distributional orderings: an approach with seven flavors

Theory Dec. (2012) 73:381–399DOI 10.1007/s11238-011-9243-x

Distributional orderings: an approach with sevenflavors

Yoram Amiel · Frank Cowell · Wulf Gaertner

Published online: 1 April 2011© Springer Science+Business Media, LLC. 2011

Abstract We examine individuals’ distributional orderings in a number of contexts.This is done by using a questionnaire-experiment that is presented to respondents inany one of seven “flavors” or interpretations of the basic distributional problem. Theflavors include inequality, risk, social welfare and justice.

Keywords Social welfare · Inequality · Justice · Risk · Questionnaire experiments

JEL Classification C13 · D63

1 Introduction

Do distributional orderings have the “right” shape? The question is relevant for severalfields of economic analysis including individual choice under risk and the evaluationof inequality. At its heart is a fundamental axiom of distributional analysis concerningmean-preserving spreads. The axiom is fundamental in two senses: first, it is com-monly applied to a broad range of problems concerning distributional comparisons,irrespective of context; second, a version of it is often regarded as essential in char-acterizing risk and inequality measures. In this article, we investigate whether thisfundamental axiom is really appropriate. Using a questionnaire experiment in seven

Y. AmielRuppin Academic Center, Emek Hefer, Israel

F. CowellLondon School of Economics, London, UK

W. Gaertner (B)Universität Osnabrück, Osnabrück, Germanye-mail: [email protected]

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different distributional contexts—the seven “flavors” of the title—we examine the waythat people appear to compare distributions in practice.

The variety of contexts include not only risk and inequality comparisons but alsocomparisons explicitly in terms of “welfare”. In fact, the welfare interpretation formsa particularly useful starting point, since it is capable of being expressed in one of twoways: (1) as social-welfare evaluations of income distributions and (2) as personal-preference evaluations of probability distributions over income. Orthodox economictheory makes a simple link between these welfare interpretations and inequality andrisk evaluations, respectively.

To address the question that we raised at the start, this article focuses on two centralfeatures of welfare economics as applied to income distributions. First, is the impliedshape of the contours used in people’s distributional comparisons independent of eco-nomic context? Although in the standard theory distributional judgments are assumedto be free of the context it would be interesting to know if, in fact, the flavor of the prob-lem has a significant effect. Second, is the essence of the fundamental principle—thatthese contours should respect mean-preserving spreads—consistently observed?

The article is organized as follows. Section 2 sets out the welfare-economic back-ground. Sections 3 and 4, respectively, explain the methodology of the paper andanalyse the results. Section 5 concludes.

2 Welfare orderings and risk orderings

We have deliberately set out to cover a number of distributional principles simulta-neously: let us begin with risk. The nature of risk comparisons developed in Rothschildand Stiglitz (1970) is founded upon the well-known concept of the mean-preservingspread (MPS)—any change in the distribution that can be represented as a sequenceof MPSs must represent an increase in risk. This concept is intended to apply both torisks in which an agent is personally involved and that thus may form the basis forindividual behavior, and also to risks that do not involve the decision-maker.

There is a well-known counterpart to the MPS principle in the welfare analysis ofincome distributions, namely the transfer principle. The view that income disparitiesare socially undesirable goes back at least as far as Plato. However, the explicit for-malization of the transfer principle is comparatively recent. Pigou (1912) formulatedthe principle in the context of just two persons, but was doubtful about extending it toother cases:

…economic welfare is likely to be augmented by anything that, leaving otherthings unaltered, renders the distribution of the national dividend less unequal.If we assume all members of the community to be of similar temperament, andif these members are only two in number, it is easily shown that any transferencefrom the richer to the poorer of the two, since it enables more intense wants to besatisfied at the expense of less intense wants, must increase the aggregate sum ofsatisfaction. In a community consisting of more than two members, the mean-ing of ‘rendering the distribution of the dividend less unequal’ is ambiguous.(pp. 24–25)

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Distributional orderings 383

An important step, reformulating the principle for an n-person society, was takenby Dalton (1920):

…we may safely say that, if there are only two income-receivers, and a transferof incomes takes place from the richer to the poorer, inequality is diminished[…] we may safely go farther and say that, however great the number of income-receivers and whatever, the amount of their incomes, any transfer between anytwo of them, or, in general, any series of such transfers, […] will diminishinequality. (p. 351)

This is the concept that was developed by Atkinson (1970), Kolm (1969), and manyother modern writers. The Dalton concept is the principle which permits the applica-tion of standard dominance criteria to be applied to the analysis of income distribution.It is embodied in the concept of S-concavity (Dasgupta et al. 1973; Sen and Foster1997) and standard interpretations of majorization (Marshall and Olkin 1979). Butthe concept clearly rests upon a specific interpretation of fundamental distributionalprinciples that may, perhaps, be overly strong.1

