Kristof Bosmans

Lorenz Comparisons of Nine Rules for the Adjudication of Conflicting Claims

Consider the following nine rules for adjudicating conflicting claims: the proportional, constrained equal awards, constrained equal losses, Talmud, Piniles’, constrained egalitarian, adjusted proportional, random arrival, and minimal overlap rules. For each pair of rules in this list, we examine whether or not the two rules are Lorenz comparable. We allow the comparison to depend upon whether the amount to divide is larger or smaller than the half-sum of claims. In addition, we provide Lorenz-based characterizations of the constrained equal awards, constrained equal losses, Talmud, Piniles’, constrained egalitarian, and minimal overlap rules.

SOCIAL WELFARE, THE VEIL OF IGNORANCE AND PURELY INDIVIDUAL RISK: AN EMPIRICAL EXAMINATION

We present the results of a questionnaire study with Belgian undergraduate students as respondents. We consider the relationship between people’s direct ethical preferences, their preferences behind a veil of ignorance, and their purely individual risk preferences over income distributions. The results reveal that, although there are important similarities between the three types of preferences, the first and third types form two extremes, while the second type lies in between the other two. Consistency of response patterns with the expected utility (EU) and rank-dependent expected utility (RDEU) models – natural analogues of the social welfare functions most frequently used in the literature on inequality and social welfare – is tested as well. For all three types of preferences the results reveal that, in the considered context, the RDEU model does not add explanatory power to the EU model. However, preferences appear to be relatively well described by some of the basic concepts from non-expected utility theory not usually considered in the income distribution literature.

Equality Preference in the Claims Problem: A Questionnaire Study of Cuts in Earnings and Pensions

Many distributional conflicts are characterized by the presence of acquired rights. The basic structure of these conflicts is that of the so-called claims problem, in which an amount of money has to be divided among individuals with differing claims and the total amount available falls short of the sum of the claims. We describe the results of a questionnaire in which Belgian and German students were confronted with nine claims problems. In the “Firm” version, respondents had to divide revenue among the owners of a firm who contribute to the activities of the firm in different degrees. In the “Pensions” version, they had to divide tax money among pensioners who have paid different contributions during their active career. Responses in the Pensions version are more egalitarian than in the Firm version. For both versions, the proportional rule performs very well in describing the choices of the respondents. Other prominent rules—in particular the constrained equal awards and constrained equal losses rules—fail to capture some basic intuitions. A substantial part of the respondents tend to become more progressive as the amount to be distributed decreases other things equal, and tend to become more progressive as the inequality in the distribution of claims becomes more unequal other things equal. All of these conclusions are robust with respect to the difference in home-country of the respondents.

A consistent multidimensional Pigou-Dalton transfer principle

The Pigou-Dalton principle demands that a regressive transfer decreases social welfare. In the unidimensional setting this principle is consistent, because regressivity in terms of attribute amounts and regressivity in terms of individual well-being coincide in the case of a single attribute. In the multidimensional setting, however, the relationship between the various attributes and well-being is complex. To formulate a multidimensional Pigou-Dalton transfer principle, a concept of wellbeing must therefore first be defined. We propose a version of the Pigou-Dalton principle that defines regressivity in terms of the individual well-being ranking that underlies the social ranking on which the principle is imposed. This well-being ranking (of attribute bundles) is induced from the social ranking over distributions in which all individuals have the same attribute bundle. It is shown that this new principle—the consistent Pigou-Dalton principle—imposes a quasi-linear structure on the well-being ranking. We discuss the implications of this result within the literature on multidimensional inequality measurement and within the literature on needs.

Comparing degrees of inequality aversion

We propose a straightforward dominance procedure for comparing social welfare orderings (SWOs) with respect to the degree of inequality aversion they express. Three versions of the procedure are considered, each of which uses a different underlying criterion of inequality comparisons: (i) a concept based on the Lorenz quasi-ordering, which we argue to be the ideal version, (ii) a concept based on a minimalist criterion of inequality, and (iii) a concept based on the relative differentials quasi-ordering. It turns out that the traditional Arrow–Pratt approach is equivalent to the latter two concepts for important classes of SWOs, but that it is profoundly inconsistent with the Lorenz-based concept. With respect to the problem of combining extreme inequality aversion and monotonicity, concepts (ii) and (iii) identify as extremely inequality averse a class of SWOs that includes leximin as a special case, whereas the Lorenz-based concept (i) concludes that extreme inequality aversion and monotonicity are incompatible.

The evolution of global inequality: absolute, relative and intermediate views

We compare absolute, relative and intermediate views on the evolution of global inequality between 1980 and 2009. According to the relative view, inequality remains invariant after a uniform proportional change of all incomes whereas the absolute view requires invariance to a uniform change of all incomes with the same amount. We use a generic intermediate view which states that an income distribution is as unequal as another one if it can be obtained as a weighted average of a uniform proportional and a uniform absolute change of the incomes. Using recent data on GDP per capita for 115 countries, we …nd considerable support for the claim that world inequality increased for the absolute view and for intermediate views which move substantially in the direction of the relative view.

Prioritarian Poverty Comparisons with Cardinal and Ordinal Attributes

The ethical view of prioritarianism holds the following: if an extra bundle of attributes is to be allocated to either of two individuals, then priority should be given to the worse off among the two. We consider multidimensional poverty comparisons with cardinal and ordinal attributes and propose three axioms that operationalize the prioritarian view. Each priority axiom, in combination with a handful of standard properties, characterizes a class of poverty measures. We provide an empirical application to European Union Statistics on Income and Living Conditions data. For this application, we develop a unanimity criterion within the setting of a single cardinal attribute (income) augmented by several binary ordinal attributes.

Who's afraid of aggregating money metrics?

We provide an axiomatic justification to aggregate money metrics. The key axiom requires the approval of richer-to-poorer transfers that preserve the overall efficiency of the distribution. This transfer principle, together with the basic axioms anonimity, continuity, monotonicity, and a version of welfarism, characterizes a standard social welfare function defined over money metric utilities.

Should fines depend on income? A questionnaire study on values and institutions

How do we make sense of the cross-country heterogeneity in value judgments emerging from international surveys? Our study suggests that the answer needs to go beyond the adaptation of values to existing institutions and should tap into deeper beliefs. In our case, Finnish respondents do support their country´s system of income-dependent fines more strongly than respondents in countries using a fixed fine system. However, they also hold different beliefs on the relationship between income and well-being and hence on the burdens imposed by fining offenders at different income levels. A further illustration is provided in the context of income taxation.

Inequality and Quasi-Concavity

We discuss a property of quasi-concavity for inequality measures. Defining income distributions as relative frequency functions, this property says that a convex combination of any two given income distributions is weakly more unequal than the least unequal income distribution of the two. The quasi-concavity property is not essential to the idea of inequality comparisons in the sense of not being implied by the fundamental, i.e., Lorenz type, axioms on their own. However, it is shown that all inequality measures considered in the literature—i.e., the class of decomposable inequality measures and the class of normative inequality measures based on a social welfare function of the rank-dependent expected utility form—satisfy the property and even a stronger version). The quasi-concavity property is then shown to greatly reduce the possible inequality patterns over a much studied type of income growth process.