Measuring Social Polarization with Ordinal and Categorical Data

• Author: IÑAKI PERMANYER,CONCHITA D'AMBROSIO
• Published date: 01 June 2015
• Date: 01 June 2015
• DOI: http://doi.org/10.1111/jpet.12093

MEASURING SOCIAL POLARIZATION WITH ORDINAL

AND CATEGORICAL DATA

I˜

NAKI PERMANYER

Centre d’Estudis Demogr`

afics, Universitat Aut`

onoma de Barcelona

CONCHITA D’AMBROSIO

INSIDE, Universit´

e du Luxembourg

Abstract

We examine the measurement of social polarization with

categorical and ordinal data. We partition the society into

groups on the basis of salient social characteristics, such as

race and ethnicity, and we take into account the extent to

which these groups are clustered in certain regions of an

attribute’s distribution. This is particularly useful in many

contexts where cardinal data are not available. The new

measures we propose are characterized axiomatically.

1. Introduction

The measurement of polarization has received increasing attention in re-

cent years (see, amongst others, Foster and Wolfson 1992, Esteban and Ray

1994 (henceforth ER), Wolfson 1994, Wang and Tsui 2000, Chakravarty and

Majumder 2001, Rodriguez and Salas 2003, Duclos, Esteban, and Ray 2004

(henceforth DER), and Bossert and Schworm 2008). One of the principal

reasons for this interest is the effect that polarization has on a number of so-

cial, economic, and political phenomena, and in particular those related to

social tensions and conflict. However, while most researchers have focused

their attention on the measurement of “income polarization” alone, that

is, on clustering around local means of income distribution, only relatively

few have attempted to analyze what might be broadly referred to as “social

I˜

naki Permanyer, Centre d’Estudis Demogr`

afics, Universitat Aut`

onoma de Barcelona,

Spain (Inaki.Permanyer@uab.cat). Conchita D’Ambrosio, INSIDE, Universit´

eduLuxem-

bourg (conchita.dambrosio@uni.lu).

We thank Myrna Wooders and an anonymous referee for comments and suggestions.

I˜

naki Permanyer gratefully acknowledges financial support from the research projects

ERC-2009-StG-240978 and ECO2010-21668-C03-02.

Received January 15, 2013; Accepted February 17, 2013.

C2013Wiley Periodicals, Inc.

Journal of Public Economic Theory, 17 (3), 2015, pp. 311–327.

311

312 Journal of Public Economic Theory

polarization” (see, for example, D’Ambrosio 2001, Zhang and Kanbur 2001,

DER, and Montalvo and Reynal-Querol 2005). Social polarization refers to

the situation where the factors determining individuals’ identities, and there-

fore social groups, are culturally, ideologically, biologically, or socially driven

and do not depend solely on income (classic examples are ethnic, racial,

religious, and political polarization). The measurement of social polariza-

tion is clearly relevant, as in many circumstances the distribution of income

is not the only pertinent cause of social conflict (see Easterly and Levine

1997, Esteban and Ray 1999, Montalvo and Reynal-Querol 2005, Collier and

Hoeffler 2004 for empirical and theoretical contributions on the existing

links between polarization and conflict and other related issues).

Traditional income-polarization measures are implicitly or explicitly

based on the assumption that the individuals who are clustered around

certain income levels form a cohesive group that might potentially express its

unrest via social action or revolt. Following ER, individuals are assumed to

feel (1) identified with other individuals possessing the same income level as

them, and (2) alienated from individuals with different incomes. Within the

bipolarization framework, measures are also implicitly constructed under

the assumption that the problems of a society with a declining middle class

derive from the presence of large and cohesive “poor” and “rich” classes.

However, there are obviously a number of other salient characteristics

(such as race, ethnicity, and gender) that exert considerable influence

in the definition of individuals’ sense of identity. As argued by Dasgupta

and Kanbur (2007, p. 1816), “the nominal distribution of income could give a

misleading picture of tensions in society, both within and across communities. Ide-

ologies of community solidarity may well trump those of class solidarity because of the

implicit sharing of community resources brought about by community-specific public

goods”.

The only polarization measure that, to the best of our knowledge,

explicitly accounts for the distribution of groups along ethnic or religious

lines is the Reynal-Querol index (henceforth RQ). This index is only defined

on the basis of the population-weights that these groups represent as it is an

indicator of ethnic diversity in the population. It disregards differences in

their economic status which, in our opinion, do very often play a role in the

polarization process experienced by societies.

One of the aims of the present contribution is to define a social polariza-

tion index which combines the intuition of both of the approaches described

above: on the one hand, the partition of the society into groups is performed

on the basis of salient social characteristics (race and ethnicity, to mention

just two); and, on the other hand, we take into account the extent to which

these groups are clustered in certain regions of an attribute’s distribution. Al-

ternative approaches with similar aims are described in D’Ambrosio (2001)

and Zhang and Kanbur (2001). Our contribution differs regarding the type

of attribute variables taken into consideration, which are here qualitative in

nature (see below).