The wording of Pigou’s discussion clearly expresses social welfare in terms ofsums of individual utilities and appeals to diminishing individual marginal utility asa basis for a social preference for greater equality. Such a view might not commandmuch support today were it not buttressed by additional argument.2 The additionalargument for the sum-of-utilities approach to social welfare might be sought in theform of appealing to concern for inequality as a kind of consumption externality; thisis clearly an approach for which there is no close counterpart in terms of individualchoice under uncertainty. However, an alternative approach to the sum-of-utilities canbe found in the connection between inequality and risk analysis. This connection wasat the heart of Atkinson’s (1970) approach who pointed out a natural affinity betweenaversion to risk and aversion to inequality but there is an important further argumentbased on individual choices in the face of risk. Harsanyi (1953, 1955, 1977, 1978) in anumber of contributions made the case for considering social choice amongst incomedistributions as a reflection of individual choice amongst lotteries: this argument hasbeen expressed either in the form of an impartial outside observer of society or thatof personal involvement in that the individual decision-maker is supposed to imagineextending his preferences to social choice by imagining himself as being, with equalprobability, in the situation of any of the n members of society.3

A further argument for social concern with inequality can be based on the Rawl-sian approach to distributional justice (Rawls 1971). This explicitly uses the conceptof a “veil of ignorance” behind which an individual is imagined to make judgmentsabout alternative states of the society of which he is supposed to be member. We thushave a collection of six alternative “flavors” of a fundamental distributional issue, asillustrated in the first three rows of Table 1: do MPSs increase risk, increase inequality,

1 For example, a less demanding and relatively under-exploited concept is that of dominance in termsof differentials—see Marshall and Olkin (1979, pp. 275–276) for a general treatment, Moyes (1994) andBosmans (2007) in the context of inequality and Quiggin (1991) in the context of risk.2 For a summary of alternative approaches, see Moulin (2003, Chap. 2).3 We have discussed the detailed issues raised by the Harsanyi approach in Amiel et al. (2009).

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Table 1 Flavors of thedistributional problem

Negative connotation Positive connotation

Risk; non-involvement Harsanyi welfare; non-involvement

Risk; involvement Harsanyi welfare; involvement

Inequality Rawlsian justice

Fairness

lower social welfare, create a more unjust state of society? These flavors collectivelyform the basis for our investigation into distributional attitudes below. However, theremay be other reasons which drive people’s concern about income distributions; toallow for this we have introduced a seventh flavor under the vague term “fairness” forwhich we do not attempt to give a precise definition.

3 The Approach

The issue was investigated by using a questionnaire-experiment with student respon-dents using the method described in full in Amiel and Cowell (1999, 2007). The specialfeature of the current study was the simultaneous presentation of several distinct vari-ants of the basic welfare-economic issue within the same questionnaire-experimentalformat.

3.1 The questionnaires

Seven types of questionnaire—the seven flavors—were distributed in controlled ses-sions with student respondents during lecture or class time in 2003; within each session,the seven flavors of questionnaire were distributed randomly. The questionnaire typeswere similar to each other in most respects but differed in one key feature as explainedbelow.

As in Amiel and Cowell (2007), respondents were invited to consider distributionaljudgments in a mythical country, Alfaland. Alfaland consists of five regions that maydiffer from each other in terms of living standards (income) but that are internallyhomogeneous in terms of income. The realized incomes in each region of Alfalanddepend on which of two policies A or B is pursued in the near future. Respondentsare first asked to compare the distributional outcomes across the regions of Alfalandin each of six scenarios represented by pairs of income-vector; in each pair there is adistributional outcome from the A policy and an outcome from the B policy. Respon-dents are asked “In each of questions (1) to (6) two alternative lists of incomes A andB (in Alfaland local currency) are given. Each of these pairs represents the outcomesof the A-policy and the B-policy on the five regions in each of six different situationsin which Alfaland might find itself next year. In each case please state which policyyou consider XXX by circling A or B.” The symbol XXX stands for wording that isspecific to each of the seven flavors as follows:

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1. (Ineq) “…would result in higher inequality in Alfaland.”2. (Risk) “…would result in higher risk for a person immigrating to Alfaland.”3. (Risk-i) “…would result in higher risk for you as an immigrant to Alfaland.”4. (Hars) “would result in a better situation in Alfaland.” To create a sharp distinction

between this and the next flavor respondents here were also told “Imagine that youare invited to be an outside observer of Alfaland…”

5. (Hars-i) “…would result in a better situation in Alfaland.” In contrast to the flavorHars respondents were told “Imagine that you have been assigned to one of theregions in Alfaland with an equal chance of being in any one of the five regions.”

6. (Just) “…as more just for Alfaland.” In contrast to the flavors Hars and Hars-irespondents here were told “Imagine that you have been assigned to one of theregions in Alfaland, but you do not know which one.” This captures the idea of theveil-of-ignorance approach of Rawls (1971).

7. (Fair) “…would result in a fairer situation in Alfaland.”

The respondents are also told that they can indicate indifference between the twooutcomes by circling both A and B. Thus, seven types of questionnaire were createdfrom one. In each questionnaire, the pattern of numerical questions was exactly thesame as depicted in Fig. 1. Clearly, the A vectors can always be obtained from theB-vectors by a MPS (in other words a disequalizing transfer). This means that for Ineq,Risk and Risk-i a person answering in line with orthodoxy would check A, whereas forthe other four flavors the orthodox response is B.4 Note that the questionnaire makesno implication about the status quo; nevertheless, in considering the implications ofthe distributional comparisons in the six separate scenarios, it is interesting to notethe “implied transfer” in each pair of distributions. If we were to interpret A and B as“After” and “Before” : in two cases (questions 4 and 5) this involves relatively largeamounts; in one case (question 2) this involves a small amount from poorest to richest;in one case (question 3) a small transfer to the richest, but not from the poorest; andin two cases (questions 1 and 6) small transfers involving neither the poorest nor therichest. Question 4 is slightly different from the others in that the “implied transfer”involves a reordering.5

The numerical questions were then followed by a verbal question that covered thesame issues (see Sect. 4.4) and then a short list of questions on personal details; how-ever, as noted in the introduction to the questionnaire, each questionnaire-experimentalsession was run anonymously. Two examples of the seven flavors of questionnaire areprovided in Appendix.

