Optimal Voting Rules in International Organizations, with an Application to the United Nations

This dissertation examines the optimal self-enforcing voting mechanism for an international organization that interacts repeatedly over time. The study provides a theoretical explanation for some of the known voting systems of international organizations such as the World Bank, International Monetary Fund, European Union, and United Nations. The first part of this dissertation establishes the primitives of the model, provides examples, and finds the optimal equilibrium restricting attention to stationary payoffs. The three main assumptions of the model are that: (i) the decisions made at the organization must be self-enforcing, (ii) the members are ex-ante heterogeneous, and (iii) the organization cannot rely on monetary transfers. In every period, the members observe a random preference shock. This shock determines which members would agree with taking a collective action. Moreover, I assume that the preferences are common knowledge because I want to focus on the provision of incentives for taking the action rather than revealing preferences. I show that the optimal stationary equilibrium is equivalent to a weighted voting system that is repeated in every period.;On the second part, I keep the primitives of the model described on chapter one, but I remove the assumption that payoffs are stationary. When this assumption is removed, the optimal equilibrium has the following properties: when the members of the organization are very patient, the payoffs are stationary; when the members are moderately patient, the optimal equilibrium assigns voting weights that are history dependent and, in order to provide incentives, countries who disagreed yet complied with unfavorable actions should be rewarded with higher future decision power; finally, if the members are impatient, the best they can do is to follow the unanimity decision rule.;On the third part, I study the special case of the United Nations. Using the tools developed in chapters one and two, I explain why there could be a Security Council with permanent and rotating members. The existence of permanent members is a mixture of historical reasons and feasibility within the model. I provide a numerical example showing that this is the case. Moreover, the way members rotate in the Security Council could be rationalized by a structure that is similar to the most interesting equilibrium described in chapter two; that is, voting weights are history dependent. I find empirical evidence suggesting that compliance with unfavorable resolutions has a positive effect on the probability of getting a seat at the Security Council.