Mathematics – Statistics Theory
Scientific paper
2010-07-04
Mathematics
Statistics Theory
11 pages
Scientific paper
The process of consensus voting, or decision making by unanimous agreement, has many distinct advantages: it fosters discussion and participation, empowers minorities and independent thinkers, and is more likely, after a decision has been made, to secure the participants' support for the chosen course of action. These considerations, among others, have lead many institutions to adopt consensus voting as a practical method of decision making. The disadvantage of consensus decision making is, of course, the difficulty of reaching consensus. While this challenge is largely overcome in many theoretical settings such as Aumann's "agree to disagree" result and its related literature, a hitherto unsolved difficulty is the lack of a framework offering rational (i.e., Bayesian) consensus decision making that can be performed using simple and efficient calculations. We study a stochastic model featuring a finite group of agents that have to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some indication as to which action is optimal. To come to a common decision, the participants perform repeated rounds of voting. In each round, each agent casts a vote in favor of one of the two courses of action, reflecting his or her current conditional probabilities, and observes the votes of the rest in order to calculate an updated conditional probability. We prove four results: - Consensus is always reached. - Each round of voting improves the aggregation of information. - The chance of a correct decision quickly approaches one as the number of agents increases. This is achieved already at the second round of voting. - Most importantly, we provide an efficient algorithm for the calculation the agents have to perform.
Mossel Elchanan
Tamuz Omer
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