3.2 The respondents

The seven flavors of questionnaire-experiment were run simultaneously with each ofthree groups of undergraduate students in Germany (Universität Osnabrück), Israel

4 Notice that, strictly speaking, this applies also in the case of risk if the principle of mean-preservingspreads is satisfied. The risk in A is unambiguously higher than the risk in B irrespective of whether aperson cares about that risk—whether a person is risk averse or not.5 In previous work with a similar format, we checked whether the order of the scenarios or the order ofpresentation of the A and B vectors matter; they do not (Amiel and Cowell 1999, p. 143).

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Fig. 1 The structure of the numerical questions

Table 2 Sample of respondentsGermany Israel UK All countries

Ineq 44 51 39 134

Risk 47 50 37 134

Risk-i 42 43 46 131

Hars 47 50 42 139

Hars-i 51 52 40 143

Just 49 52 42 143

Fair 52 49 42 143

All flavors 332 347 288 967

(Ruppin Academic Center) and the UK (London School of Economics). The break-down is as in Table 2 where it is clear that our goal of distributing the seven fla-vors in roughly equal proportions in each subgroup of respondents was achieved.Also the 1,000 odd respondents were spread fairly evenly among the threecountries.

4 Results

4.1 Numerical questions: overview

The overall results are depicted in Table 3. The leading column again gives the dif-ferent flavors of the questionnaires. The columns labeled Q1 to Q6 give the propor-tions of orthodox responses to each of the six numerical questions for each flavor ofthe questionnaire and the column labeled “joint Q1–Q6” gives the proportion of therespondents who gave the orthodox response to all six questions jointly.

Recall that in all seven flavors full support for the orthodox position would imply100 for all of Q1,…,Q6 and, of course, for the joint Q1–Q6 as well. It is striking

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Table 3 Proportion of orthodox responses in the whole sample (%)

Q1 Q2 Q3 Q4 Q5 Q6 Joint “NearQ1–Q6 miss”

Ineq 35.8 70.9 59.0 56.7 74.6 44.0 13.4 29.9

Risk 41.8 57.5 57.5 57.5 59.0 50.0 14.9 33.6

Risk-i 42.7 54.2 50.4 49.6 57.3 41.2 12.2 26.7

Hars 59.0 80.6 71.9 60.4 80.6 56.1 25.9 48.9

Hars-i 56.6 79.7 65.0 56.6 76.2 53.1 25.2 46.2

Just 60.8 89.5 79.0 62.9 78.3 76.2 32.2 54.5

Fair 51.7 83.2 72.0 60.8 74.8 58.7 25.9 42.7

All 50.1 74.0 65.3 57.9 71.8 54.5 21.6 40.6

that support for the orthodox position is so low—from 12 to under 33%, according toflavor.6

It might be argued that the criterion of getting all six answers in line with theorthodox view is overly demanding. If one allows for simple mistakes by the respon-dent it might be reasonable to consider “at least five out of six” as an indication of anorthodox response. Allowing for near misses yields the results in the last column ofTable 3.

Clearly allowing for one mistake slightly more than doubles the proportion of“orthodox” responses for negative-worded flavors (upper half of table) and slightlyless than doubles it for positive-worded flavors (lower half). But only in one case, Just,does the proportion of orthodox responses exceed 50%, even allowing for near-misses.

Now consider the pattern of responses, question by question. The relatively highdegree of conformity with orthodox views in the case of question 2 (column Q2) isnot, perhaps, a surprise. This involves an implied transfer between richest and poorest.Even in the case of risk these usually command a greater degree of support than isimplied by the responses to the other numerical questions, although it is much lowerthan on other flavors. Also note that across all the flavor patterns there is usually muchless support for the orthodox position in the case where the implied transfer is smalland does not involve either the richest or the poorest region (questions 1 and 6)—acommon-sense result that applies for all the flavors.7

One can say more. Most support for the orthodox position is found in those instanceswhere the richest position has to give (situations 2, 3, and 5) and the lowest position isnot necessarily the recipient. This manifests itself clearly in the lower half of Table 3,

6 The results corroborate the outcomes in previous studies run on different samples. For example, thequestion-by-question ordering of inequality and risk in Table 3 is the same as in Amiel and Cowell (2002);the size of the percentage value of orthodox responses for inequality and for risk is also similar to that inAmiel and Cowell (2002). Also the rank order of orthodox percentages on Hars, question by question, isthe same as for the preference-under-uncertainty question in Amiel and Cowell (2007).7 The case of question 5 (column Q5) is similar to that of question 2. Notice that a distributional comparisonthat conforms to the principle of dominance in terms of differentials (see Footnote 1) would concur withthe mean-preserving spread principle in the case of Q2 and Q5, but not on the other questions.

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in particular for Just but also for the other flavors, including the rather diffuse Fair.This is definitely not a maximin-guided behavior.

