Prioritarian Poverty Comparisons with Cardinal and Ordinal Attributes

• Author: Erwin Ooghe,Kristof Bosmans,Luc Lauwers
• Published date: 01 July 2018
• DOI: http://doi.org/10.1111/sjoe.12238
• Date: 01 July 2018

©The editors of The Scandinavian Journal of Economics 2017.

Scand. J. of Economics 120(3), 925–942, 2018

DOI: 10.1111/sjoe.12238

Prioritarian Poverty Comparisons with

Cardinal and OrdinalAttributes*

Kristof Bosmans

Maastricht University, NL-6211 LM Maastricht, The Netherlands

k.bosmans@maastrichtuniversity.nl

Luc Lauwers

KU Leuven, B-3000 Leuven, Belgium

luc.lauwers@kuleuven.be

Erwin Ooghe

KU Leuven, B-3000 Leuven, Belgium

erwin.ooghe@kuleuven.be

Abstract

The ethical view of prioritarianism holds that if an extra bundle of attributes is to

be allocated to either of two individuals, then priority should be given to the worse

off among the two. We consider multidimensional poverty comparisons with cardinal

and ordinal attributes and propose three axioms that operationalize the prioritarian view.

Each priority axiom, in combination with a handful of standard properties, characterizes

a class of poverty measures.

Keywords: Correlation increasing majorization; multidimensional poverty measurement;

priority; uniform majorization

JEL classification:D31; D63; I32

I. Introduction

“Benefiting people matters more the worse off these people are.”

This quote of Parfit (1997, p. 213) summarizes the ethical view of

prioritarianism.1The view is straightforward to operationalize in the

*We thank Koen Decancq, Jean-Yves Duclos, Tony Shorrocks, and the participants of the

OPHI workshop in Oxford (University of Oxford) and the ProRESP conference in Wavre

(CORE, Universit´e catholique de Louvain) for fruitful discussion. The authors are responsible

for any remaining shortcomings.

1Parfit (1997, p. 214) presents prioritarianism as an alternative to egalitarianism. From the

prioritarian view, the worse off should be prioritized “but that is only because these people

are at a lower absolute level. It is irrelevant that these people are worse off than others.…

Egalitarians are concerned with relativities: with how each person’s level compares with the

level of other people.”

926 Prioritarian poverty comparisons

unidimensional setting of income distributions. Standard properties in

unidimensional welfare and poverty measurement (with a central role for

the Pigou–Dalton transfer principle) do the job (e.g., Fleurbaey, 2001;

Tungodden, 2003; Esposito and Lambert, 2011).2The implementation of

prioritarianism is considerably more challenging in the multidimensional

setting. In particular, the absence of a unique well-being indicator (such

as income) complicates the identification of the worse off individuals

to be prioritized. We consider the setting of multidimensional poverty

comparisons and discuss three alternative axioms that operationalize the

prioritarian view. The attributes included are either cardinal (e.g., income

and life expectancy) or ordinal (e.g., subjective health and physical

security). We start with cardinal attributes.

The weakest priority axiom is based on attribute dominance. Suppose

that a benefit (an extra bundle of attributes) can be given to either of

two poor individuals. If one of the two individuals is worse off in each

attribute, then she should receive the extra bundle according to the axiom.

If not, then the axiom remains silent. We refer to this axiom as dominance

priority. Dominance priority is in the spirit of the Pigou–Dalton bundle

dominance principle of Fleurbaey and Trannoy (2003).

The strongest priority axiom is based on the ranking of bundles by

the poverty measure itself. As comparing one-person distributions boils

down to comparing single bundles, a poverty measure also generates a

poverty ranking of individual bundles. Suppose again that an extra bundle

of attributes can be given to either of two poor individuals. This version

of priority requires that the extra bundle goes to the poorer among the

two individuals as judged by the poverty measure itself. We refer to

this second axiom as poverty priority. Poverty priority is related to the

consistent Pigou–Dalton principle of Bosmans et al. (2009). Provided

that the poverty measure is monotone in the attributes (an assumption

maintained throughout the paper), poverty priority is stronger than (i.e.,

implies) dominance priority.

Figure 1 illustrates dominance priority and poverty priority. Individual

1’s bundle dominates individual 2’s bundle. Hence, dominance priority

prescribes giving priority to individual 2 over individual 1. Given

monotonicity, so does poverty priority. The depicted curve represents

2Esposito and Lambert (2011) stress that the distributional concern in unidimensional poverty

measurement originates from a prioritarian rather than an egalitarian view. In his pioneering

contribution, Watts (1968, p. 326) justifies this concern as follows: “poverty becomes more

severe at an increasing rate as successive decrements of income are considered; in other words,

…poverty is reduced more by adding $500 to a family’s command over goods and services

if the family is at 50 percent of the poverty line than if it is at 75 percent.” This justification

is clearly prioritarian.

©The editors of The Scandinavian Journal of Economics 2017.