基于可识别信息的集体决策机制有效性的研究——策略性投票、审议与表决规则

Examining the efficiency of a collective decision-making process with verifiable information: Strategic voting, deliberation and voting rules

投票一直以来是集体决策理论的重要研究对象。本文从博弈论的角度出发,分析一个有二元备选项的集体决策问题,并允许集体成员在投票前互相交流其可能获得的关于备选项优劣的信息,这一交流过程被称为审议。本文假定信息是可识别的,集体成员至多只能选择隐瞒而不能撒谎。本文通过考察不同投票规则下集体决策的结果以研究不同决策机制的效率。理论结果表明,多数表决的投票规则可以引导信息被充分披露的均衡存在从而使得集体决策的结果有效,而一致表决的投票规则不能做到,因此多数表决比一致表决在引导成员说真话的意义上表现得更好。此外,当信息被部分披露时,本文通过构造一类偏见驱动的审议均衡证明了集体决策的结果在一致表决下有时反而更好,因此多数表决并不总是优于一致表决。本文为一致表决的实际存在提供了理论解释,并指出集体决策的结果依赖于表决规则与具体的均衡路径,盲目地选择少数服从多数往往会导致低效的选择结果。

A key assumption of the Condorcet Jury Theorem(1785) is that individuals behave sincerely. That is, individuals will behave in the same manner when they alone decide the outcome or when they are part of a committee where members jointly make a decision. However, several articles have demonstrated that it is not always rational for individuals to vote sincerely. In fact, a strategic voter should vote based on the event where she is pivotal, i.e., her decision will unilaterally decide the outcome. Conditional on that event, voters can infer extra information about the realization of the payoff-relevant information and will thus choose their best response based on that inference. The literature on deliberation has examined situations where voters are able to communicate before voting. In real life, committee members often have an opportunity to communicate with each other in exchange for opinions. Indeed, over the past few years, there has been a growing literature that aims to better understand how communication affects the efficiency of collective decision-making processes. Knowing the efficiency of different institutional forms of collective decision-making processes is essential for the formulation of public policies.We study a basic jury framework with preference uncertainty and incomplete information from a game theory perspective. Following the introduction, the first section of the paper presents the model. Specifically, a three-person jury is going to choose whether to acquit or convict a defendant of being guilty or innocent. Each jury member has access to incomplete information regarding the true state of the defendant(guilty or innocent). Jury members also hold different attitudes towards the threshold of convicting. They may differ in opinions about the culpability of the defendant, but they all value making the right choice, i.e. convicting the guilty or acquitting the innocent. After all jurors observe their private information, there is a communication stage where all jurors share their information regarding the true state. After all reports have been made, all jurors simultaneously vote following a given voting rule and the outcome is realized. This study departs from the existing literature in two aspects. First, we assume that information is verifiable. Informed jurors can choose to conceal information but they cannot lie, while uninformed jurors have no choice but to reveal their ignorance. Consequently, informative reports can be verified immediately, while no further inference can be made from uninformative reports. Secondly, by using a proper criterion that is defined to compare different institutional forms of collective decision-making processes, we analyze both majority and unanimity rules. The central question we seek to answer is conditional on verifiable information, does a collective decision-making process under majority rule always outperform a process under unanimity rule?In the second section, we compare equilibrium properties under majority rule and unanimity rule, paying attention to the character of communication in the collective decision-making process and the quality of decision in each instance. We first provide necessary conditions under which majority rule can induce all individuals to truthfully reveal their signals, then we demonstrate that such efficient result will never happen under unanimity rule. Moreover, we explore bias-driven equilibria where only partial information is credibly revealed. Our study shows that, in some cases, voters in a collective decision-making process with communication under unanimity rule can select the correct alternative that exhibits full information equivalence, while voters in a process under majority rule select the wrong alternative. In some other cases, however, the reverse is true. In the third section we provide some comparative static analysis on the conditions under which the equilibrium in which the jurors reveal the truth, in order to better understand the role of pivotality.The last section summarizes our results and concludes. Two main conclusions can be derived from our results. First, as we show that the equilibrium exhibiting full information equivalence can be achieved only under the majority rule, it is reasonable to conclude that the majority rule performs better than the unanimity rule in the sense of inducing all jurors to reveal the truth. Second, the previous argument does not imply that majority rule outperforms unanimity rule in all cases. Our study also shows that the unanimity rule sometimes makes correct choices while the majority rule cannot result in correct choices when only partial information is revealed during deliberation. Therefore, despite the fact that the majority rule is ubiquitous, unanimity is also reasonable in many cases, and this research provides some explanations for the existence of unanimity rule itself. Finally, we provide some insights for policy-makers. For example, the government could be more careful when choosing the proper rule to aggregate individuals′ opinions on some policies. In summary, this paper contributes to the deliberation literature by showing the fundamental impact of the communication process and different voting rules on collective choice theory.