Perspective Elections, information aggregation, and strategic voting

Elections have two distinct roles in society. First, they serve as a mechanism to decide policies when individuals disagree about appropriate actions. Second, they aggregate information dispersed in the population. This second role can be found even in situations where all individuals agree on the appropriate policies. The focus of this essay is on information aggregation in elections and on the incentives private information creates for strategic behavior by voters. As an illustration, consider a jury in a criminal trial. All jurors agree that the defendant should be convicted if guilty and acquitted if innocent. However, jurors may have different information about the guilt or innocence of the defendant. This informational difference may come about because each juror has a different area of expertise that allows her to evaluate some of the evidence more effectively. By voting, a jury may aggregate this information and collectively reach a better decision than any individual juror could. The idea of viewing elections as devices to aggregate information goes back to Condorcet (1) and has generated substantial literature (2–5). The basic insight of this literature may be summarized as follows. Assume that each juror votes to convict with probability PG if the defendant is guilty and with probability PI if the defendant is innocent and that, conditional on the guilt of the defendant, the behavior of jurors is independent. The assumption of independence captures the idea that jurors have private information that the election might aggregate. Let q be the fraction of voters required for conviction. If PG.q.PI, then under the rule requiring a q fraction to convict, a large jury will convict a guilty defendant and acquit an innocent one with probability close to one. However, if q.PG, then even large juries may acquit the guilty. Similarly, if q,PI then large juries may convict the innocent. For a general heterogeneous population, necessary and sufficient conditions for information aggregation are described in ref. 2. By changing q in the example above, we can change the frequency of each error. For example, requiring a supermajority to convict the defendant will reduce the probability of convicting an innocent individual. This model then provides a rationale for the requirement of unanimous jury verdicts as a rule that minimizes the probability of convicting innocent defendants (6). Recent work (7–9) has shown that the behavioral assumption at the foundation of Condorcet’s analysis, that voters will reveal their private information through their vote, is inconsistent with individual optimizing behavior. The following example illustrates this behavior.