Information and Institutions Redux

Abstract

In “Information and Institutions Revisited,” Fey et al. point out some corrections to the equilibrium analyzed in Chapman. In this brief response, we argue that while these corrections are appropriate, they do not address the larger substantive question of when conditions exist that would facilitate information transmission between an international security organization and a domestic audience. We show an equilibrium in which the core logic of the information transmission argument in Chapman remains. We also discuss the particular modeling choices that facilitate information transmission (or prevent it) in equilibrium.

Keywords

international institutions domestic politics information transmission

In “Information and Institutions Revisited,” Fey, Jo, and Kenkel (hereafter, FJK) point out some corrections to the equilibrium analysis in the article “International Security Institutions, Domestic Politics, and Institutional Legitimacy (Chapman 2007).” In particular, FJK argue that the original analysis in this article did not properly take into account belief updating and the presence of profitable deviations in some of the purported equilibria and then conclude that their reanalysis casts doubt on the empirical implications of the model. We appreciate the close consideration FJK have given to this article. However, as we show in what follows, their critique, while entirely appropriate of the particular analysis in question, fails to investigate whether equilibria with the same substantive lessons as the misidentified equilibria exist. We show that such equilibrium exist for areas of the parameter space that are relevant for real-world examples.

We further argue that in focusing on a limited reanalysis of a very specific extensive form game, FJK neglect one important purpose of formal modeling, namely, providing a theoretical explanation for observed empirical phenomena (cf. Clarke and Primo 2012, 13-15, 90-92). In this case, the phenomena is the tendency, as revealed by public opinion polling and analysis, of the US public and audiences in many other countries to prefer United Nations (UN) Security Council authorization over other forms of multilateral authorization for military action, as well as the tendency of the US public to sometimes discount UN Security Council opposition. One candidate explanation for this tendency is that the ordinary citizen may respond in different ways to new information presented by a third party with some private information. In particular, the reaction of an uninformed audience to decisions by International Organization (IO) member states can be conditional on the audience’s perceptions of the motives of those states. This explanation suggests that when audiences are worried about the expense of foreign policy proposals relative to the status quo, and also think that member states are unlikely to sanction policies that deviate exceedingly far from the status quo, supportive votes from those member states may increase audiences’ confidence that foreign policy proposals fall within a range that they also find acceptable. However, if these audiences believe their preferences over various foreign policy options are closer to their own leader’s (or the government initiating the policy proposals) than they are to foreign governments who are reluctant to authorize policy proposals that diverge from the status quo, opposition may do little to deter audience support.

This explanation is rooted in standard ideas from game theoretic literature. Namely, in a conventional principle–agent context in which an agent possesses private information and can issue a cheap talk signal about that information to its principal, the presence of both truth-telling and partial information revelation depends on the degree of preference alignment between the principal and agent.¹ If one extends this logic to the relationship between a citizen, a government, and a third-party actor, where the government and third party have access to some private information, it follows from an application of these basic ideas that the degree of preference convergence between the citizen and the two potential sources of information can influence how citizens update their beliefs and make choices about supporting policies.

We also argue that FJK’s conclusion about empirical implications does not follow from the argument and analysis they present in the article. This is because the presence of a nonunique uninformative equilibrium in an information transmission game does not necessarily imply that informative equilibria do not exist or that they do not have important implications for empirical analysis. In fact, it is quite unsurprising that FJK find uninformative equilibria when the parameter space is restricted to one in which the IO member would rather vote for policies that it does not prefer to the status quo in order to avoid not having to implement costly opposition. Later, we argue that substantively, it is more accurate to think of voting behavior as expressing some preferences about the policy, and any signaling of intent to impose costs on the proposing state is largely secondary. Thus, while FJK have identified some mistakes in the analysis of a particular extensive form game, the claim in their conclusion that we should doubt empirical implications about perceived preference distance between audiences, IO members, and leaders only follows if we have cause to select particular equilibria over others for generating empirical hypotheses. As we show, there are equilibria (as FJK acknowledge there may be) in which the possibility of an audience updating its prior beliefs depends on the preference ordering of the audience, the leader, and the IO member. As a result, we remain confident that for many conditions the information tranmission argument is a viable candidate for empirical exploration.²

Of course, models are not true or false, only more or less useful. To the extent that simpler models of information transmission can be applied to the substantive phenomena in question, yielding the same general insights as the original analysis, we should also retain confidence that preference similarity between an IO like the UN Security Council and a domestic audience influences how that audience reacts to IO decisions. The idea that the preference similarity between a sender and a receiver determines the possibility of information transmission is not new and has been applied across an array of signaling models.

