Redistribution under general decision rules

• Published date: 01 February 2022
• Author: Giri Parameswaran,Hunter Rendleman
• Date: 01 February 2022
• DOI: http://doi.org/10.1111/jpet.12529

J Public Econ Theory. 2022;24:159–196. wileyonlinelibrary.com/journal/jpet © 2021 Wiley Periodicals LLC

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Received: 2 January 2020

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Revised: 15 November 2020

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Accepted: 17 May 2021

DOI: 10.1111/jpet.12529

ORIGINAL ARTICLE

Redistribution under general decision rules

Giri Parameswaran

1

|Hunter Rendleman

2

1

Department of Economics, Haverford

College, Haverford, Pennsylvania, USA

2

Department of Government, Harvard

University, Cambridge,

Massachusetts, USA

Correspondence

Giri Parameswaran, Department of

Economics, Haverford College, 370

Lancaster Ave, Haverford, PA 19041,

USA.

Email: gparames@haverford.edu

Abstract

We study the political economy of redistribution over a

broad class of decision rules. We suggest a simple and

elegant procedure to select a robust equilibrium from

the multiplicity in the core. Equilibrium policy de-

pends on the full income profile, and, importantly, the

preferences of two decisive voters. We show that the

effect of increasing inequality depends on the decision

rule and the shape of the income distribution; redis-

tribution will increase if both decisive voters are

“relatively poor,”and decrease if at least one is suffi-

ciently “rich.”Additionally, redistribution decreases as

the polity adopts increasingly stringent super‐majority

rules.

1|INTRODUCTION

Beginning with the seminal contributions of Romer (1975), Roberts (1977), and Meltzer

and Richard (1981), a long literature has developed that explains the features of redis-

tribution schemes as a consequence of the preferences of the median voter (see Besley &

Coate, 1997; Epple & Romer, 1991; Gans & Smart, 1996; Moene & Wallerstein, 2001;

Persson & Tabellini, 1999, amongst many others). However, the logic of the median

voter theorem requires that decisions be made by simple majority rule, and under most

alternative decision procedures, the result does not obtain. And, in many contexts,

decisions are indeed made by decision procedures other than simple majority rule. For

example, in the United States, at both the federal level and in most states, decision‐

making requires the assent of majorities in both the House of Representatives and Senate,

and the assent of the President (or Governor), unless two‐thirds majorities exist in both

chambers. Super‐majority rules have become increasingly common, especially in the

realm of fiscal policy.

1

And, of course, given its cloture rule, the United States Senate

often operates under an effective super‐majority rule.

Within the context of redistribution, models that assume decision‐making by simple ma-

jority rule often generate stark predictions that are at odds with the data. For example, em-

pirical evidence suggests that median income is not sufficient to predict the level of

redistribution in a polity—income at other quantiles matter as well (see Karabarbounis, 2011).

Similarly, standard median voter models of redistribution typically predict that redistribution

should be increasing in the level of inequality (see Meltzer & Richard, 1981). However, as we

discuss in more detail below, the evidence for this claim is strongly contested. These findings

further motivate the need for a general approach to analyzing redistribution under decision

procedures other than simple majority rule (see Alesina & Giuliano, 2011).

In this paper, we provide an analysis of redistribution under a broad class of decision

procedures. Our approach retains the spirit of the median voter theorem in that we associate

the equilibrium with a policy in the core.

2

However, unlike the case of simple majority,

where the core is uniquely the median voter's ideal policy, for most decision procedures the

core generically contains (infinitely) many policies. Moreover, amongst this multiplicity, the

core will often (and certainly whenever the decision procedure requires a super‐majority)

contain policies that are both above and below the median voter's ideal policy—providing little

guidance as to even the qualitative effect of non‐simple‐majority rules.

In this paper we explore an approach that selects a unique equilibrium redistribution policy

for every social decision procedure within a very general class. Our approach is similar to

Cardona and Ponsatí (2014) in that we focus on the limit policy chosen in a bargaining game à

la Baron and Ferejohn (1989) and Banks and Duggan (2000), as delay becomes costless (see

Predtetchinski, 2011). Our approach is analogous to Cho and Duggan (2009), who establish

that, under simple majority rule, the limit policy is the median voter's ideal. For generic

decision rules, the limit policy instead coincides with the policy that results from asymmetric

Nash Bargaining between two decisive voters whose identities depend on the decision, and

with endogenous bargaining weights that depend on the full income profile. We provide a more

substantial justification for our focus on the Nash Bargaining solution in Section 3.

