why measure inequality? a discussion of the concept of equality

DOI: 10.1111/j.1752-5209.2009.0030.x

Why Measure Inequality? A discussion of theconcept of equalitySophie ElliottUniversity of Otago, New Zealand

Foreword: Peter J. Lambert and Frank StahlerUniversity of Oregon, USA, and University of Wurzburg, Germany

In February 2007, we shared the teaching inan upper level Microeconomics seminar at theUniversity of Otago in Dunedin, New Zealand.Sophie Elliott was one of the students. Sophie’sscholarly term paper, ‘Why measure inequal-ity? A discussion of the concept of equality’,presented here in slightly abridged form, waseasily the best essay on equity and equality ei-ther of us had ever read. Sophie completed herdegree in November 2007 and was on the brinkof an exciting career. And then we learned ofSophie’s death. Sophie died on January 9th2008, just one day before she was supposed totravel to Wellington to take up her first posi-tion at the New Zealand Treasury. She wasbrutally attacked and stabbed to death in herown bedroom.

In her paper, Sophie examined the con-trasting viewpoints and analyzes of a dozenof the main thinkers - both philosophers andeconomists - who are today concerned with eq-uity as a fundamental value in society, and indi-cated at many points, gently but firmly, whatshe herself believes. We found Sophie’s essaystunningly to-the-point, thoughtful and mature.

Jean-Yves Duclos, editor of the Journal of Eco-nomic Inequality, wrote to one of us about So-phie’s paper in these terms: ‘It is a remarkablepiece of research for such a young person. Injust a few paragraphs, the paper is able to strikeright to the core of welfare economics and tograsp with many of its complex philosophicaland ethical issues. Elliott certainly had a beau-tiful mind’.

In Sophie’s paper, the reader will find manyquestions to ponder. Should a policy be aboutthe people who deserve to be treated equallyrather than those who are treated equally? Howshould we treat benevolence in society? Do wewish to make people in society equal in terms ofthe things that do generate welfare, or in termsof the things that should generate welfare? Doesthe prosperity of one person negatively affectthe fortunes of some others? What do we meanby equal opportunities, and by equal reward forequal effort? Are market-generated outcomesnecessarily unfair? If so, is the lack of compen-sation for this unfairness morally wrong?

We have both felt Sophie’s loss, in this awfulcalamity, very deeply indeed. We are proud tohave been her teachers and we commend herinspirational essay to the readers of Oxonomics.There was something magical about Sophie El-liott - everybody who knew her felt it, and ev-erybody who knew her loved her, all but for oneperson. Rest in peace, Sophie.

Introduction

Equity is probably one of the most fundamentalvalues common to all people in a society. Equitycan be elusive, however. It is usually definedin terms of how equals are treated by govern-

32 Oxonomics 4 (2009). c© 2009 The Author. Journal compilation c© 2009 The Oxonomics SocietyPublished by Wiley-Blackwell

Why Measure Inequality? Sophie Elliott

ment policies and the legal system, and how wedecide who these equals are. The concept ofequality is multifaceted; the literature on theo-ries of equality is immense and the applicationof these theories is complex. Nevertheless, thegreat philosophical and legal minds of our timerecognize that a comprehensive investigation ofequality, and its measurement, is vital in thequest for justice. In this essay, I consider someof the major theories of equality as defined byvarious players in the literature, each of whomattempts to answer the question, ‘What type ofequality will promote equity in society?’

Equity, equality and efficiency

Horizontal equity is conventionally defined as theprinciple that equals should be treated equally,and vertical equity, that unequals should betreated unequally. Galbiati and Vertova (2008)focus on horizontal equity, arguing that theabove definition is flawed, as policies, by de-fault, treat those they define as ‘equals’ equally.The correct assessment of the horizontal inequitycaused by a policy is in the policy’s choice of rele-vant characteristics1 that determine the ‘equals’.If these characteristics are seen to be norma-tively inappropriate in reference to the intendedeffect of the policy, then the policy is said to behorizontally inequitable to some degree. That is,if those who should be treated as equals underthe policy, in that they share relevant charac-teristics, are treated as unequals by the policyrule, the policy is considered unfair under thisdefinition. It is as Peter Westen states in hisbook on equality (see Westen, 1990): the pre-sumption of equality is that people should betreated equally in the absence of good reasonsfor treating them unequally, such as a differencein relevant characteristics.

