Group identification with (incomplete) preferences

• Author: Alejandro Saporiti,Wonki Jo Cho
• DOI: http://doi.org/10.1111/jpet.12387
• Published date: 01 February 2020
• Date: 01 February 2020

J Public Econ Theory. 2020;22:170–189.wileyonlinelibrary.com/journal/jpet170

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© 2019 Wiley Periodicals, Inc.

Received: 30 April 2018

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Revised: 2 April 2019

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Accepted: 8 June 2019

DOI: 10.1111/jpet.12387

ORIGINAL ARTICLE

Group identification with (incomplete)

preferences

Wonki Jo Cho

1

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Alejandro Saporiti

2

1

Department of Economics, Korea

University, Seoul, South Korea

2

School of Social Sciences, University of

Manchester, Manchester, UK

Correspondence

Alejandro Saporiti, Arthur Lewis Building,

School of Social Sciences, University of

Manchester, M13 9PL, Manchester, UK.

Email: alejandro.saporiti@manchester.ac.uk

Abstract

We consider the problem of identifying members of a

group based on individual opinions. Since agents do

not have preferences in the model, properties of rules

that concern preferences (e.g., strategy‐proofness and

efficiency) have not been studied in the literature.

We fill this gap by working with a class of incomplete

preferences derived directly from opinions. Our

main result characterizes a new family of group

identification rules, called voting‐by‐equitable‐com-

mittees rules,usingtwowell‐known properties:

strategy‐proofness and equal treatment of equals.

Our family contains as a special case the consent

rules (Samet & Schmeidler. J. Econ. Theory, 110

(2003), pp. 213–233), which are symmetric and

embody various degrees of liberalism and democracy;

and it also includes dictatorial and oligarchic rules

that value agents’opinions differently. In the

presence of strategy‐proofness, efficiency turns out

to be equivalent to non‐degeneracy (i.e., any agent

may potentially be included or excluded from the

group). This implies that a rule satisfies strategy‐

proofness, efficiency, and equal treatment of equals

if, and only if, it is a non‐degenerate voting‐by‐

equitable‐committees rule.

1

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INTRODUCTION

The axiomatic theory of group identification begins with the seminal article of Kasher &

Rubinstein (1997), who relate the problem of ethnic and racial identity to social choice theory.

1

The building blocks of this theory are (i) a group of agents, who seek to identify those with, or

without, a certain qualification; (ii) the agents’opinions about each other, including

themselves, which are the main input for qualifying or disqualifying an individual as a group

member; and (iii) a rule that aggregates those opinions into a (social) decision.

2

From the

standpoint of an economist, an important disadvantage of this framework is that the lack of

information about individual preferences prevents any analysis of incentive compatibility and

efficiency of rules.

Motivated by this limitation, we derive from each agent’s opinion a partial ordering that

captures his preferences over decisions. Our preference specification ranks the agent’s opinion

as his most preferred decision; and it partially orders other decisions by looking at each agent’s

membership separately from the others’and by comparing it to the opinion. For instance,

suppose that agent

i

views agent

j

as a member. Consider any pair of decisions that differ only

in agent

j

’s membership. Then agent

i

prefers the decision that qualifies agent

j

as a member to

the decision that disqualifies him.

3

With preferences defined, we proceed to study properties of rules that involve these

preferences. The first one is an incentive property known as strategy‐proofness. This property

ensures that no agent ever benefit from misrepresenting his opinion. We find that strategy‐

proofness completely characterizes the family of voting‐by‐committees rules (Theorem 1).

These rules appear first in the abstract social choice model of Barberà, Sonnenschein, and Zhou

(1991), who study selecting a subset from a finite set of alternatives. In our setup, a voting‐by‐

committees rule determines each agent’s membership using a committee for the agent that

consists of winning coalitions (subsets of agents). An agent is qualified as a member if he

obtains the approval of a winning coalition in his committee.

Our proof for the characterization of the voting‐by‐committees rules hinges on two results

that are interesting in their own right. First, strategy‐proofness is equivalent to a local notion of

incentive compatibility, called adjacent strategy‐proofness (Proposition 1). Two opinions are

adjacent if they differ in only one agent’s membership. Adjacent strategy‐proofness requires

that no agent gain by reporting an opinion that is adjacent to the truth. In general, adjacent

strategy‐proofness is weaker than strategy‐proofness. Yet on the universal domain, the two are

equivalent. Moreover, this equivalence implies that a strategy‐proof rule responds to changes in

opinions in an intuitive way: when agent

i

changes his opinion about agent

j

while keeping his

opinions about all other agents the same, agent

j

’s membership, if it is affected, changes in the

same direction while all the other agents’memberships remain unaffected. Conversely, any rule

satisfying this property is strategy‐proof (Corollary 1).

The second result upon which our characterization relies concerns two properties proposed

by Samet & Schmeidler (2003): monotonicity and independence. Monotonicity requires

1

See Dimitrov (2011) for a recent and comprehensive literature review and List (2008) for a discussion about the relationship between group identification and

judgment aggregation.

2

Opinions and decisions are represented by profiles of 0's and 1's, with 0 meaning “out”and 1 “in”.

3

This way of extending opinions to preferences resembles the way in which preference relations over alternatives are extended to preferences over preferences

relations by Grandmont’s (1978) notion of betweenness (Bossert & Sprumont, 2014) and preferences over alternatives are extended to preferences over lotteries

by first‐order stochastic dominance (Gibbard, 1977; Bogomolnaia & Moulin, 2001). Our discussion of the related literature provides further details on this

matter.

CHO AND SAPORITI

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