VOTING AND SOCIAL PRESSURE UNDER IMPERFECT INFORMATION

• DOI: http://doi.org/10.1111/iere.12401
• Published date: 01 November 2019
• Author: Nicholas H. Tenev,Alexander T. Clark
• Date: 01 November 2019

INTERNATIONAL ECONOMIC REVIEW

Vol. 60, No. 4, November 2019 DOI: 10.1111/iere.12401

VOTING AND SOCIAL PRESSURE UNDER IMPERFECT INFORMATION∗

BYALEXANDER T. CLARK AND NICHOLAS H. TENEV1

Peloton Interactive,Inc., U.S.A.; Ofce of the Comptroller of the Currency,U.S.A.

We develop a model in which costly voting in a large, two-party election is a sequentially rational choice of

strategic, self-interested players who can reward fellow voters by forming stronger ties in a network formation

coordination game. The predictions match a variety of stylized facts, including explaining why an individual’s

voting behavior may depend on what she knows about her friends’ actions. Players have imperfect information

about others’ voting behavior, and we find that some degree of privacy may be necessary for voting in equilibrium,

enabling hypocritical but useful social pressure. Our framework applies to any costly prosocial behavior.

1. INTRODUCTION

A growing body of empirical work suggests that social influence may have a critical role

in motivating costly prosocial behaviors such as voting. Gerber et al. (2008) find that people

are more likely to vote if their neighbors will learn of their participation, for example, and

DellaVigna et al. (2016) estimate the value of voting “because others will ask” to be around

$5–$15. Perez-Truglia and Cruces (2016) find that partisans give more to political campaigns

if like-minded neighbors will learn of their contributions. These results suggest that social

sanctions may be at play: Civic duty may be enough to motivate some, but cannot explain why

others only vote if their neighbors will find out. If social pressure is indeed critical, privacy

would seem to undermine participation. We show that this is not always the case: Our main

result is that a certain degree of privacy and hypocrisy may actually be necessary for voter

turnout or provision of a public good. These results are important because policy interventions

often intentionally or unintentionally change social incentives or privacy, so understanding how

information interacts with social mechanisms is critical to making sense of policy effects.

We write down a model of costly prosocial behavior enforced by social pressure in a setting

with imperfect information. For ease of exposition and to make the application to an adversarial

context clear, we follow the example of voting throughout the article, despite a larger scope to

the model.2We proceed from the simple idea that people interact in many contexts, and so it

may be myopic to ignore interdependence among these interactions. In our model, players first

simultaneously decide whether to abstain, vote for the left-wing candidate, or vote for the right-

wing candidate. Voting actions are public knowledge for some players but nonverifiable for

others, who can lie about whether they voted (throughout, we use the term “privacy” to mean

that an individual’s voting action is private information). Then, each player chooses a level of

cooperation with her peers. Intuitive restrictions lead us to focus on strategies in which players

∗Manuscript received April 2017; revised January 2019.

1This article was previously entitled “Hypocrisy and Strategic Social Pressure.” The views in this article are those

of the authors and do not reflect those of the Office of the Comptroller of the Currency or the Department of the

Treasury. We are very grateful to Masaki Aoyagi, Steven Durlauf, Andrea Galeotti, George Loginov, Dan Quint,

Marzena Rostek, Bill Sandholm, Marek Weretka, seminar participants at the University of Wisconsin–Madison and

EconCon, participants at the 27th Jerusalem School in Economic Theory, and our anonymous referees for their helpful

comments. We are particularly indebted to Antonio Penta for exceptionally thorough consideration and advice. Please

address correspondence to: Nicholas Tenev, Office of the Comptroller of the Currency, 400 7th Street SW, Washington,

DC 20219. E-mail: nicholas.tenev@occ.treas.gov.

2Frey and Meier (2004), for example, provide experimental evidence that individuals are more likely to contribute

to a charity if they learn others are as well; such behavior can be explained by our model.

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(2019) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1706 CLARK AND TENEV

cooperate more with friends similar to themselves. Although the model is uncomplicated, it

is able to explain a variety of stylized facts from literatures in economics, political science,

and psychology.

Our focus is on large elections in which no individual expects to have much effect on the

outcome, in contrast to studies of small elections such as Borgers (2004). Nevertheless, voting

can be induced by conditional network formation. Even self-interested individuals who obtain

no intrinsic benefit from voting may vote in equilibrium, as they expect to be rewarded with

stronger friendship with other voters of the same political affiliation. Others may abstain,

because the cost of voting outweighs their benefits of stronger ties to voting peers. This social

pressure may operate alongside other forces such as expressive utility, whereby voters are

motivated by concerns apart from influencing the outcome of the election, but we can capture

the main stylized facts about voting without expressive utility.

In our model, those who know that peers will learn of their participation will be more inclined

to vote, as in the empirical literature. Despite this, we derive an unexpected nonmonotonicity

in the provision of information: Maintaining the privacy of some individuals’ participation may

actually increase overall turnout (Proposition 5). If someone cannot be induced to vote even by

social pressure, allowing them privacy at least enables hypocritical encouragement of others to

vote. This can occur even if the cost of voting is identical across players (owing to asymmetries in

network structure) and even if hypocrites’ abstention can be inferred. Another counterintuitive

finding is that increasing the level of punishment can in some cases lower turnout: If there are

complementarities in the value of friendship, for example, raising punishment can lower overall

cooperation to the point that social punishment loses its sting (Proposition 4).

Our model features a weighted and directed network that describes the capacity for benefit

from cooperation among all pairs of players. This affords us specific predictions for how an indi-

vidual’s place in the network facilitates prosocial behavior. For any network, we characterize the

information structure that maximizes voter turnout and give conditions under which increasing

privacy can increase maximal equilibrium turnout. For any network and a given information

structure, we find the turnout-maximal equilibrium. Our model features, as an equilibrium out-

come instead of an assumption, homophily in prosocial behavior: Voters are more likely to have

friends who also vote, and partisans are more likely to have like-minded friends.3Furthermore,

our model can explain not just voting but other costly prosocial behaviors as well. Appendix A.1

uses Add Health data for empirical verification of both homophily and correlation with number

of friends for voting as well as blood donation, community service, and organ donor registration.

These results corroborate prior evidence of homophily (e.g., Knoke, 1990).

Ours is not the first article to theorize that social pressure may be a key motivation to vote.

Levine and Mattozzi (2017) consider a voter turnout model featuring players arranged in a circle

network where a social norm specifies a participation rate, and the norm is enforced by audits

and punishment. Two political parties choose the social norm that is optimal according to a group

objective function. One party will be advantaged depending on its size and properties of the

cost of enforcing a social norm. Imperfect information is treated through comparative statics on

the reliability of the auditing technology, where a less reliable audit results in more punishment.

Our article focuses on individuals, and a social norm specifies the extent to which norm

adherents should punish friends observed violating the norm. Instead of considering a single

auditing technology, we consider the potential privacy of a player’s decision to vote or abstain.

This may be thought of as allowing for the possibility that a player could fool an auditor. Further,

social pressure is exerted in our model through the opportunity to withhold cooperation in a

friendship game with connections on a rich network. By considering privacy and social pressure

at the individual level, we are able to consider how different network positions expose an

individual to varying levels of social pressure, facilitating different levels of prosocial behavior.

3This adds to the work of Kets and Sandroni (2015), who show that homophily can arise despite the lack of a direct

preference for similar friends as a way to reduce uncertainty when matched agents must play a coordination game.