Lambert and Yitzhaki (1995) explain thathorizontal and vertical equity serve different pur-poses. The former is an idea relating to justice,helping to ‘ensure that the law does not serveanybody’s self-interest’. The latter is a principlethat prevents warped applications of the former,

and, if satisfied, is sufficient to implement theformer. Consider a country with two types ofpeople, those who love ducks and those whohate ducks. If the government gives everyonethree ducks each, it has treated all the duck-lovers equally, and all the duck-haters equally,thus satisfying the principle of horizontal equitywhen given its conventional definition. How-ever it does not satisfy the principle of verticalequity, as the two distinct groups are treatedthe same in relation to a characteristic thatmust be considered relevant in the distributionof ducks. Distributing the ducks in this appar-ently even-handed way actually results in anunfair outcome; hence we have an example ofan equal distribution that does not achieve itsfundamental aim of equity.2 This illustrates theimportance of considering both horizontal andvertical equity in theories of equality.

We can consider taxation with reference tothe tenets of horizontal and vertical equity. InNew Zealand, we have a progressive income tax-ation system, where the tax rate on a marginaldollar of income is a function of one’s total in-come. Two people with equal incomes underthis system will contribute the same amountof tax to government revenues each year. Inthis way, this system is treating equals as equals.But income taxation is only one half of the redis-tribution story. Also pertinent are the variouswelfare programmes that provide income sup-port to those deemed to be in need. Are equalstreated equally (and unequals unequally) in thisprocess? Certainly, if two people have the samecircumstances, they will both be eligible for thesame benefits. But from Galbiati and Vertova’sdefinition of horizontal equity, that ‘the individ-uals treated equally by a policy should be thosewho are deemed normatively equals’, we see thatthe correct question to ask is, ‘Do the eligibilitycriteria for New Zealand welfare programmesinclude all and only those characteristics consid-ered normatively relevant for the redistributionof income to achieve equality?’ The answer tothis question is complex, and beyond the scopeof this essay3, however it is a pertinent one for

1Note that these characteristics should be determined by someone wishing to evaluate the policy, not by thepolicymaker.

2One might also wonder about the equity of awarding ducks to duck-haters in terms of duck welfare!3But see my University of Otago dissertation, ‘Participation in New Zealand Welfare Programmes: Just Plain

Good (Cents) Sense?’ an edited version of which appears as Elliott (2008).

Oxonomics 4 (2009). c© 2009 The Author. Journal compilation c© 2009 The Oxonomics Society 33

Sophie Elliott Why Measure Inequality?

policy makers concerned with achieving greaterequality in the distribution of income in NewZealand.

An important consideration in the pursuit ofequity is whether equality is an efficient meansof achieving it. Few would argue that equality(under whatever definition is chosen) is a ‘fun-damental property’ of an ideal society. Givenan alien society of clones — individuals bornequal in every way, with identical tastes andabilities4 — for whom equality naturally exists,we would not say prima facie that this societywill be inefficient. Equality may be inefficient interms of the process of achieving equity, but notin and of itself. A progressive taxation schemecauses disincentives to effort for both the bene-factors and the beneficiaries: the former feelingunder-rewarded for their efforts and the latterbelieving any lethargy on their part to have ledto worthwhile benefits. These disincentives arerepercussions of the distortionary effects of theprogressive tax, which skew employment awayfrom its optimal level, lowering the effectivenessof the scheme on the economy as a whole. Whilethe solution to the problem of taxation beingdistortionary is far from clear, there must bevalue in the acknowledgement that equality andefficiency are not necessarily mutually exclusivestates.

