Inequality‐averse well‐being measurement

• DOI: http://doi.org/10.1111/ijet.12140
• Published date: 01 March 2018
• Date: 01 March 2018

doi: 10.1111/ijet.12140

Inequality-averse well-being measurement

Marc Fleurbaey†and Franc¸ois Maniquet‡

Weconstruct individual well-being measures that respect individual preferences and depend on

the bundles of goods consumed by the individual. Building on previous work in which general

families of well-being measures are identified, we introduce basic transfer principles that apply

either to bundles or directly to indifferencesets, and we characterize specific well-being measures

that involve either the ray utility or the money-metric utility.

Key wor ds fairness, well-being measure, preference

JEL classification D63, I32

Accepted 28 May2017

1 Introduction

The measurement of individual well-being is one of the most vexing issues in welfare economics.

In previous work (Fleurbaey and Maniquet 2011, 2017a) we have argued that it is possible to make

progress by relying on fairness principles that can guide interpersonal comparisons. Fairness princi-

ples tell us that an individual, in a particular situation depicted by a commodity bundle and a prefer-

ence ordering, should be considered better off than another individual in a situation also described

by his bundle and preferences. That is, fairness principles allow us to replace interpersonal utility

comparison with a combination of commodity bundle comparisons and the use of ordinal “non-

comparable” preferencesas the only data on subjective well-being. It may seem counter-intuitive that

comparability can be constructed with non-comparable data on preferences, but it directly follows

from fairness principles that do allow interpersonal comparisons of relative advantage with such in-

formation. And it aligns very well with the common practice of interpersonal comparisons in terms

of income or wealth, which has received support from philosophers of equality of resources suchas

Rawls (1982) and Dworkin (2000).

Let us note that the informational basis of our well-being judgements, commodity bundles and

ordinal non-comparable preferences is the same as that under which the Kaldor–Hicks–Scitovsky

compensation principle has been developed (for a discussion of this approach, see Suzumura 1980).

On the other hand, our informational basis is poorer than that of the extended sympathy approach,in

which individuals are allowedto make judgements comparing any two other individuals in two differ-

ent situations, an approach which Kotaro Suzumura has thoroughly analyzed (Suzumura 1981a,b).

Fairness requirements, such as no envy, which Suzumura has examined in the extended-sympathy

context, are more traditionally defined in our more parsimonious framework.

†Princeton University,Princeton, NJ, USA. Email: mfleurba@princeton.edu

‡CORE, Universit´

e Catholique de Louvain, Louvain-la-Neuve, Belgium.

The research leading to these results has received funding from the European Research Council under the European

Union’sSeventh Framework Programme (FP7/2007-2013) and ERC grant agreement no. 269831.

International Journal of Economic Theory 14 (2018) 35–50 © IAET 35

International Journal of Economic Theory

Inequality-averse well-being measurement Marc Fleurbaey and Franc¸ ois Maniquet

In Fleurbaey and Maniquet (2017a), two general families of well-being measures were charac-

terized on the basis of properties that considered how to compare indifference sets; note that if one

respects individual preferences, only indifference sets matter,not the par ticular bundle that is effec-

tively consumed. The most basic property is that an indifference set that is everywhere above another

one corresponds to a better situation. It is less obvious to deal with crossing indifference sets, and

in that earlier paper we proposed two principles dealing with crossings, which implied two different

approaches to well-being measurement. However, these results did not pin down specific measures

and remained at the level of general classes of measures.

In this paper, we propose an extension of the analysis that introduces a new set of properties

having to do with inequality aversion. These properties require that, the better off an individual in a

specific situation, the less of a well-being improvement follows from any given commodity bundle

increment to it. These properties turn out to pin down specific members of the families of well-being

measures, namely, the ray utility and the money-metric utility. The ray utility measures well-being

by the fraction of a reference bundle that is as good as the current bundle for the individual’s

preferences. The money-metric utility measures it by the income needed to obtain the current

satisfaction of the individual, at given reference market prices. These measures are in fact standard,

but have generally been considered to be rather arbitrary and merely used as examples. For instance,

Samuelson (1977) mentions the ray utility as an example of a utility function that could be used

in a Bergson–Samuelson social welfare function. The money-metric utility has been criticized by

Donaldson (1992) and recently defended by Fleurbaey and Blanchet (2013).

The well-being measures we justify in this paper are intended to be arguments of social welfare

functions, but the precise way of aggregating individual well-being remains outside the current

analysis. Remember, however, that considering indifference sets as we do here is sufficient to escape

Arrow’s impossibility and build Paretianand fair social welfare functions, as has been established by

several authors, including Suzumura (see Fleurbaey et al. 2005a,b).

The paper is organized as follows. In the nextsection we introduce the model and recall the results

obtained by Fleurbaey and Maniquet (2017a) with properties about the comparison of crossing and

non-crossing indifference sets. Then, in Section 3, we introduce the inequality aversion properties

and state the results characterizing the ray utility and the money-metric utility. Section 4 gathers the

proofs. Section 5 contains a brief conclusion.

2 Two general families

In our model, identical to Fleurbaey and Maniquet (2017a), there are Kdivisible goods. The con-

sumption set is X=RK

+and over this set, individual preferences are assumed to be continuous,

convex and monotonic.1Let Rdenote the set of all such preferences. A well-being measure is a

function W:X×R→R, such that W(x, R) is the well-being level of an agent consuming bundle

xwith preferences R. Observe that Wdoes not depend on any additional data; in particular, it does

not depend on subjective well-being, as the only subjective information used by Wis contained in

the ordinal preference ordering R.

Throughout the paper,we require Wto be continuous in x, and to respect individual preferences,

in the sense that for all x, x∈X,R∈R,

xRx

⇔W(x, R)≥W(x,R).

1Weuse >, >and to denote vector inequalities. Preferences Rare monotonic if and only if x>x

implies xRx

and

xximplies xPx

.

36 International Journal of Economic Theory 14 (2018) 35–50 © IAET