The fact that support for the fundamental distributional principle appears to differaccording to where the implied transfer occurs could be taken as a simple exam-ple of the importance of context. However, the fine detail of our results revealsanother important context effect according to “flavor” which we now wish to dis-cuss in greater detail. The point is that where the story-context in the question-naire focuses on something that is desirable (welfare, justice, fairness) rather thanundesirable (inequality, risk), support for the orthodox position appears to be muchlarger.8

4.2 Positive versus negative

If we compare the first three rows of Table 3 with the next four, it is clear that there is amarked difference in orthodox responses depending on whether the flavor concernedrepresents a positive or a negative statement of the distributional issues. It is evidentfrom the bottom part of the Table that Fair elicits responses that are very similar toHars but that Just almost always elicits the highest percentage of orthodox responsesamong all seven flavors. As it happens Just is also the flavor with the smallest numberof indifference responses—see Table 4: it may be that this is an intrinsically unam-biguous concept that does not leave much room for indifference. What makes thedifference between the two groups of flavors in Table 3? Although the first groupare all “negative” flavors and the second group all “positive” flavors, we should notconclude it is simply because they are positive/negative that the contrasting responsepatterns arise: the label “positive” just categorizes those flavors where the orthodoxposition is B�A (B should be circled) and for the “negative” group of flavors theorthodox position requires that A should be circled.9 Table 4 suggests that a clear-cut answer was more difficult to give when the issue was couched in terms of eitherinequality or risk. It is clear that for both risk flavors (Risk and Risk-i) the proportionof indifferent responses was much higher than for any flavor in the “positive” group( Hars, Hars-i, Just and Fair); this may be because respondents are risk neutral orbecause they find it harder to make up their mind. Further evidence on this is pro-vided by the number of cases where respondents abstained from giving a response.Although we did not provide an explicit option “cannot compare,” individuals werefree to leave particular (A, B) pairs unchecked and it is clear that this non-response wasnot distributed uniformly across flavors and questions as the following Table 5 shows.The highest non-response rate by flavor is Risk-i ; by question the non-response rateis higher for the cases where neither the richest nor the poorest region is involved inthe implied transfer.

8 Another interesting aspect is the supposed involvement of the respondent in the distributional comparison,in contrast to a position of Olympian detachment. This point is addressed in Amiel et al. (2009).9 Though we know from Tversky and Kahneman (1981) and other studies that a negative or positivewording can elicit a framing effect.

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Table 4 Proportion ofindifference responses in thewhole sample (%)

Q1 Q2 Q3 Q4 Q5 Q6

Ineq 38.8 12.7 17.9 6.7 6.0 26.1

Risk 37.3 20.1 20.1 16.4 14.9 24.6

Risk-i 32.1 16.8 19.8 11.5 16.8 26.7

Hars 25.2 11.5 12.2 7.2 9.4 23.0

Hars-i 26.6 11.2 14.0 8.4 9.8 17.5

Just 13.3 4.2 4.2 3.5 6.3 7.7

Fair 22.4 7.0 11.9 7.7 6.3 13.3

All 27.7 11.8 14.2 8.7 9.8 19.6

Table 5 Proportion of blankresponses (%)

a Calculated as nblanks/6Nb For all flavors combined

By flavora By questionb

Ineq 1.4 Q1 1.6

Risk 1.7 Q2 1.1

Risk-i 2.7 Q3 1.3

Hars 0.7 Q4 1.8

Hars-i 0.8 Q5 1.1

Fair 1.9 Q6 1.6

Just 1.3

Table 6 Orthodox responses:involvement versusnon-involvement (%)

Q1 Q2 Q3 Q4 Q5 Q6

Non-involved 50.5 69.2 64.8 59.0 70.0 53.1

Involved 50.0 67.5 58.0 53.3 67.2 47.4

4.3 Involvement

As we noted in the Sect. 1, an interesting issue concerning risk and certain aspects ofwelfare is that of involvement—whether the respondent is invited to place him/herselfin the situation about which the judgment is made. There is greater conformity withthe orthodox position when there is no involvement implied in the wording of thequestionnaire. Consider the percentage of respondents who replied in line with theorthodox position on each of Q1,…,Q6: it is clear that there is vector dominance ofthe non-involved compared to the involved in Table 6 (rows 1 and 2) where the riskand Harsanyi-welfare responses have been aggregated together.10

10 This vector-dominance result holds for the Harsanyi-welfare flavors taken separately (rows 4 and 5 ofTable 3); for risk flavors taken separately, the percentages are higher for the non-involved in five out ofsix questions (rows 2 and 3 of Table 3). Underlying this is a more complex pattern: males are more likelyto conform to the orthodox position if the issue is presented without involvement but that the situationregarding females appears ambiguous.

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Fig. 2 The alternatives in the verbal question (risk flavor)

4.4 Verbal question

The verbal question presented the underlying ordering principle precisely by meansof an example. Only the detail of the wording of the context differed amongst theseven flavors—the substance of the question was the same in all cases. Respondentswere asked to think about a mean-preserving income transfer from a richer region toa poorer region, other things being equal. They were then invited to select from fiveresponses, as illustrated in Fig. 2.