The equality of welfare

We shall consider three major theories of equal-ity, beginning with the equality of welfare. Thistheory is discussed (and rejected) by egalitar-ian philosopher Ronald Dworkin (see Dworkin(1981, Part I)), where resources are distributedto achieve the most equal distribution of wel-fare possible. Equalizing welfare as opposedto resources has the theoretical advantage thatit focuses on making people equal in what isfundamentally valued by each of them, but thepractical disadvantage of having a basis thatis intangible. In short, it is a nice ideal, butessentially unworkable. Nevertheless, Dworkinscrupulously considers the theoretical implica-tions and concludes that impracticability aloneis not the only downfall of the equality of wel-fare.

Dworkin divides theories of equality of wel-fare into two categories: success theories andconscious state theories. The former view wel-fare as a function of a person’s success in ful-filling their preferences, goals and ambitions,whereas the latter attempts to make peopleequal in some aspect or quality of their lives,such as the enjoyment they gain from living. ‘Agood society is one which treats the conceptionof equality that society endorses, not simply asa preference some people might have but as amatter of justice that should be accepted byeveryone because it is right,’ Dworkin writes.How should we treat benevolence in society, forexample? Should the altruistic be given more re-sources, since they are likely to act less selfishly,spending additional resources in a way that willbenefit society as a whole? Under the equalityof success, it is selfish people who need extracompensation, since they do not benefit fromreductions in inequality unless those reductionsdirectly affect their level of welfare. In responseto this conundrum, Dworkin writes, ‘It is surelya mark against any conception of equality that itrecommends a distribution in which people havemore for themselves the more they disapprove[of equality].’

Success theories of the equality of welfare aredivided into theories pertaining to relative suc-cess and those relating to overall success. Theequality of relative success requires that peopleare equal in the degree to which they fulfill theirgoals. However this is a problematic formulation.Imagine two people with identical qualifications,jobs, incomes, assets and families, but differ-ing in that the standards of the first are as lowas the standards of the second are high. Thefirst believes he has achieved the perfect life: hewants for nothing and is happy. The second be-lieves herself to be a failure, feeling that she hasadded little value to the world. The disparitybetween these two individuals is a difference intheir beliefs, not a difference in their lives. Doesanyone really believe the ‘failure’ deserves moreresources than the ‘success’?

Perhaps the concept of overall success, wherea person’s situation is compared with some setideal (or anti-ideal), is less problematic. Thisjudgement is a more difficult one for a person

4One finds this an amusing thought until the irony that this is the basis for many an economic model dawns.

34 Oxonomics 4 (2009). c© 2009 The Author. Journal compilation c© 2009 The Oxonomics Society


to make than one regarding their relative suc-cess however, and one wonders about anyone’sability to summarize their own success in life.There is also the complication that a person maybe fooled by the illusion of success. To makethis point, Dworkin asks which the reader wouldchoose, before beginning their life, between be-ing a success in life, but thinking that they havefailed, and being a failure in life, but believingthemselves to be a success. I would be verysurprised to find a person who does not hesitatein his answer upon first hearing this question.Dworkin eventually rejects overall success theo-ries as he considers the concept too difficult forpeople to evaluate.

Another problem related to equalizing wel-fare is the inefficiency inherent in the processdue to the heterogeneity of individual agents.Consider a group in society who are difficultto please because of their so-called ‘champagnetastes’.5 In order to be as happy as a personwithout expensive preferences, these people needfar more resources. Should the social decisionmaker ignore these people in order to preserveaverage utility, even if, in doing so, he preventsthe attainment of ‘perfect equality’ and discour-ages the formation of new, interesting prefer-ences? Dworkin writes that discouraging expen-sive tastes ‘might well end, for all we know, in adull, conformist, unimaginative, and otherwiseunattractive community’. Clearly this shouldnot be taken to the point of absurdity, how-ever. A person who cultivates expensive tastesin order to be allocated more resources, or aneccentric who shuns normal society to live anunconventional life, should not be pampered bythe authorities, if for no other reason than thatit would encourage such antisocial behaviour inothers.

