Optimal voting rules for international organizations, with an application to the United Nations

• Published date: 01 December 2022
• Author: Johann Caro‐Burnett
• Date: 01 December 2022
• DOI: http://doi.org/10.1111/jpet.12607

Received: 6 April 2021

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Accepted: 9 July 2022

DOI: 10.1111/jpet.12607

ORIGINAL ARTICLE

Optimal voting rules for international

organizations, with an application to the

United Nations

Johann Caro‐Burnett

International Economic Development

Program, Hiroshima University,

Hiroshima, Japan

Correspondence

Johann Caro‐Burnett, International

Economic Development Program,

Hiroshima University, 1‐5‐1

Kagamiyama, Higashihiroshima,

Hiroshima 739‐8529, Japan.

Email: johanncb@hiroshima-u.ac.jp

Abstract

This paper studies a self‐enforcing mechanism for

an international organization that interacts repeat-

edly over time. A random shock determines which

countries would be in favor of or against taking a

collective action. If the organization wants to take

the action, incentives must be provided. The

optimal stationary equilibrium is equivalent to a

mechanism characterized by voting weights. When

the discount factor is not too high, the voting

weights are random. Moreover, within a class of

parameters, the optimal mechanism mimics the way

voting power is distributed among United Nations

members via Security Council seats. That is, the

model rationalizes the existence of a council with

permanent members who have veto power, non-

permanent members, and the exact number of

permanent and nonpermanent members observed

at the Security Council.

1|INTRODUCTION

The outcomes implemented by organizations depend, roughly speaking, on the members'

preferences and the decision‐making process. On the one hand, in economic theory, it is

common to assume that the preferences are exogenous. On the other hand, there is no

justification to make the same assumption for the decision‐making process. However, a large

J Public Econ Theory. 2022;24:1463–1501. wileyonlinelibrary.com/journal/jpet © 2022 Wiley Periodicals LLC.

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proportion of the literature, especially in political economy, regards the mechanism used to

aggregate preferences as exogenous.

1

This paper designs the decision‐making process for an international organization.

2

The

model uses a repeated game with three elements that international organizations typically

have. First, countries cannot rely on external enforcers. Thus, any set of rules they use must be

self‐enforcing. Second, members are heterogeneous; countries have large differences in, for

example, income, military power, and natural resources. Some countries have a stronger

opinion on global problems, and other countries are concerned primarily about their local

issues. Third, the organization cannot use or rely on monetary transfers.

3

Note that neither the

absence of transfers nor the perfectly and unrestricted use of them are realistic assumptions; in

practice, organizations would be somewhere in between those two cases. However, I want to

examine the provision of incentives purely by choosing the appropriate preference

aggregation rule.

The payoff‐maximizing equilibrium of the repeated game can be implemented via different

equivalent mechanisms, one of which is voting weights. These voting weights can be constant

over time or stochastic, depending on the discount factor. Constant voting weights implement

the Pareto‐efficient allocation when countries are very patient. Moreover, the heterogeneity of

the members' preferences allows for differences in the voting weights.

4

This first result

resembles some international organizations where members have different voting weights,

such as the World Bank or the European Union. Although a folk theorem is valuable, the

analysis focuses on parameter conditions that do not allow the efficient outcome to be

implemented.

Then, as a first step to show how rotation can be optimal in the United Nations Security Council,

Proposition 3shows that random voting power can implement the optimal equilibrium when

countries are not so patient. Moreover, to map more closely how randomness and rotation are

related, the model requires further structure. Therefore, Section 3characterizes the solution under

parameter conditions that mimic how the UN was created. Namely, the set of countries is divided

into two groups. One group is composed of the creators of the UN, which are called the “mechanism

designers.”They have a positive Pareto weight and (loosely speaking) a relatively higher cost of

1

See the discussion of the literature for examples of studies on endogenous voting systems.

2

Although the model could fit a broader class of organizations with similar characteristics, this study will focus the

exposition on international organizations for two reasons: First, the structure of the model fits most international

organizations, while it is more difficult to argue that the assumptions in this paper resemble other types of

organizations. Second, as it will be shown below, under certain parameter conditions, the results of the model closely

resemble how the United Nations (UN) distributes power among its members via Security Council seats; to the best of

my knowledge, there is no other theoretical model that rationalizes the UN's way of distributing power.