An important point to note here is that the question explicitly allowed for the possi-bility of multiple answers. The summary of results is depicted in Table 7. The leadingcolumn again gives the various flavors and the columns labeled a to d give the pro-portions of the respondents who selected the corresponding choice and no other. Foreach row, the numbers in categories a to d sum to less than 100 for three reasons: (1)responses in the category “none of the above” are not reported; (2) not everyone pro-vided an answer to this question; (3) people sometimes selected more than one of theoptions and with one exception these multiple choices are not reported. The exceptionis as follows. If one were to observe the standard theory strictly then the appropriateresponse should be d and nothing else. But apart from this strictly orthodox response itmay also be interesting to consider a “fuzzy-orthodox” case that allows for the respon-dent to select something else as well as option d. The proportion of respondents whodo this is given in column d+.

It is clear that the level of agreement with the strict orthodox response d is rathermodest, some 17 to 22%; which is broadly consistent with the answers to the numericalquestions— see the “joint Q1–Q6” column in Table 3. Relaxing the orthodox positionto the “fuzzy” version raises the level of agreement by about another 6 percentagepoints. Among the single-choice responses there is an obvious “winner.” Option bfocuses just on the extreme incomes in the hypothesised redistribution and leavesopen the impact of transfers not involving the extremes: this distinction is crucial aswe have seen from the numerical questions where it was clear that responses were morelikely to be orthodox if the richest or the poorest region of Alfaland were involved. Asis clear from column b of Table 7 support for this option dominates that for options

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Table 7 The verbal responses(%)

a b c d d+Ineq 7.1 34.9 15.9 20.6 23.0

Risk 10.9 30.3 21.8 21.8 26.9

Risk-i 9.9 28.1 22.3 20.7 24.0

Hars 14.5 25.2 22.1 21.4 28.2

Hars-i 8.0 30.7 22.6 16.8 19.7

Just 12.9 30.2 19.4 20.1 23.0

Fair 20.1 26.1 17.9 19.4 24.6

All 12.0 29.3 20.3 20.1 24.1

a, c or d. It is interesting to note that this strong support for b is consistent with thehigh proportion of orthodox responses for the second numerical question (the “Q2”column in Table 3) —question 2 involved a notional transfer involving only the richestand poorest in society.

As with the numerical questions there is less support for the orthodox answer (d ord+) if one is “involved” rather than “non-involved” (compare the Risk and Risk-i rowsand the Hars and Hars-i rows). However, in contrast to the numerical questions it isevident from Table 7 that there is no striking difference between positive and negativeflavors in terms of the degree of support for the orthodox answer.

4.5 Personal characteristics and orthodox distributional rankings

Let us look in more detail at the issue of positive versus negative formulation or con-notation. This is done using an ordered probit analysis of orthodox responses.11 Lety ∈ R be a measure of orthodox attitude. The underlying model is:

y = b1x1 + b2x2 + · · · + bn xn + ε (1)

where (x1, . . . , xn) is a vector of personal or other characteristics and (b1, . . . , bn) arecoefficients to be estimated. In principle y is unobservable, but we do observe categor-ical responses that result from y. Suppose that there is a collection q of m > 1 mutuallyexclusive response categories (Y1, . . . , Ym) where the Y j can be strictly ordered interms of orthodoxy of attitude. Specifically, let us take it that the individual’s responseis Y j if c j − 1 ≤ y < c j where c0 = −∞, cm = +∞ and (c1, . . . , cm−1) are alsoto be estimated. We investigated a number of interpretations of q and specificationsof Eq. 1 that determines y. The results from our three principal specifications of theordered-probit regression are given in Tables 8, 9, and 10. All three specifications usethe following definitions of independent variables

11 We also carried out a number of simple probit analyses where we modelled the probability that theperson gave an orthodox response either on one question in isolation or on all six questions together. Theresults from these were consistent with those from the ordered probit.

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• sex: equals 1 if reported male, 0 otherwise• age: in years• emp: 1 if employed before, 0 otherwise• pol: self-rated political views on a seven-point scale from extreme left (1) to extreme

right (7)• inc−10: self-rated income position of family looking back 10 years, on a seven-point

scale from extremely poor (1) to extremely rich (7).• inc+10: self-rated prospective income position of self looking forward 10 years,

coded as above.• ukd, deutd: dummies for respondents from, respectively, UK and Germany.

In addition specifications I and II (Tables 8, 9) use the following dummies:

• ssecon: takes the value 1 if student’s special subject is “core economics” as definedin the Appendix, 0 otherwise (specification I only)

• ssbroad: takes the value 1 if student’s special subject is “broader economics” asdefined in the Appendix, 0 otherwise (specification II only)

• negform: takes the value 1 if questionnaire flavor is Ineq, Risk or Risk-i, 0 otherwise.

In Tables 8, 9, and 10, the columns labeled q1, . . . , q6 focus on the ordered probitmodel applied to the responses for each of questions 1 to 6 taken independently. Ineach case, the response categories are

Y1 : strictly heterodox response to question

Y2 : indifference response to question

Y3 : strictly orthodox response to question.

Column q̄ interprets “orthodoxy” using a combination of responses to all six questions.Here the response categories are:

Y j : # strictly orthodox responses to questions 1–6

where j = 1, . . . , 6.In specifications I and II, it is clear that composite dummy negform is usually

significant—being confronted with a negative questionnaire that is phrased in termsof inequality or risk is more likely to produce heterodox responses than one that iscouched in the positive language of welfare; this confirms the impression from sum-mary statistics discussed in Sect. 4.2. However, there is a slight surprise: specializingin economics appears relatively unimportant (ssecon in Table 8) and remains fairlyunimportant even if one broadens out the definition of economics to related subjects(ssbroad in Table 9).