The consideration of champagne tastes givesrise to another policy-related question: do wewish to make people in society equal in terms ofthe things that do generate welfare, or in termsof the things that should generate welfare? Wecan imagine a situation in which certain mem-bers of society get the most pleasure from apastime the state considers indecent, say, writ-

ing economics essays. In order to equalize thewelfare of these people, should the social deci-sion maker require some of them to increase thisactivity, even though society on average disap-proves of it? This writer fears that a governmentwhich answers no to this question is at risk ofbecoming totalitarian. Certainly, while we maydisapprove of many of the activities of others,few of us wish to lose our liberty, perhaps themost sacrosanct of all the rights we have.

One influential author in the literature oninequality is Amartya Sen, who discusses theequality of welfare in Sen (1980). Sen describesutilitarian equality, which is achieved when themarginal utility of each person in society isequal and total utility is maximized. Advo-cates of utilitarianism argue that equalizingmarginal utility implies that everyone’s inter-ests are treated equally. Sen quotes Harsanyi’s1977 claim that utilitarianism has an exclusiveability to avoid ‘unfair discrimination’ between‘one person’s and another person’s equally urgenthuman needs’. If we accept the assumption ofdiminishing marginal utility, utilitarianism pro-vides support for rich-to-poor transfers, whichwill decrease the utility of the rich person lessthan they increase the utility of the poor per-son. Equalizing marginal utility thus is not onlyhailed as treating equally the interests of all,but is also said to result in higher total utility(provided we believe that these sorts of transfersdo not affect the level of output available forredistribution in an economy). Sen criticizesutilitarian equality as a very narrow concept,concentrating on distributional questions at themarginal level only, ignoring, for example, theextra resource claims of disadvantaged people.

Sen argues that ‘the concept of needs doesnot get adequate coverage through the informa-tion on... utility’. He states that the frameworkfor assessing equality is missing some notion of‘basic capabilities’, insisting that a person whois unable to do basic things should be compen-sated with more income.6 Is it a well-foundedconception, that people should have equality inthe basic things they are able to do? Considerthe example of a ‘jolly cripple’. He is happy with

5We will see shortly that this discussion can also be applied to those with disabilities.6One might note the similarity between this concept and John Rawls’ concept of primary goods, which he proposed

should be equalized instead of utility in his seminal book (Rawls, 1971) .



his lot, despite his unfortunate circumstances,and has an average level of utility. In consid-eration of the favourite economic truism thatresources are scarce, it does not seem expedientto redistribute resources towards jolly cripplespurely on the basis of their disadvantage.7 Pro-vided these individuals have access to the sameopportunities in life as those with normal capa-bilities, there seems to this writer no reason toallocate to them additional resources to furtherimprove their level of utility. On that note, wemove on to a consideration of another type ofequality: the equality of resources.

The equality of resources

Dworkin (1981) considers in detail the equalityof privately owned resources in an economy, stat-ing that the aim of this theory is that ‘an equalshare of resources should be devoted to the livesof each person’. He notes that economic marketshave long been blamed for resulting inequalitiesin the distribution of resources, despite the gen-eral belief that they foster liberty, efficiency andprosperity. Indeed, it has been suggested thatthere is a trade-off between equality and thesestates of economic wellbeing; a statement whichDworkin refutes, arguing instead that the mar-ket system is essential as a foundation for anytheory of resource equality. Specifically, the mar-ket mechanism for determining the value of aresource - an auction in some form or other -allows a natural distribution of resources thatensures that each unit of resource is awardedto the individual who gains from it the highestbenefit.

