“Combining equity and utilitarianism”—additional insights into a novel approach

• Author: Johanna C. Gerdessen,Argyris Kanellopoulos,G.D.H. (Frits) Claassen
• DOI: http://doi.org/10.1111/itor.12415
• Date: 01 May 2018
• Published date: 01 May 2018

Intl. Trans. in Op. Res. 25 (2018) 983–1000

DOI: 10.1111/itor.12415

INTERNATIONAL

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RESEARCH

“Combining equity and utilitarianism”—additional insights

into a novel approach

Johanna C. Gerdessen , Argyris Kanellopoulos and G.D.H. (Frits) Claassen

Operations Research and Logistics, Wageningen Universiteit,The Netherlands

E-mail: joke.vanlemmen@wur.nl [Gerdessen]; argyris.kanellopoulos@wur.nl[Kanellopoulos];

frits.claassen@wur.nl [Claassen]

Received 1 September 2016; receivedin revised form 28 December 2016; accepted 15 March 2017

Abstract

Recently, a novel approach (to be referred to as CEU) was introduced for the frequently arising problem

of combining the conflicting criteria of equity and utilitarianism. This paper provides additional insights

into CEU and assesses its added value for practice by comparing it with a commonly used extended goal

programming (EGP) approach. The comparison comprises the way of balancing equity and utilitarianism,

the number and spacing of solutions, discrete versuscontinuous nature, method-specific parameters, distance

to the Pareto front, and computationaleffort. CEU balances between equity and utilitarianism in a way thatis

basically different from using a convex combination of these twocriteria. Moreover, CEU’sparameter has an

intuitive interpretation. The set of solutions generatedby CEU is smaller and more widely spaced than EGP’s

set of solutions, which can be an advantage for the decision maker. CEU generates solutions on the Pareto

front of the decision maker’s n-criteria problem. However, CEU’s way of balancing equity and utilitarianism

causes a (small) distance to the Pareto front of the associated bicriteria problem on the aggregate criteria.

Reporting this distance will support the decision maker to assess whether the achieved balance is worth its

price. Using CEU may require a larger computational effort than using EGP.

Keywords:multiple criteria decision analysis; multiple objective programming; goal programming; comparison

1. Introduction

Hooker and Williams (2012) introduce a novel approach to combine the often conflicting criteria

of equity and utilitarianism in a single mathematical model (from here on referred to as CEU).

To the best of our knowledge, no follow-up research has been reported that compares CEU with

a commonly used approach for combining equity and utilitarianism. Neither have any additional

insights been generated regarding the properties and (dis)advantages of CEU. This paper provides

additional insights into CEU by comparing it with a commonly used goal programming approach

in a practical context.

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984 J. C. Gerdessen et al. / Intl. Trans. in Op. Res. 25 (2018) 983–1000

Goal programming can be regarded as one of the most widelyused multicriteria decision-making

techniques (Caballero et al., 2009), and is often cited as the “work horse” of multiobjective op-

timization (Charnes and Cooper, 1977; Romero, 2004). Romero (2001) introduces extended goal

programming (EGP) to combine the often conflicting criteria of equity and utilitarianism. The

achievement function of EGP balances between equity and utilitarianism by minimizing a convex

combination of the maximum deviation from a goal (equity) and the weighted sum of deviations

from all goals (utilitarianism). A dimensionless parameter λis used to control the importance of

equity and utilitarianism in the achievement function. Romero (2004) states that the right choice

of the achievement function is a key element for the success of a goal programming model; if the

chosen achievement function is wrong, then it is very likely that the decision maker will not accept

the solution. Romero (2004) also points out that determination of the precise value of parameter λ

is a key question that is still open. The problem is how to justify and interpret any particular value

of λ(Hooker and Williams, 2012). Jones and Jimenez (2013) recommend to carry out sensitivity or

parametric analysis on λ. However, the problem of determining the appropriate value of λremains

unsolved.

Hooker and Williams (2012) introduce a novel approach to combine equity and utilitarianism

(CEU) in a single mathematical model. For formulating equity, CEU uses the maximin principle

of Rawls (1971), that is “one seeks to allocate goods so as to maximize the welfare of the worst

off.” Hooker and Williams (2012) argue that most people regard it as unreasonable to take a

Rawlsianpolicy to its extreme. Hence, the authors propose to switchfrom a Rawlsian to a utilitarian

criterion when inequality exceeds a threshold value . This has the effect of adhering to a Rawlsian

criterion unless the decrease in total utility is too great (Hooker and Williams, 2012). Hooker

and Williams (2012) describe CEU’s parameter as the level of inequality at which efficiency

considerations takeover. So,both EGP and CEU are single-parameter approaches for combining the

conflicting criteria of equity and utilitarianism. Therefore, we investigateCEU by comparing it with

EGP.

This paper aims to contribute to the insight into the properties and (dis)advantages of CEU and

to assess its added value for practice by comparing it with EGP. The comparison comprises the

way of balancing equity and utilitarianism, method-specific parameters and their interpretation,

location of the solutions, number of solutions, differences between neighboring solutions, discrete

versus continuous nature of the methods, distance to the Pareto front, and computational effort.

As a practical case, we use a diet-modeling problem. In order to provide a self-contained paper,

Section 2 summarizes CEU and Section 3 outlines the core of the diet-modeling case.

2. Combining equity and utilitarianism

Hooker and Williams (2012) suppose that a population consists of individuals (or classes of indi-

viduals), and the decisions result in an allocation of utilities u1,u2,...,unto these individuals. The

authors present a model that maximizes the utility of the worst off—that is, maximize(mini{ui})—

unless this takes too many resources from the others. For the two-person case, the switch from

a Rawlsian1to a utilitarian criterion takes place when inequality between u1and u2exceeds a

1Here, we follow the terminology of Hooker and Williams (2012) who denote mini{ui} as the Rawlsian criterion.

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2017 The Authors.

International Transactionsin Operational Research C

2017 International Federation of OperationalResearch Societies