Group incentives and rational voting1
| Author | Alastair Smith,Tom LaGatta,Bruce Bueno de Mesquita |
| DOI | 10.1177/0951629816630439 |
| Published date | 01 April 2017 |
| Date | 01 April 2017 |
| Subject Matter | Articles |
Article
Group incentives and rational
voting1
Journal of Theoretical Politics
2017, Vol. 29(2) 299–326
©The Author(s) 2016
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DOI:10.1177/0951629816630439
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Alastair Smith
Department of Politics, New York University, USA
Bruce Bueno de Mesquita
Department of Politics, New York University, USA and Splunk, Inc.
Tom LaGatta
Courant Institute of Mathematical Sciences, New York University, USA
Abstract
Our model describes competition between groups driven by the choices of self-interested vot-
ers within groups. Within a Poisson voting environment, parties observe aggregate support from
groups and can allocate prizes or punishments to them. In a tournament style analysis, the model
characterizes how contingent allocation of prizes based on relative levels of support affects
equilibrium voting behavior. In addition to standard notions of pivotality, voters influence the
distribution of prizes across groups. Such prize pivotality supports positive voter turnout even
in non-competitive electoral settings. The analysis shows that competition for a prize awarded
to the most supportive group is only stable when two groups actively support a party. How-
ever, competition among groups to avoid punishment is stable in environments with any number
of groups. We conclude by examining implications for endogenous group formation and how
politicians structure the allocation of rewards and punishments.
Keywords
Pivotality; pivotal voting; random population model; turnout; voting
1. Introduction
To attain and retain power in an electoral setting politicians need to motivate their sup-
porters to turn out and vote. While simply offering more or better rewardsis one means to
Corresponding author:
Alastair Smith, 19 West 4th St New York, New York 10012, USA.
Email: Alastair.Smith@nyu.edu
300 Journal of Theoretical Politics 29(2)
elicit support, we contend that politicians can do more with fewer resources by offering
to allocate benefits across groups in a contingent manner—a mechanism we refer to as
a Contingent Prize Allocation Rule (Smith and Bueno de Mesquita, 2012). As a simple
illustrative example, a politician might offer to build a park (the prize) in the precinct
(the group) that provides her with the most votes. Most rational choice explanations of
voting examine pivotality and the extent to which an individual’s vote is likely to influ-
ence who wins the election. In contrast, we contend that voters can be pivotal on other
dimensions (Schwartz, 1987); in particular we focus on the extent to which an individual
voter shapes the distribution of prizes and punishments across groups. Hence we provide
a link between individual rational choices at one level and the importance of groups in
shaping political outcomes at another.
Our approach is akin to the tournaments approach of Lazear and Rosen (1981). They
examine how firms set wage schedules to incentivizethe effort workers make by awarding
a wage bonus to the most productive worker. However, within the political setting, sim-
ple wage competitions are more difficult to structure, not least because individual votes
are anonymous. Vote buying occurs and patronage-style parties attempt to undermine
the secret ballot. However, monitoring and rewarding each individual voter is expen-
sive, time consuming and, empirically, appears the exception rather than the rule (Stokes,
2007). Instead, here we examine a setting where politicians observe political support (in
terms of vote totals) at the group level (such as precincts, wards, or districts). Supportive
groups are disproportionately rewarded, or alternatively, non-supportive groups are pun-
ished. Analogous to Lazear and Rosen’s wage bonus for the most productive worker, we
examine the implications of winner-take-all schemes that allocate a prize to the most sup-
portive group. In addition, we model how punishing the least supportiveg roup shapes the
incentives of individuals within groups. In our analysis, group competition takes a pre-
eminent role in shaping political outcomes although, and importantly, the power of these
groups is derived by the actions of individual voters and their self-interested motivations.
We are not concerned here with comparing the properties of all possible reward
or punishment mechanisms. Rather, our interest is to establish that contingent rules
can significantly incentivize voting. Elsewhere we investigate the effects of a broader
range of rules on group effort in political competition (Bueno de Mesquita and Smith,
2015). Here, we model the waythat a winner-take-all tournament system influences voter
turnout and voter incentive to form groups. We will see that politicians can exploit those
incentives to mobilize turnout even when they face no credible political opposition.
Winner-take-all is a useful starting place. The tournament literature which we apply
assumes a winner-take-all environment and anecdotal evidence supports the idea that
political parties routinely use such a mechanism. Stories of snow removal, for instance,
in New York City and in Chicago’s Democratic wards abound indicating that the most
supportive neighborhoods are privileged. Likewise, as we discuss later, American polit-
ical parties formalize the winner-take-all prize mechanism in awarding participation in
their national nominating conventions. As Grossman and Helpman (2001: 226) observe,
reward mechanisms need not include an explicit quid-pro-quo. In their analysis of rent-
seeking by Special Interest Groups (SIG), they contend, ‘Influence can be bought and
sold by a subtle exchange in which both sides recognize what is expected of them. The
SIG can make known by words and deeds that it supports politicians who are sympa-
thetic to its cause. Then the policy maker can appear to be taking actions to promote
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