Dworkin describes an auction amongst ship-wreck survivors on an island with plentiful natu-ral resources, each of whom is given an identicalnumber of clamshells with which to bid. This ex-ample satisfies what Dworkin calls the envy test:at the completion of the auctioning process, norational individual will strictly prefer another’sbundle to his own. The author says that marketauctions are ‘an institutionalized form of theprocess of discovery and adaptation that is atthe center of the ethics of [the theory of equalityof resources]’. The distribution of resources that

results ensures that each person pays for the lifehe wants to lead, where the value of this life ismeasured as the resources given up by others sothat he can do so. As individuals with varyingskills employ their resources differently over time(altering the distribution of resources across thecommunity), will the envy test continue to hold?If envy was simply a case of desiring anotherperson’s resources, the envy test would fail assoon as the distribution of resources changeddue to the hard work of some and the indolenceof others. Dworkin suggests instead that envyneeds to be defined over something broader thaneach individual’s stock of resources at a point intime - it should include some consideration of theeffort required to improve one’s resource bundle.It is apparent that a redistribution based solelyon what we might call ‘consumption envy’ wouldresult in huge disincentives for effort. Dworkinwrites, ‘Since people are different it is neithernecessary nor desirable that resources shouldremain equal thereafter and quite impossiblethat all envy should be eliminated by politicaldistribution’, adding later that the distributionof resources should be allowed to be ‘ambitionsensitive’ but not ‘endowment sensitive’.

Dworkin also argues that provided there isinitially equality of resources in an economy,the prosperity of one person will (negatively)affect the prosperity of some others within thateconomy. He supports this claim by giving theexample of a successful, wealthy person biddingup the price of other goods he demands, there-fore making it more difficult for others to affordthese goods. One could argue however, thatthe successful person, through his effort andnatural ingenuity, may have in his occupationmade some good more efficiently than otherscould have made it, therefore reducing its price(in a perfectly competitive world); it does notseem certain to this writer that a prosperousperson will necessarily make worse the fortunesof others.

The jolly cripple strikes again in the equalityliterature, as Dworkin considers his plight fromthe perspective of equality of resources. Theauthor suggests that perhaps mental and phys-ical powers be considered in conjunction with

7In fact, Dworkin goes one step further than this and argues that the transfers required to make equal the welfareof handicapped and non-handicapped people may be very inefficient in that they drastically reduce total welfare.



the other resources with which people are en-dowed. An initial equality of resources could beachieved by transfer payments made to disadvan-taged people, before all in society are left to liveout their lives undisturbed by government inter-vention. But how should a social decision makerdecide who is disadvantaged? Perhaps a ‘normallife’ is not something that can be pinpointed, butinstead a distribution of capabilities, where adisadvantaged person is below some sub-averagethreshold of this distribution. Dworkin notesthat no transfer would be capable of compensat-ing completely for certain disabilities. Consider,for example, how much you would be willing topay to avoid full body paralysis. For many of us,the answer is, ‘everything I have’. This suggeststhere may be no upper bound on compensation,and thus no way to ensure that handicappedpeople, through resource redistribution, havethe same opportunities as able people.

The equality of opportunity

The equality of opportunity inherent in an econ-omy is discussed as two distinct principles byRobert Sugden (Sugden, 2004). The first, re-ferred to as ‘starting-line equality’, states thateveryone should be able to choose their life froman ‘equally rich range of options’. This is anobjective requiring the equalisation of resourcesto ensure equal opportunity before one’s lifecommences and any decisions are made. Thesecond states that if agents expend equal effort,they should be compensated with equal rewards.This form of equality is designed to foster free-dom and responsibility: freedom to choose thelife one wants to lead, and responsibility to ac-cept the consequences of this decision.8 It isexpected that the reward received will be a func-tion of the choices made, but it should not bea function of circumstances beyond the controlof the individual. This idea appears frequentlyin the literature on equity and equality, and isdiscussed in detail by John Roemer (1998, 2006).