Specification III drops the subject dummies and replaces the simple negformdummy with flavor-specific dummies ineq, risk, risk-i, hars, hars-i and just: it is clearthat the three negative flavors ineq, risk and risk-i predispose a heterodox response onalmost all of the interpretations of “orthodoxy.” It is interesting that the hars dummyis significant for exactly two questions q1 and q5, i.e., in the case of those numerical

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Table 8 Responses to numerical questions—specification I

q1 q2 q3 q4 q5 q6 q̄

sex −0.0686 0.1003 0.1684‡ 0.0479 0.0090 0.1880‡ 0.1502‡

age 0.0049 0.0170 0.0295 −0.0208 0.0131 −0.0089 −0.0061

emp 0.0354 0.0026 −0.0474 −0.0195 0.0569 0.1525† 0.0600

pol −0.0661† −0.0425 −0.0514 −0.0070 −0.0170 −0.0257 −0.0557†

ssecon 0.1145 0.0056 0.1294 0.0514 −0.0099 0.0587 0.1283†

inc−10 −0.0148 −0.0478 −0.0392 0.0149 −0.0147 −0.0647† −0.0149

inc+10 −0.0005 −0.0159 −0.0667 −0.0034 0.0491 −0.0556 −0.0129

negform −0.3050∗ −0.6960∗ −0.3656∗ −0.0965 −0.3800∗ −0.3165∗ −0.5199∗

ukd 0.1078 −0.2529† −0.0076 0.0208 −0.0705 0.0245 −0.1208

deutd 0.1054 −0.2457† −0.1031 −0.1197 0.0879 −0.1140 −0.0634

† Significant at 10% level, ‡ significant at 5% level, ∗ significant at 1% level

Table 9 Responses to numerical questions—specification II

q1 q2 q3 q4 q5 q6 q̄

sex −0.0555 0.1040 0.1829‡ 0.0546 0.0155 0.1969‡ 0.1651‡

age 0.0035 0.0173 0.0269 −0.0213 0.0133 −0.0095 −0.0072

emp 0.0404 0.0092 −0.0469 −0.0142 0.0663 0.1573† 0.0654

pol −0.0639† −0.0430 −0.0478 −0.0067 −0.0179 −0.0252 −0.0538†

ssbroad 0.3283 0.2519 0.1806 0.3053 0.4288† 0.2920 0.4130‡

inc90 −0.0209 −0.0527 −0.0442 0.0103 −0.0197 −0.0704† −0.0214

inc10 0.0049 −0.0125 −0.0641 0.0000 0.0504 −0.0536 −0.0075

negform −0.3120∗ −0.7020∗ −0.3688∗ −0.1035 −0.3862∗ −0.3223∗ −0.5277∗

ukd 0.0507 −0.2859‡ −0.0544 −0.0264 −0.1200 −0.0219 −0.1938†

deutd 0.0596 −0.2441† −0.1603 −0.1394 0.0956 −0.1374 −0.1162


problems where neither the richest nor the poorest is involved in the transfer. In eachof the three specifications it appears that sex plays a role:12 On two questions specif-ically, male respondents are more likely to respond in conformity with the orthodoxposition.

5 Conclusions

We asked whether distributional orderings have the right shape. As we have discussed,the question can be posed more precisely as: Do the rankings implied in individuals’

12 This corresponds with what was found in Amiel and Cowell (2002). By contrast the country subsampleto which the respondent belongs plays only a minor role: being from UK or Germany (ukd, deutd) ratherthan Israel decreases the probability that an individual will respond in line with economic orthodoxy.

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Table 10 Responses to numerical questions—specification III