Using our selection procedure, we explore various comparative static results. First, in the

context of super‐majority rules, we explore the effect of varying the required super‐majority. We

identify conditions under which raising the super‐majority requirement reduces taxation and

redistribution, and show that, absent those conditions, the effect may be ambiguous. Second, we

explore the effect of increasing inequality on the equilibrium demand for redistribution. When

inequality increases, redistribution may either be higher or lower depending on incomes of the

decisive voters (which are determined by the decision rule) and the shape of the income dis-

tribution. We provide conditions under which either of these outcomes may obtain; in brief,

increasing inequality is likely to increase redistribution, unless at least one decisive voter has

1

Indeed, 15 states require legislative super‐majorities to raise taxes, or in some come cases, to pass a budget at all (see

Rueben & Randall, 2017). In 2018, voters in Florida endorsed a ballot initiative requiring a super‐majority to raise taxes,

whilst voters in Oregon rejected a similar proposal. A similar ballot initiative was originally proposed in California,

although was removed before the election. Moreover, proposals to institutionalize super‐majority budget rules at the

federal level via a constitutional amendment have been repeatedly introduced into Congress, albeit unsuccessfully (see

H. J. Res. 111, 1998; H. J. Res. 41, 2001).

2

The core is the set of unbeatable policies; that is, those for which there does not exist some other policy that is strictly

preferred by a decisive coalition of agents.

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significantly above‐average income—that is, there is elite capture. Third, we explore the effect of

changing reversion policies (such as graduated sequesters) on redistribution.

We present a simple public finance model in which there is a continuum of agents dis-

tinguished by their income. Redistribution is via a linear income tax (a proportional tax coupled

with a uniform transfer to all agents), akin to the simplest model of a Universal Basic Income.

For simplicity, we capture the dead‐weight losses from taxation in reduced‐form by assuming

that redistribution is via a “leaky‐bucket”(see Dixit & Londregan, 1998; Moene & Wallerstein,

2001, amongst others). We micro‐found these dead‐weight losses in a model with elastic labor

supply, in an Supporting Information Appendix. Since the benefits of taxation are shared

equally, but the costs fall more heavily on higher income earners, voters' most preferred income

tax rates are decreasing in their incomes.

The core is the set of unbeatable, and thus stable, policies. Given a decision rule, it can be

shown that the core is an interval of policies bounded by the ideal policies of two particular

agents, whom we call the left and right decisive voters, and whose identities are determined by

the decision rule. (Under simple majority rule, both decisive voters coincide with the median

voter, and so the core is uniquely the median voter's ideal policy.)

The decisive voters are crucial to determining the focal policy that will be selected in

equilibrium amongst the many in the core. Indeed, the focal policy is chosen as if by bilateral

asymmetric Nash Bargaining between the left and right decisive voters, with endogenous

weights that depend on the entire distribution of voters' incomes. Our approach, thus, provides

a theoretical basis for the empirical finding that redistribution depends on the entire income

profile, and not merely the median income (see Karabarbounis, 2011).

We can think of our endogenous Nash Bargaining characterization in the following way:

Although voters are heterogeneous in their preferences, in equilibrium, they separate into two

cohesive factions led by the left and right decisive voters. Policy is chosen as if by asymmetric

Nash Bargaining between the factional leaders whose bargaining strengths depend on the size

of their respective coalitions. Voters in turn understand that their factional choice affects the

policy that results, and choose which faction to join, accordingly. The equilibrium coalitions

must be stable, in the sense that, given the policy that results, no voter would want to switch

factions. Our result can thus be interpreted as a generalization of Duverger's Law, in that it

micro‐founds the emergence of two cohesive factions or “parties.”However, these endogenous

factions need not be equally sized, and will typically have non‐median factional leaders.

Having characterized our refinement, we turn our attention to comparative statics in three

dimensions. First, we highlight that the selected policy typically depends on the reversion

policy that would have been implemented in the event of disagreement. (By contrast, under

simple majority rule, the equilibrium policy is the median voter's ideal regardless of the re-

version of policy.) Importantly, the relationship between reversion and equilibrium policies is

non‐monotone. As the reversion policy becomes more extreme, the equilibrium policy becomes

more moderate, in the sense of being further from either boundary of the core. These results are

consistent with the political logic of the 2013 budget sequester, which, by making disagreement

more costly, was expected to generate a budget compromise in an otherwise gridlocked Con-

gress. The results also suggest a particular logic for building sunset clauses into policy reforms

that revert to an ex ante Pareto inferior policy and provide further support for theoretical and

empirical work describing the US President's strategy of committing to extreme executive

orders to force Congress to adopt more moderate policy (Howell, 2003). We also briefly explore

dynamic reversion policies, such as the one advocated in the End Government Shutdowns Act,

in which the reversion policy becomes more extreme the longer the duration of disagreement.

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