Roemer considers equality by evaluating an‘advantage’ and its distribution across a popula-tion. This advantage could be income, education

or health; or any other societal outcome that isconsidered significant by the members of thatsociety. Roemer proposes that a person’s ad-vantage should be thought of as a function oftwo main factors. The first is the person’s cir-cumstances, defined as environmental factors ofa social or economic nature, in addition to anygenetic characteristics of the person (such asrace, sex, natural talents, and so on) that givethem an advantage or disadvantage with respectto the variable of interest. Circumstances, bydefinition, cannot be affected by the individual;a person with ‘good circumstances’ might bedeemed ‘lucky’ (this idea is discussed in moredetail in the following section). The secondmain factor determining advantage is effort, alsocalled ambition or drive, which is a catch-all forany part of one’s life an individual has controlover and thus must take responsibility for. Ifthe advantage is education, a boy living in apoverty-stricken area and having uneducatedparents may be said to be disadvantaged; yethis poor grades might also be the result of histenacious refusal to do his homework. When weconsider redistribution of resources, if we ignoreeffort as an explanatory variable, this boy will beawarded resources such that he is compensatedfor his idleness, a result that surely cannot beoptimal. Another determinant of advantage isthe policy that is effective in society, which, asdemonstrated in the preceding example of thedisobedient boy, can have significant affects onincentives and efficiency.

How can we partition advantage into the partdue to circumstances (which are to be compen-sated for) and that due to effort? Roemer sug-gests partitioning society into groups of circum-stantial type.9 A distribution of effort withineach circumstantial type should then be formed,so that effort (as described by a quantile value)can be compared across types, eliminating thebias of circumstance. If there is equality of op-portunity, two people who are in the same placeon the effort distribution of their distinct typesshould have the same level of advantage. ‘Thephilosophical idea behind equality of opportu-

8I am reminded of an interesting line from the song ‘God is a DJ’, by the artist Pink: ‘You get what you’re givenand it’s all how you use it’.

9Clearly not all circumstances can be taken to be relevant in this exercise or we would have N groups, eachcontaining one distinct individual.



nity,’ Roemer writes, ‘is that individuals shouldnot be held responsible for their circumstances,but it is morally all right to hold them responsi-ble for their effort.’

Dworkin states that redistribution should off-set the effects of different circumstances withoutchanging the consequences of a person’s occu-pational choice. That is, it must not distortthe incentives associated with various ways oflife (ignoring the possibility that the governmentmay wish to discourage certain occupations). Asoutlined above, this is a challenging objectivefor a redistributional tool: how can we knowwhat part of a person’s situation is due to effortor ambition, and what part is due to so-calledGod-given ability?10 There is no doubt thateffort and circumstances such as natural talentare positively correlated, yet it is more complexthan this: they may be intertwined in a waythat would make it impossible to separate onefrom the other. We do see occasional examplesin society of people with much natural abilitybut no ambition, and of talentless individualswho bubble with diligence, but for the most part,people lie between these two extremes, makingthe problem of isolating the two effects a thornyone.

In response to this problem of compensatingfor poor circumstances, Dworkin discusses a hy-pothetical insurance market, for the purpose ofdetermining how income should be redistributedvia a taxation scheme based on endowmentsof talent. The theory is that this hypotheticalmarket determines an income threshold belowwhich a compensatory sum is paid out to thoseinsured against the risk of being endowed withwhat is considered an unsatisfactory level oftalent. The market determines an appropriatepremium associated with this income threshold,and this premium becomes the levy in our taxa-tion scheme. Everyone pays the tax (we assume),but some people–ironically because they ‘lose’in life–win in the insurance gamble, and end upwith positive net transfers from the governmentin the form of income support.

This theoretical idea is problematic in morethan just its impossibility. The tax paid by each

person is the same in absolute terms, though theproblem can alternatively be solved through aninsurance premium that is an increasing func-tion of income - corresponding to a progressivetaxation system. The welfare payments made tothose under the income threshold are designedto compensate exactly for the difference betweenthese persons’ earned incomes and the threshold.But once the labour market opens, how can weensure that people do not flout the system byfeigning ineptness, in order to gain a higher levelof income support? Theoretical considerationsaside, moral hazard is a very relevant problemin reality. There are entire government depart-ments in all Western-world countries devotedto the enforcement of eligibility criteria withintheir social welfare systems. The level of admin-istration required to ensure the smooth workingof a chosen taxation scheme begs a question: isthe generated inefficiency worth the achievementof a more equal society?