q1 q2 q3 q4 q5 q6 q̄

sex −0.0543 0.0966 0.1727‡ 0.0447 0.0126 0.1799‡ 0.1565‡

age 0.0033 0.0177 0.0270 −0.0220 0.0135 −0.0091 −0.0071

emp 0.0252 −0.0025 −0.0520 −0.0222 0.0432 0.1482† 0.0538

pol −0.0662† −0.0318 −0.0478 −0.0079 −0.0124 −0.0250 −0.0485

inc90 −0.0196 −0.0472 −0.0387 0.0140 −0.0154 −0.0682† −0.0174

inc10 0.0065 −0.0151 −0.0618 −0.0025 0.0510 −0.0435 −0.0092

ukd 0.0864 −0.2485† −0.0247 0.0167 −0.0689 0.0200 −0.1353

deutd 0.0519 −0.2433† −0.1586 −0.1445 0.0984 −0.1338 −0.1156

ineq −0.2612† −0.4600∗ −0.3448‡ −0.1290 0.0188 −0.2622† −0.3697∗

risk −0.0943 −0.7491∗ −0.3326‡ −0.0134 −0.3735‡ −0.1198 −0.4521∗

risk-i −0.1126 −0.8598∗ −0.5178∗ −0.2420 −0.3533‡ −0.3163‡ −0.5915∗

hars 0.2395† −0.0878 −0.0366 −0.0317 0.2747† 0.0379 0.0411

hars-i 0.1786 −0.1219 −0.2155 −0.1012 0.1271 −0.1333 −0.0792

just 0.1851 0.2692 0.1549 0.0240 0.1416 0.5044∗ 0.2581‡


perceptions of income distribution conform to the standard approaches to a broad classof economic problems? The short answer would appear to be “no” : across all sevenflavors of the study the number of respondents who give numerical answers that fitwith the “orthodox” position is relatively low. In this respect the principle of MPSdoes indeed appear to be “overly strong” as we mentioned in Sect. 2. However, thereis more to be said: two features of the structure of responses are particularly strik-ing. First, the positions of the worst-off and of the best-off always appear to be focalpoints. The questions that have implied transfers involving these extremes (Q2 andQ5) elicit similar responses across all seven flavors and these questions often attract amuch higher proportion of orthodox responses than other numerical questions. Whatis remarkable is the low degree of variation among the six different questions in theRisk and Risk-i flavors: it may be that these two flavors are conceptually speaking thehardest to evaluate or that, in connection to risk, small transfers, independent of wherethey occur, are not sufficient enough to change the evaluation of the respondents. Thesecond point concerns a class of flavors or contexts. As far as the numerical questionsare concerned there is evidently much greater conformity with the standard view onthe transfer principle if the context of the question is a “positive” (welfare, justice)rather than a ”negative” (inequality). This conclusion comes through strongly bothfrom Table 3 and from the role of the dummy negform in the regression analysis.

Appendix

The questionnaires

Following are two of the seven questionnaires (flavors Risk and Hars-i) that weredistributed to each of the response groups. The wording of the other five flavors can

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be inferred from the description in Sect. 3 and are also found on http://darp.lse.ac.uk/7flavors/. As explained in the text the experiment was run so that each respondent hadapproximately an equal probability of receiving any one of the seven questionnaires.

Risk questionnaire

This questionnaire concerns people’s attitude to risk. We would be interested in yourview, based on hypothetical situations. Because it is about attitudes there are no“right” answers. Some of the possible answers correspond to assumptions consciouslymade by economists: but these assumptions may not be good ones. Your responses willhelp to shed some light on this, and we would like to thank you for your participation.The questionnaire is anonymous.

Alfaland consists of five regions that are identical in every respect other than theincomes of their inhabitants. Everyone within a given region receives the same income,but personal incomes differ from region to region. An immigrant to Alfaland wouldbe assigned at random, with equal probability, to any one of these five regions. Such aperson would therefore have a 20% chance of being on any one of five income levels.

Two economic policy proposals A and B are being considered for implementationin Alfaland next year. It is known that—apart from their impact on personal incomes—the two policies would have the same effect on the population. The impact upon theregions’ incomes would depend upon the particular state of the Alfaland economy atthe time the policy (A or B) is to be introduced.

In each of questions (1) to (6) two alternative lists of incomes A and B (in Alfalandlocal currency) are given. Each of these pairs represents the outcomes of the A-policyand the B-policy on the five regions in each of six different situations in which Alfal-and might find itself next year. In each case, please state which policy you considerwould result in higher risk for a person immigrating to Alfaland by circling A or B. Ifyou consider that the two policies will result in the same risk to a potential immigrantthen circle both A and B.

(1) A = (2, 5, 9, 20, 30) B = (2, 6, 8, 20, 30)(2) A = (2, 5, 9, 20, 30) B = (3, 5, 9, 20, 29)(3) A = (2, 5, 9, 20, 30) B = (2, 6, 9, 20, 29)(4) A = (2, 5, 9, 20, 30) B = (2, 10, 9, 15, 30)(5) A = (10, 10, 10, 10, 30) B = (10, 10, 10, 20, 20)(6) A = (2, 5, 9, 20, 30) B = (2, 6, 9, 19, 30)

In question 7, you are presented with a hypothetical income change and some pos-sible views about the effects on risk of that change. The views are labeled (a),…,(e).Please circle the letter alongside the view that corresponds most closely to your own.You can check more than one answer, provided that you consider they do not contradicteach other. Feel free to add any comment that explains the reason for your choice.

(7) Suppose we transfer income from the inhabitants of a relatively high-incomeregion to those of a relatively low-income region, without changing the incomeof any other region. The transfer is not so large as to make the “rich” region “poor”and the “poor” region “rich”, but it may alter their income rankings relative tothe other, unaffected regions.

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http://darp.lse.ac.uk/7flavors/

http://darp.lse.ac.uk/7flavors/

396 Y. Amiel et al.

(a) Risk for a potential immigrant to Alfaland must fall if the ranking by incomeof all the regions remains the same. If there is any change in the incomeranking of the regions then it is possible that risk increases or remains thesame.

(b) If the transfer is from the richest to the poorest region, and after the transferthe richest region remains the richest and the poorest remains the poorest,risk must fall. In other cases we cannot say a priori how risk will change.

(c) The transfer may change the relative position of other regions. So we cannotsay a priori how risk will change.

(d) Risk for a potential immigrant to Alfaland must fall, even if there is a changein the income ranking of the regions as a result of this transfer, and even ifthe transfer is not from the richest region to the poorest.

(e) None of the above

In the light of your answer to question 7, would you want to change your answers toquestions 1 to 6? If so, please state your new response here.

(1) (2) (3)(4) (5) (6)

Finally, we would be grateful for some information about yourself:

• Are you male or female? M/F• What is your age? _____ years• What is your special subject of study? __________• Were you employed before university? Yes / No• How would you rate your political views? Please put a � on this scale

“extreme left”

“extremeright”

• How would you rate your family’s income 10 years ago? Please put a � on this

scale.

