 1, such behavior is all that trade-sophisticated voting requires and involves no coordination on the part of these voters. Each is acting in his own self-interest to forestall an outcome he dislikes. It is also a simple strategy to determine, not requiring a great deal of strategic acumen. Thus we have located an important class of vote trades that can be prevented by a simple type of individual voting strategy. Theorem 3 states a more general result about the efficacy of trade-sophisticated voting against minority-supported trades. It establishes that individually optimal voting by those who are not trading votes is sufficient to prevent any minority-supported trade from succeeding. It is obvious that no such trade can be immune to optimal voting by a coalition comprising those not in support of this trade. What is not obvious is that even if these same individuals fail to organize, individual self-interest alone provides sufficient incentive for them to block all or part of any such trade. For 2-way consecutive trades, of course, the entire trade is blocked. For other minority-supported trades only part of the trade may be blocked, as in Figure 2. Figure 2 raises an interesting possibility. If trade-sophisticated voting does not block a minority-supported vote trade entirely, perhaps it can dissuade some member of the vote trading coalition from joining it in the first place. One way this may be done is to produce an outcome by trade-sophisticated voting that is worse for that individual than the no-trade outcome. This is precisely what happens in Figure 2. Voter 5 is punished for his participation in the identified vote trade with voters 3 and 4, and so we expect this trade will not occur. No other trades exist for this example so we predict that no vote trading will occur. Theorem 4 generalizes this finding to all 3-way consecutive minority-supported trades for which a majority is worse off after trade-sophisticated voting than without vote trading. It establishes that for such trades, trade-sophisticated voting can always deter at least one of the vote traders from trading votes. Thus such trades, as well as 2-way consecutive minority-supported trades, can be expected never to occur. Individuals acting alone can either nullify or deter such trades simply by adopting an individually optimal response to them. It has been shown elsewhere (Enelow, 1978) that under certain conditions this result generalizes to a larger class of minority-supported vote trades. Our final result, Theorem 5, underscores the rationality of trade-sophisticated voting. It demonstrates that in cases where fewer than 5 issues are before the voting body, if trade-sophisticated voting cannot restore the no-trade outcome, some nontrader is better off than in the absence of trade. It is therefore irrational for him to cooperate to restore the no-trade outcome. Thus, while organization costs may prevent nontraders from adopting a joint strategy in response to a vote trade, individual rationality may also prevent them from doing so. What we have accomplished in this paper is to show that individual strategic voting can have considerable effect on a joint voting strategy adopted by a coalition. Such effects, if taken into account by a coalition, may convince its members to abandon their plan. It is not sufficient for vote traders to predicate their activities merely on the absence of other coalitions. To achieve their goal, it is also necessary to assess the consequences of trade-sophisticated voting. Minority-supported vote trades would appear to be strongly advantaged by an unorganized majority. Such is not the case. The individuals comprising this majority can exert considerable influence over such vote trading even when they themselves are completely unorganized. Copyright Martinus Nijhoff b.v 1979