The role of luck

An extension of equality of opportunity con-siders the role of luck. Lefranc et al. (2006)introduce, in addition to circumstances and ef-fort (where the latter is considered an acceptablesource of inequality, as in Roemer), the possi-bility of outcomes being determined in part byluck (as exogenous uncertainty). They argue forcompensation of those affected by bad luck.

Sugden argues that the pure equality of op-portunity theory does not protect people againstadvantages or disadvantages arising from luckin the form of unanticipated market outcomes.Surprise outcomes spring from various sources:risk-taking entrepreneurs who introduce newproducts to markets, not knowing ex ante howsuccessful the available technology will be inproduction or what people will be willing to pay;industry- and firm-specific risk that is born byworkers who make the gamble of changing jobs;the choice faced by a high-school graduate ofwhether to obtain specific training in a field thatsuits his talents, sacrificing time and money withno guarantee of employment at the conclusion ofyears of effort. If we consider the representative

10The parallel between people who lack this sort of ability and people who have handicaps - since both are impairedin some way in the utilisation of their share of resources - is also noted by Dworkin. I am in agreement with his beliefthat most arguments which can be made for one, in terms of deserving compensation, can also be made for the other.



consumer’s optimization problem over a lifetime,the effects of market uncertainty will be huge.

The idea of luck is also considered byDworkin, who defines two major forms of luck.Option luck is the uncertainty in a person’s lifethat she chooses to accept by undertaking a gam-ble. Dworkin asks, should people be given differ-ent levels of resources due to differing degrees ofoption luck? There is an instinctive desire to an-swer no to this question - a person who choosesto gamble and loses simply experiences the con-sequence of their own choice. Dworkin makes aneven stronger argument, stating that if we taxedwinners to compensate losers in an attempt torestore the pre-gambling level of equality, wewould make pointless (and thus halt) the act ofgambling. The group of those risk-loving indi-viduals who would have chosen to gamble hada higher expected level of utility from gamblingthan they would have had otherwise: preventinggambling would lower the average utility level ofsociety. Also defined by Dworkin is brute luck,when unexpected events occur in a person’s lifethat they have no control over. Should the gov-ernment compensate those who are debilitatedby random, unpreventable cerebral aneurisms?The existence of an insurance market suggeststhat it should not: such a market allows thetranslation of brute luck into option luck. Pro-vided each individual has equality of access tothis market and to information pertaining tothe likelihood of brute luck, the argument forcompensation of unlucky stroke victims is weak.

One might wonder whether the existence ofluck is simply too strong for any kind of envy test(as described by Dworkin) to hold. Consider twopeople who are endowed with identical talentsand ambitions. When the labour market opens,one obtains employment as a fabulous moviestar earning millions and the other as an exoticdancer earning below the subsistence level. Thelatter surveys the success of her clone, express-ing that had she had the opportunity, she wouldhappily have done the work of the movie star forthe movie star’s wage -indeed, she would havedone it for much less than that wage. Few read-ers would find this example an exaggeration;certainly, there are numerous cases in realityof people whose earnings must far surpass theirmarginal product, and to describe many of these

cases as superbly good luck does not seem a hy-perbole. Sugden comments, ‘It is commonplaceto say that an individual’s success in her careeroften depends on whether she happens to be inthe right place at the right time.’ These cases ofbrute luck are certainly a challenge for the envytest, though we have considered the translationof brute luck into option luck by actual insur-ance markets. The problem is that, in reality,people are struck down with brute luck beforethey have the chance to insure. We return to thepossibility of compensation awarded to all theexotic dancers who would have liked instead tobe movie stars; this writer doubts whether, hadshe been born the former, any sum of moneywould compensate her fully for not having theluck of the latter. Dworkin writes, ‘The brutefact remains that some people have much morethan others of what both desire, through noreason connected with choice.’