3

This third assumption may seem the most restrictive of those in this paper. However, there are many reasons to justify

the absence of transfers. First, transfers are, in general, not openly used (if used at all). For example, the United Nations

Charter does not mention monetary transfers between countries as a means of compensating affected countries. There

are studies (see, e.g., Kuziemko & Werker, 2006) showing that being elected as a nonpermanent member of the United

Nations Security Council is correlated with foreign aid. However, foreign aid usually entails several restrictions. For

instance, the resources may be targeted (e.g., towards health and education), or there could be implicit inefficiencies

(e.g., bureaucracy, corruption). Additionally, transfers do not necessarily solve the provision of incentives in a trivial

way. Any transfer has to be self‐enforcing itself, so countries have to be willing to comply with any transfer prescribed

by an equilibrium. This may introduce additional constraints, and as a consequence, it is beyond the scope of the

present study.

4

As shown in Maggi and Morelli (2006), with homogeneous members, a repeated game can only explain either

supermajority or unanimity as the optimal equilibrium.

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complying with the organization's demands.

5

The second group has zero Pareto weight and a

relatively lower cost of complying.

6

For a large range of discount factors, the optimal mechanism assigns voting power only to a

subset of countries, composed of both the mechanism designers and the zero Pareto weight

countries. This distribution of power depends on the profile of preference shocks and resembles

a council (Propositions 4–6). Moreover, as discussed in Corollary 1, there is a way to attain

uniformity in the council size, regardless of the current shock: that is, whether there is general

agreement or divided opinions.

7

This mechanism is remarkably similar to how the UN rotates

decision‐making power among the nonpermanent members of the Security Council.

8

1.1 |Related literature

The content of this study can be placed in three large categories. 2: (i) endogenous decision‐

making rules, (ii) voting weights, and (iii) the distribution of power on the United Nations

Security Council. Therefore, the discussion of the related literature is organized according to

those three categories.

The interpretation of an organization finding its own optimal set of rules is related to the

literature on endogenous decision‐making rules. Broadly speaking, some of them (including

the present paper) focus on welfare‐maximizing rules, and others focus on self‐selective rules.

The paper most related to the present study is Maggi and Morelli (2006). One key difference is

that here the members of the organization are heterogeneous. With this difference, it is possible

to explain why some organizations use different weights for their members (such as

the International Monetary Fund (IMF), World Bank, and European Union) and, more

important, why some other organizations have some form of randomness (implemented via

rotation) in their decision‐making power, such as the United Nations Security Council.

Another key difference is that Maggi and Morelli (2006) restrict attention to symmetric

equilibria.

9

In the present paper, it would not make sense to assume symmetric payoffs, since

countries are heterogeneous. Instead, payoffs are restricted to be stationary. Although in

principle this restriction may seem stronger, the reader should note that homogeneous players

plus symmetric equilibria implies stationary equilibrium payoffs when examining optimal

equilibria.

10

A final key difference from their study is that the decision variable can take values

on a continuous interval. This feature not only enriches the maximization problem but also has

interesting implications. Namely, this property can be seen as a compromise between countries.

That is, countries in favor prefer a “full implementation”of the collective action and countries

against prefer no implementation at all. Thus, a continuous decision variable that can take

5

Large countries, which are the P5, are more involved with global issues, so they have more to win or lose from the

decisions made by the organization. Thus, it is reasonable to assume that they have a “higher cost of compliance.”See

Lemma 3for details.

6

The zero Pareto weight is just a benchmark. The results in Section 3would still hold for “small”Pareto weights in the

second group.

7

The size of the council can actually mimic the 10 rotating members of the Security Council; see Remark 2.

8

There are studies that model coalitions in two‐stage voting games, which resemble a council (Acemoglu et al., 2012;

Eguia, 2011). Other literature discusses delegation of decision‐making power (Marino, 2007).

9

The same simplifying assumption is used in Athey and Bagwell (2001).

10

Specifically, any optimal equilibrium is payoff equivalent to a stationary payoffs equilibrium, as shown in Lemma 1of

Maggi and Morelli (2006).

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