Distributive politics with other‐regarding preferences

• Published date: 01 April 2021
• Author: Minh T. Le,Alejandro Saporiti,Yizhi Wang
• Date: 01 April 2021
• DOI: http://doi.org/10.1111/jpet.12485

J Public Econ Theory. 2021;23:203–227. wileyonlinelibrary.com/journal/jpet © 2020 Wiley Periodicals LLC

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203

Received: 26 February 2019

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Accepted: 29 September 2020

DOI: 10.1111/jpet.12485

ORIGINAL ARTICLE

Distributive politics with other‐regarding

preferences

Minh T. Le

1

|Alejandro Saporiti

2

|Yizhi Wang

3

1

Department of Economics, University of

Warwick, Coventry, UK

2

School of Social Sciences, Economics,

University of Manchester, Manchester, UK

3

Ma Yinchu School of Economics, Tianjin

University, Tianjin, China

Correspondence

Alejandro Saporiti, School of Social

Sciences, Economics, University of

Manchester, Manchester, UK.

Email: alejandro.saporiti@manchester.

ac.uk

Abstract

This paper analyzes a nonsmooth model of prob-

abilistic voting with two parties and a broad family of

other‐regarding behavior, including fairness and

quasi‐maximin preferences, income‐dependent al-

truism, and inequity aversion. The paper provides

conditions for equilibrium existence and uniqueness.

It also characterizes the Nash equilibrium in pure

strategies when parties hold either symmetric pay-

offs, or minor forms of asymmetries. The character-

ization shows that the two parties converge to an

equilibrium policy that maximizes a mixture of a

“self‐regarding utilitarian”social welfare function

and an aggregate of society's other‐regarding pre-

ferences. These results are shown to be applicable to

other nonsmooth frameworks, such as probabilistic

voting with loss averse voters. The characterization

also shows that the direction and the size of the

inefficiencies emerging from electoral competition

depend in a subtle way on the nature of the other‐

regarding preferences (and resp., loss aversion).

1|INTRODUCTION

The traditional models of political economy, particularly of income redistribution, assume that

individuals are selfish and care only about their material interests. In behavioral economics,

however, there is mounting evidence that say otherwise, suggesting that people also express

concern with the well‐being of other individuals in society.

1

The implications of this behavioral

literature in political economy has just began to be studied, spanning in the past two decades a

new field of research called behavioral political economy.

2

The aim of this paper is to contribute to this new and growing literature of behavioral

political economy by extending the model of distributive politics due to Lindbeck and Weibull

(1987). The aim is to accommodate within this canonical framework of probabilistic voting a

broad family of other‐regarding behavior. This family includes among others, inequity aversion

(Fehr & Schmidt, 1999), quasi‐maximin preferences (Charness & Rabin, 2002), fairness concern

(Alesina & Angeletos, 2005a), and income‐dependent altruism (Dimick et al., 2017).

The model laid out in Section 2shares the usual features of probabilistic electoral compe-

tition. There are two political parties competing in a single election for the main office. The

candidates offer to the electorate a balanced budget redistributive policy from a multi-

dimensional policy space. Voters evaluate these policies independently and taking into account

on the one hand, their selfish utility over the individual income and an (i.i.d.) stochastic and

policy‐independent preference over the parties. However, on the other hand, and in a clear

departure from earlier work, voters also express concern about how these policies affect the

well‐being of other members of society.

To be precise, voters are endowed with an other‐regarding utility (ORU), which is assumed

to be continuous, concave, but not necessarily smooth.

3

Other than that, voters are permitted to

exhibit quite a lot of heterogeneity with regard to the ORU, and not just within a given family

(e.g., inequity aversion), but also across different families of social preferences. Parties, in the

meantime, which choose their policies to maximize the expected vote share, also care about

voters' other‐regarding preferences. This implies that the payoff functions of the parties are not

necessarily smooth on the strategy space.

The main results of the paper are displayed in Sections 4and 5and can be summarized as

follows. The paper provides a sufficient condition for equilibrium existence, called condition



,

which accommodates the other‐regarding preferences of the electorate and the resulting non-

smooth framework described above. This condition captures as a special case Lindbeck and

Weibull's (1987) requirement for existence. Taking together with the assumptions on the utility

functions, namely, continuity and concavity,



shapes the expected vote share and the parties'

payoff functions.

To be more precise, under condition



it is shown that the gradient of the expected vote

share is monotone decreasing on the differentiable subset of distributive policies (Lemma A1).

Since the latter does not always constitute a convex set, the previous result is not sufficient to

prove the concavity of the parties' payoffs. Hence, as a preliminary step it is proved using

Lemma A1 that the expected vote share of each party has a support almost everywhere

(Lemma A2). Finally, invoking the previous two lemmas and the fundamental theorem on the

support of a concave function, Proposition 1states that the expected vote share is concave on

the whole strategy space. This, together with the concavity of the ORU, guarantee that the party

payoff functions are concave as well. The existence of Nash equilibrium in pure strategies

follows then from the classical Debreu‐Glicksberg‐Fan's result for games with continuous and

quasi‐concave payoffs (Theorem 1).

1

This evidence has been documented in a large number of experimental and neuro‐imaging studies, including among

many others the work of Fehr and Schmidt (1999), Engelmann and Strobel (2004), Dawes et al. (2007,2012), Tabibnia

et al. (2008), Fehr (2009), AlmÅs et al. (2010), Tricomi et al. (2010), Zaki and Mitchell (2011), and Rilling and

Sanfey (2011).

2

See, for example, Wilson (2011) and Schnellenbach and Schubert (2015), and the references therein.

3

For instance, Fehr and Schmidt's (1999) inequity aversion preferences are not differentiable at the individual's

reference point. Similar problems appear in the case of quasi‐maximin preferences.

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