Compensating for ill luck sounds like a niceidea, doesn’t it? We could imagine a governmentthat promises its citizens certainty in some vitalparts of their lives, in order to achieve equalopportunity and improve confidence in potentialoutcomes. After careful consideration, however,it is clear that this would be no ideal: the com-pensation of luck has indirect costs associatedwith it, such as losses of efficiency and distor-tions resulting from redistributions of resources.The compensation of individuals with bad luck -like trying to equalize the welfare of a fully paral-ysed person and a person with perfect health -may come with such a hefty price tag in termsof total utility losses that the idea begins to lookfoolhardy.

Roemer (1998) states that if people expendthe same effort but are compensated differently(perhaps due to uncertainty of market outcomes),this is unfair and the state should work to cor-rect for this asymmetry if it wishes to achieveequality of opportunity. Sugden is opposed toRoemer’s position, believing that ‘unfair’ is aloaded word to describe this situation. If we saythat it is unfair for equals to receive unequalrewards, do we mean that someone has actedunfairly to bring about the end result, or do wemean only to express regret about an unsatisfac-tory outcome? We are struck by good and badluck every day - few would argue that a social



decision maker could ever hope to level out theopportunities created by this luck. It seems thatRoemer is one of these few; he believes that ifsociety does not compensate those who are neg-atively affected by circumstances beyond theircontrol, it is guilty of a moral wrong. In protest,Sugden asserts that market-generated outcomescan be unfair, but that lack of compensationfor this unfairness is not morally wrong. Heconcludes that if we want the opportunities thatonly the free market will provide, we have tolive with unfairness, calling it ‘an inescapablefeature of a market economy’.

Concluding remarks

This paper has considered the issues surroundingthe question ‘Why measure inequality?’ includ-ing why equality is desirable (and thus worthy ofmeasurement), and a discussion of three majortheories of equality, as well as various extensionsand criticisms of these by some of the leadingplayers in the literature. It is difficult to sum-marize such a maelstrom of ideas in a few words.I refer instead to F.A. Hayek, who writes sopoignantly on the topic of equity and equality:

‘Are we not all constantly disqui-eted by watching how unjustly lifetreats different people and by see-ing the deserving suffer and theundeserving prosper?... [W]e docry out against the injustice... ifof many people whose endeavoursseem equally great, some succeedbrilliantly while others utterly fail...And we will protest against such afate although we do not know any-one who is to blame for it, or anyway in which such disappointmentscan be prevented’ (Hayek, 1976).

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Afterword: Equity and equality

Tony AtkinsonNuffield College, Oxford

In the year since Sophie’s tragic death, the issues that she treated so well in her essayhave come to the forefront of public debate. Her choice of subject exhibited considerable prescience.As people learn about the full extent of the crisis in the financial markets and about the behaviour ofthose whose decisions led to the crisis, they are increasingly posing questions about the underlyingmorality of these markets. As they contemplate the consequences for the real economy, with risingunemployment and increased insecurity, they are led to ask about the fairness or otherwise ofeconomic rewards. There is concern now, not with efficient markets, but with equitable economicexchange.Sophie starts her essay ‘equity is probably one of the most fundamental values common to all peoplein a society’. But, as she rightly goes on to say, the concept of ‘equity can be elusive’. This is whywelfare economics should return to a central role in the teaching of our subject. Economics is amoral science, and economists need to understand the consequences of different concepts of equality.Many of the ambiguities and disagreements about economic policy stem, not from differing viewsabout how the economy works, but from differences about the underlying values. Sophie’s essay is atestament to the way in which clear thinking and hard analysis can contribute to advancing ourunderstanding of these crucial issues.


why measure inequality? a discussion of the concept of equality

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