ALBERT

Notes: Abstract This essay provides an explanation for the existence of stable logrolling arrangements. The model presented assumes that issues are voted on one at a time, that people are risk averse, and that each person forecasts future issue decisions with a random variable whose mean is linear in the alternatives of the present issue. We show that under this model, the expectation that logrolling will take place stabilizes the logrolling process. For this expectation to be stable, it must be symmetric, which means that revoting of issues must be possible. Since revoting is possible in institutions such as Congress, we conclude that an important set of real world voting bodies satisfies the conditions for stable logrolling.

Notes: Abstract In this paper, we construct a general probabilistic spatial theory of elections and examine sufficient conditions for equilibrium in two-candidate contests with expected vote-maximizing candidates. Given strict concavity of the candidate objective function, a unique equilibrium exists and the candidates adopt the same set of policy positions. Prospective uncertainty, reduced policy salience, degree of concavity of voter utility functions, some degree of centrality in the feasible set of policy locations, and restrictions on the dimensionality of the policy space are all stabilizing factors in two-candidate elections.

Notes: Abstract We build a model of two-candidate elections in which voters judge candidates on the basis of how well their announced campaign positions correspond with their records. Given different records, the candidates will adopt different campaign positions. Two types of reputational advantage are analyzed: proximity of the candidate's record to the median voter's ideal point, and the range of campaign positions that a candidate may adopt and still retain some credibility with the voters.

Notes: Abstract This paper presents a multicandidate spatial model of probabilistic voting in which voter utility functions contain a random element specific to each candidate. The model assumes no abstentions, sincere voting, and the maximization of expected vote by each candidate. We derive a sufficient condition for concavity of the candidate expected vote function with which the existence of equilibrium is related to the degree of voter uncertainty. We show that, under concavity, convergent equilibrium exists at a “minimum-sum point” at which total distances from all voter ideal points are minimized. We then discuss the location of convergent equilibrium for various measures of distance. In our examples, computer analysis indicates that non-convergent equilibria are only locally stable and disappear as voter uncertainty increases.

Notes: Conclusion 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.

Notes: Conclusion What do the preceding results tell us for democratic theory? First, that a majority can always defend itself against 2-issue special interest vote trades with a coalition no larger than that used by the minority. In terms of numbers counter-trades are no harder to organize than 2-issue special interest vote trades. Since we might expect that 2-issue vote trades are easier to organize than trades involving 3 or more issues, this result is encouraging. The author is currently conducting research on the incidence of various types of strategic voting in the U.S. Congress. This research indicates that voter agreements, when they can be identified, are usually quite simple. Thus 2-issue trades may be found to comprise the bulk of the vote trading that takes place in the Congress. If so, then in those cases the majority needs a coalition no larger than that used by the minority to block vote trades that are harmful to its interests. However, for special interest trades involving 3 or more issues, Figure 3 demonstrates that the size advantage may rest with the minority. If size is a major consideration in organizing vote trading coalitions, we should expect then that more of these trades will be successful than 2-issue special interest trades. Given the complexity of trades involving 3 or more issues, it seems reasonable to expect that in Congress such trades would usually be transacted at the staff or committee level. Special interest vote trading carried out at this level would then appear to be the most difficult kind to block. Thus trade size is both important for the theory of vote trading and may also be an important determinant of how vote trading is practiced.