“very poor””

“very rich” ”

• How would you rate your own income prospects 10 years from now? Please put a

� on this scale.

“very poor””

“very rich” ”

Income distribution questionnaire

This questionnaire concerns people’s attitude to income distribution. We would beinterested in your view, based on hypothetical situations. Because it is about attitudesthere are no “right” answers. Some of the possible answers correspond to assumptionsconsciously made by economists: but these assumptions may not be good ones. Your

123


responses will help to shed some light on this, and we would like to thank you for yourparticipation. The questionnaire is anonymous.

Alfaland consists of five regions that are identical in every respect other than theincomes of their inhabitants. Everyone within a given region receives the same income,but personal incomes differ from region to region.

Two economic policy proposals A and B are being considered for implementationin Alfaland next year. It is known that—apart from their impact on personal incomes—the two policies would have the same effect on the population. The impact upon theregions’ incomes would depend upon the particular state of the Alfaland economy atthe time the policy (A or B) is to be introduced.

In each of questions (1) to (6) two alternative lists of incomes A and B (in Alfalandlocal currency) are given. Each of these pairs represents the outcomes of the A-pol-icy and the B-policy on the five regions in each of six different situations in whichAlfaland might find itself next year. Imagine that you have been assigned to one ofthe regions in Alfaland with an equal chance of being in any one of the five regions.In each case please state which policy you consider would result in a better situationin Alfaland by circling A or B. If you consider that the two policies will result in anequivalent situation then circle both A and B.

(1) A = (2, 5, 9, 20, 30) B = (2, 6, 8, 20, 30)(2) A = (2, 5, 9, 20, 30) B = (3, 5, 9, 20, 29)(3) A = (2, 5, 9, 20, 30) B = (2, 6, 9, 20, 29)(4) A = (2, 5, 9, 20, 30) B = (2, 10, 9, 15, 30)(5) A = (10, 10, 10, 10, 30) B = (10, 10, 10, 20, 20)(6) A = (2, 5, 9, 20, 30) B = (2, 6, 9, 19, 30)

In question 7, you are presented with a hypothetical income change and some pos-sible views about the effects on income distribution of that change. The views arelabeled (a),…,(e). Please circle the letter alongside the view that corresponds mostclosely to your own. You can check more than one answer, provided that you considerthey do not contradict each other. Feel free to add any comment that explains thereason for your choice.

(7) Suppose income is transferred from the inhabitants of a relatively high-incomeregion to those of a relatively low-income region, without changing the income ofany other region. The transfer is not so large as to make the “rich” region “poor”and the “poor” region “rich”, but it may alter their income rankings relative tothe other, unaffected regions.(a) The situation in Alfaland must improve if the ranking by income of all the

regions remains the same. If there is any change in the income ranking of theregions then it is possible that the situation worsens or remains unaltered.

(b) If the transfer is from the richest to the poorest region, and after the transferthe richest region remains the richest and the poorest remains the poorestthe situation must improve. In other cases it is impossible to say a priorihow the situation will change.

(c) The transfer may change the relative position of other regions. So it isimpossible to say a priori how the situation will change.

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398 Y. Amiel et al.

(d) The situation in Alfaland must improve, even if there is a change in theincome ranking of the regions as a result of this transfer, and even if thetransfer is not from the richest region to the poorest.

(e) None of the above.

In the light of your answer to question 7, would you want to change your answers toquestions 1 to 6? If so, please state your new response here.

(1) (2) (3)(4) (5) (6)Finally, we would be grateful for some information about yourself:

• Are you male or female? M/F• What is your age? _____ years• What is your special subject of study? __________• Were you employed before university? Yes / No• How would you rate your political views? Please put a � on this scale.

“extreme left”

“extremeright”

• How would you rate your family’s income 10 years ago? Please put a � on this

scale.

“very poor””

“very rich” ”

• How would you rate your own income prospects 10 years from now? Please put a

� on this scale

“very poor””

“very rich” ”

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approach. In F. Andersson & H. J. Holm (Eds.), Experimental economics: Financial markets,auctions, and decision making (Chap. 9, pp. 85–115). Dewenter: Kluwer.

Amiel, Y., & Cowell, F. A. (2007). Social welfare and individual preferences under uncertainty: Aquestionnaire-experimental approach. Research on Economic Inequality, 14, 345–362.

Amiel, Y., Cowell, F. A., & Gaertner, W. (2009). To be or not to be involved: A questionnaire-experimentalview on Harsanyi’s utilitarian ethics. Social Choice and Welfare, 32, 299–316.

Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2, 244–263.Bosmans, K. (2007). Comparing degrees of inequality aversion. Social Choice and Welfare, 29, 405–428.Dalton, H. (1920). Measurement of the inequality of incomes. The Economic Journal, 30, 348–361.Dasgupta, P. S., Sen, A. K., & Starrett, D. A. (1973). Notes on the measurement of inequality. Journal

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Marshall, A. W., & Olkin, I. (1979). Inequalities: Theory and majorization. New York: Academic Press.Moulin, H. (2003). Fair division and collective welfare. Cambridge, MA: MIT Press.Moyes, P. (1994). Inequality-reducing and inequality-preserving transformations of incomes: Symmetric

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