In the following pages, we identify an equilibrium that leads to the same substantive insights as the those analyzed in “International Security Institutions, Domestic Politics, and Institutional Legitimacy.” We motivate and discuss this equilibrium and then conclude with some thoughts on the larger substantive questions surrounding this debate.

Model and Substantive Motivation

As FJK reintroduce, the model in question has the following sequence: nature selects a policy, x on the interval between 0 and 1, which a leader (L) can choose to propose unilaterally, multilaterally, or not at all.³ The status quo, or no action, is assumed to be at 0. If the leader chooses to propose the policy through multilateral channels, the pivotal member of an IO (V) can choose to signal support or opposition, a domestic audience (D) can choose support or opposition for their leader, the leader chooses whether or not to implement the policy, and the pivotal IO member decides whether or not to implement obstruction. Utilities for each actor are given by quadratic loss functions of the form $- {(x - x_{i})}^{2}$ , where $x_{i} \in [0, 1]$ is actor i’s ideal policy. The value of x is private information to V and L, but D has prior beliefs over its location that are distributed uniformly over the interval [0, 1]. The motivation for this assumption is that governments often possess private information about the likely outcomes of foreign policies.

FJK’s critique arises because of the cost structure built into the original extensive form game. Namely, L pays a cost, σ, for implementing a policy that the audience opposes. D pays a cost, λ, for policies that receive active obstruction from abroad. The pivotal IO member, V, pays a cost, γ, for implementing obstruction, but also pays a cost, δ, for voting in opposition to the policy but not for implementing obstruction. This modeling choice has the unfortunate effect of turning the model into one about the credibility of the IO member’s threat of imposing costs on the domestic audience, in addition to a model about transmitting information about likely policy merits and consequences. This choice thus generates equilibrium behavior in which L, knowing that it can “force the hand” of the pivotal member by committing to implementation of the policy regardless of V’s signal, always implements the proposed policy and the pivotal member has no choice but to signal support in order to avoid the political cost of voicing opposition and not implementing active obstruction. In turn, the audience does not update its beliefs in accordance with a standard information transmission logic.

We argue that such perverse behavior—voting for policies that V does not like in order to avoid political costs for failing to mount costly obstruction—is not a substantively accurate depiction of most empirical cases of member state behavior within IOs. We can examine several examples of vetoing behavior on the UN Security Council to see why this is so. First, consider the very public signals of opposition by France, then by Russia and China, in early 2003 to a proposed draft Security Council resolution to authorize the 2003 Iraq War. European public opinion was largely antiwar at the time, and the French government likely opposed the war both for domestic political and for substantive foreign policy reasons. France did not form an alliance with Iraq, attack the United States, propose economic sanctions on the United States, or otherwise engage in foreign policy to actively stop the US invasion and prosecution of the war (beyond simply not contributing troops) after the war proceeded. Yet, there is little evidence to suggest that the French government suffered reputational costs for signaling opposition but failing to raise the costs of the war.⁴ In fact, it may have received a political boost domestically by signaling opposition to perceived US unilateralism and overreach, even if there was little expectation of direct obstruction that would raise the costs of war directly for the United States.⁵ It is also difficult to imagine that the French government could have been swayed to support the war in order to avoid the appearance of opposing the war in principle but not taking further obstructionist efforts in practice.

Likewise, during the cold war, Soviet and US vetoes of each others’ resolutions were meant primarily to signal disapproval of policies, as opposed to threats to attack one another for behaving in a way contrary to one anothers’ interests. This was a relatively low stakes way of publicly signaling disapproval of an adversary’s policies in an era of high tension and may have also served as a public attempt at influencing attitudes around the world.

In short, there is simply no strong substantive reason to believe that votes in a multilateral forum like the UN Security Council are about the credibility of governments’ threats to impose costs on one another. Rather, as others have argued, they serve as a signal that might affect global or domestic attitudes and thus impose costs indirectly by influencing other actors' behavior through the information they convey (cf. Voeten 2005; Thompson 2006, 2009; Hurd 2007).⁶

In the equilibrium we analyze next, therefore, we focus on a situation in which δ = 0, which allows the pivotal member to voice opposition even if they do not intend to expend scarce resources to implement material obstruction to the policy. We believe such a situation is substantively accurate across a large range of cases and, importantly, creates a strategic environment that is fundamental to explaining why votes in a body like the Security Council might influence public attitudes about war.

Equilibrium

Let $x_{V} < x_{D} < x_{L}$ and δ = 0.

S_D : In the multilateral subgame, D supports if V supports. If V does not support in the multilateral game or L proposes unilaterally, then D does the following: when $σ \geq 4 x_{V} (x_{L} - x_{V})$ D supports if $x_{D} \geq x_{D}^{'}$ and opposes if $x_{D} < x_{D}^{'}$ , when $σ < 4 x_{V} (x_{L} - x_{V})$ D supports if $x_{D} \geq x_{D}^{''}$ and opposes if $x_{D} < x_{D}^{''}$ .⁷

Beliefs for D: If L proposes multilaterally and the IO supports, then D believes that x ∼ Unif(0, 2x_V ). If L proposes multilaterally and the IO opposes, D believes x ∼ Unif(2x_V , 2x_L ). If L chooses status quo, then D believes x ∼ Unif(2x_L , 1). If L proposes unilaterally D believes x ∼ Unif(2x_V , 2x_L ).

S_V : If $x \leq 2 x_{V}$ , V signals support and does not implement obstruction. If $x > 2 x_{v}$ then V signals opposition and does not obstruct.

S_L : If $x \geq 2 x_{L}$ , then L chooses status quo. If $x < 2 x_{L}$ , L proposes multilaterally. If $x \in (x_{L} - \sqrt{x_{L}^{2} - σ}, x_{L} + \sqrt{x_{L}^{2} - σ})$ or D supports, then L implements. Otherwise, L does not implement.

In this equilibrium, the audience supports the policy if the IO supports the policy and may support or oppose otherwise, depending on its ideal point relative to the leader and pivotal member. When the leader prefers the policy to the status quo, the leader proposes the policy multilaterally and implements the policy only if the audience supports the policy or it is in the interval in which it prefers to implement even though it will suffer a cost for doing so with domestic opposition. The pivotal member signals support if $x \leq 2 x_{V}$ , but signals opposition otherwise and never implements costly obstruction.⁸ A full proof is in the Appendix, but to motivate this equilibrium, here we walk through the basic dynamics driving actors’ decisions.

First, consider the constraints on actors moving at information sets that are singletons. In the multilateral subgame, having signaled support, the pivotal member will not implement obstruction if

- {(x - x_{V})}^{2} \geq - {(x - x_{V})}^{2} - γ .

This is true by construction. In the unilateral subgame, the same constraint applies at the final node.

If it has signaled opposition, the pivotal member will implement obstruction only if

- {(x - x_{V})}^{2} - γ \geq - {(x - x_{V})}^{2} - δ,

which is never true in this equilibrium as long as δ = 0 and λ > 0.

Next, conditional on audience support, the leader will implement the policy with audience support if

\begin{matrix} - {(x - x_{L})}^{2} \geq - {(0 - x_{L})}^{2} \\ x \leq 2 x_{L} \end{matrix} .

The leader will implement the policy with audience opposition when

\begin{matrix} - {(x - x_{L})}^{2} - σ \geq - {(0 - x_{L})}^{2} \end{matrix} .

Next, consider the audience’s decision, which now involves beliefs over the true value of x. We denote the audience’s Bayesian belief over x as $\hat{x}$ . The audience believes that the leader prefers the status quo to implementing the policy with public opposition, and prefers the policy with public support above all, when the following is met:

\begin{matrix} - {(\hat{x} - x_{L})}^{2} - σ < - {(0 - x_{L})}^{2} < - {(\hat{x} - x_{L})}^{2} \end{matrix} .

The audience itself believes that it prefers the status quo to the policy when the following is met:

\begin{matrix} - {(\hat{x} - x_{D})}^{2} \geq - {(0 - x_{D})}^{2} \end{matrix} .

What actions support such beliefs? Recall that the audience has uniform priors over the ultimate location of the policy, x. In this equilibrium, the audience has two opportunities to update its beliefs. First, the audience sees the leader propose the policy multilaterally. Second, the audience sees the IO’s signal. We show in the Appendix that the leader proposes the policy multilaterally when the IO member is expected to signal support. When the IO member is expected to oppose the policy, it is weakly dominant for the leader to propose the policy multilaterally and the leader may sometimes implement the policy despite opposition depending on the costliness of domestic opposition σ. This slightly complicates the belief updating for the audience as we show in the Appendix. However, the condition for the IO member to issue a signal of support depends primarily on its policy preferences, given the constraints on δ and γ earlier:

\begin{matrix} - {(x - x_{V})}^{2} \geq - {(0 - x_{V})}^{2} \end{matrix} .

Given this, a signal of IO support allows the audience to update its beliefs that $x \leq 2 x_{V}$ , which implies that $x < 2 x_{D}$ (since $0 < x_{V} < x_{D}$ ). If the IO opposes, the audience updates its beliefs that $2 x_{V} < x \leq 2 x_{L}$ , since the leader does not propose policies it prefers to the stuats quo and the IO member does not support policies it prefers to the status quo. In such a case, the audience is not able to learn with certainty that the policy is one it prefers to the status quo and the threshold for which it will support the policy despite IO opposition depends on its relative preference affinity with its own leader and the IO member.⁹ Generally, speaking, holding the audience’s ideal point constant, the audience is more likely to support the policy even with IO opposition as the IO’s ideal point moves closer to the status quo and as the leader’s ideal point moves closer to the audience’s own.

To recap, in this equilibrium, the leader proposes the policy multilaterally, the IO member signals support or opposition conditional on the location of the proposal relative to its ideal point, and the audience supports the policy in the event of IO support and may or may not support the policy in the event of IO opposition. Hence, the core substantive implications of the information transmission approach are supported: the audience reaction is conditional on relative preference ordering and preference distance, and IO support can spur audience support while IO opposition may only sometimes spur audience opposition. The one substantive modification necessary for such an equilibrium to hold is that cost conditions have to be set such that the IO member is free to signal opposition without suffering a political cost for failing to carry through with direct, material, costly obstruction. We believe this is a substantively appropriate modification that helps us analyze how voting and position taking with international organizations might influence outside audiences.

Discussion and Conclusion

In the equilibrium we identify, the support of a pivotal member results in the support of a domestic audience and the leader seeks multilateral support given sufficient desire to acquire domestic support. When the pivotal member voices opposition, the audience may or may not support the policy, depending on their beliefs, which are influenced by the relative distance of the pivotal member’s and their own leader’s ideal points. This equilibrium holds for instances in which the pivotal member is relatively “conservative,” or reluctant to authorize the use of force.

In the original article, the core substantive claim is that the relative preferences of these actors can influence whether an uninformed audience updates its beliefs about the ultimate location of foreign policy initiatives and subsequently conditions its support of foreign policy proposals on the strategic behavior and information revealed by their own leader and an international organization. This claim is supported by an equilibrium of the type we identify here. Due to space limitations, we do not analyze other equilibria, but to the extent that we show that a substantively appealing parameter restriction in the original model results in equilibrium behavior consistent with the original argument, we should remain confident that the strategic information perspective is a valid and reasonable candidate explanation for the perceived importance of international organizations like the UN Security Council.

The debate in this instance revolves around a core substantive question: namely, what is the appropriate way to model the decision making and position taking of member states in an IO and its impact on domestic politics? The original model conflated two types of signaling processes—one in which the pivotal member’s position revealed something about policy location and one in which the pivotal member’s position potentially revealed something about the member’s intent to behave punitively should the leader implement its policy proposal. Subsequent work (Chapman 2011) and our preceding argument make the case that the latter is secondary to the former, as states routinely take public stances in opposition to policy but fail to impose direct material costs on the initiators of foreign policy actions. Instead, consistent with earlier work (e.g., Voeten 2005; Thompson 2006, 2009), this perspective sees voting and vetoing efforts as largely about communicating preferences and influencing global attitudes.

We think promising future alternatives for theoretical modeling on this topic should focus on trying to understand how public positions and arguments made in global forums influence the beliefs and attitudes of various audiences around the globe. An important question for future empirical inquiry is the degree to which nonelites and public audiences form consistent and reasonable perceptions about the motives of member states in security institutions. In recent years, some studies have applied experimental methods to the understanding of citizens’ attitudes at the micro level (e.g., Chapman 2011; Grieco, Gelpi, and Feaver 2011; Tingley and Tomz 2013). Given debates about political knowledge, political sophistication, and political behavior, empirically investigating how international events influence public attitudes is an area for more creative and sophisticated research to explore.

Footnotes

Appendix

Acknowledgments

The authors thank Phil Arena, Pat McDonald, Scott Moser, and Scott Wolford for helpful feedback.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

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