Consistency between tastes and values: A universalization approach

The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that transform individuals ‘tastes’– which reflect the self-interested view point of the individuals – into (social) ranking of alternatives. In addition to her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of income inequality aversion, the so-called ‘ethics of responsibility’ and the aggregation of individual ranking of opportunity sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of ‘laundering’ individual preferences is also provided. Received: 25 June 1998/Accepted: 16 March 1999     

Inequality, new directions: full ethical foundation and consequences

Deriving comparisons and measures of inequality from full ethical foundations was a main innovation of the 1960s and pursuing it is still a most fruitful direction. This implies using “equal equivalents” and some principles particularly rich in meanings. Multidimensional inequalities can be measured and compared thanks to the “equal-equivalent manifolds”. The “equal-equivalent utility function” defines individual “welfare” cleaned of differences in sui generis individual tastes and hedonic capacities deemed irrelevant for “macrojustice”. Then, equal allocation is a deeper end-value than equal welfare but has to be complemented by free choice for freedom, Pareto efficiency and a demanded partial self-ownership. The result is the richly multi-meaning “equal-labour income equalization”.     

Essential alternatives and freedom rankings

We study the problem of ranking opportunity sets in terms of freedom of choice. The analysis is based on the notion of essential alternatives introduced in Puppe (J Econ Theory 68:174–199, 1996). An alternative in an opportunity set is called essential if by deleting it, the reduced opportunity set offers less freedom than the original set. We provide an axiomatic characterization of the ranking according to which an opportunity set offers more freedom than another opportunity set if its share of essential elements in their union is larger.     

Social welfare functions with a reference income

A foundation of social welfare functions is considered with a given reference income (or utility): relative and absolute invariance of the underlying welfare ordering are defined to hold for societies with either all members having incomes below the reference income or all members having incomes above the reference income. These conditions, alongside standard properties of a social preference relation, provide reference income dependent extensions of traditional classes of welfare functions. Dalton’s principle of positive transfers is incorporated, under which relative invariance leads to a class of piecewise (rank-)linear welfare functions, including the class of generalized Gini social welfare functions as a special case. To ensure quasi-concavity a new preference condition is proposed, which has the interpretation of aversion to income dropping below the reference income.     

Choosing subsets: a size-independent probabilistic model and the quest for a social welfare ordering

“Subset voting” denotes a choice situation where one fixed set of choice alternatives (candidates, products) is offered to a group of decision makers, each of whom is requested to pick a subset containing any number of alternatives. In the context of subset voting we merge three choice paradigms, “approval voting“ from political science, the “weak utility model” from mathematical psychology, and “social welfare orderings” from social choice theory. We use a probabilistic choice model proposed by Falmagne and Regenwetter (1996) built upon the notion that each voter has a personal ranking of the alternatives and chooses a subset at the top of the ranking. Using an extension of Sen's (1966) theorem about value restriction, we provide necessary and sufficient conditions for this empirically testable choice model to yield a social welfare ordering. Furthermore, we develop a method to compute Borda scores and Condorcet winners from subset choice probabilities. The technique is illustrated on an election of the Mathematical Association of America (Brams, 1988). Received: 18 August 1995 / Accepted: 13 February 1997     

The measurement of opportunity inequality: a cardinality-based approach

We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on a given ranking of individual opportunity sets, we define the notion of an equalizing transformation. Then, assuming that the opportunity sets are ranked according to the cardinality ordering, we formulate the analogues of the notions of the Lorenz partial ordering, equalizing (Dalton) transfers, and inequality averse social welfare functions – concepts which play a central role in the literature on income inequality. Our main result is a cardinality-based analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of rank preserving equalizations, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functions. In addition, we characterize the smallest monotonic and transitive extension of our cardinality-based Lorenz inequality ordering. Received: 2 May 1995 / Accepted: 11 October 1996     

Freedom of choice and rational decisions

The paper formalizes a notion of preference-based freedom and examines to which extent such a notion is consistent with otherwise standard conditions of rational decision making. The central result is as follows. Suppose that a preference-based ranking of opportunity sets satisfies a very mild condition of preference for freedom of choice. Then, either the ranking is degenerate in being discontinuous, or the underlying preference relation among the basic alternatives is incomplete. Hence, in any case preference-based rankings of freedom will violate at least some of the basic assumptions of traditional choice modelling. This conclusion is enhanced if the conditions on preference-based freedom are slightly strengthened.I would like to thank the participants of seminars held at the Universities of Karlsruhe and Vienna for valuable comments and stimulating discussions. I am especially indebted to Thomas Christ, Egbert Dierker, Georg Kirchsteiger, Dieter Puppe and anonymous referees for helpful comments. The research has been made possible by a fellowship of the DFG (Deutsche Forschungsgemeinschaft) which is also gratefully acknowledged.     

Ranking linear budget sets

We consider the problem of ranking linear budget sets. After discussing a difference between two approaches suggested by Xu (Soc Choice Welf 22:281–289, 2004) and Kolm (Soc Choice Welf 2009), we introduce three axioms which are motivated by Kolm’s approach. Using the three axioms, we characterize a ranking rule named the pointed distance rule proposed by Kolm (Soc Choice Welf 2009).     

On the relative rewards to immigration: a comparison of the relative labour market position of Indians in the USA,the UK and India

While most studies of the decision to immigrate focus on absolute income differences between countries, we argue that relative change in purchasing power or status, as captured by an individual’s ranking in the wage distribution, may also be another important determinant of the migration decision. Using data on Indian immigrants in the US and the UK matched to comparable data on individuals who remained in India, we show that the average Indian immigrant will experience a fall in their relative ranking in the wage distribution compared to the position similar individuals achieve by remaining in the origin country. The fall in relative rankings is larger for immigrants to the UK than to the US, and largest of all for those with intermediate skills.     

Extended preferences and freedom of choice

The common choice theory in economics is based on the assumption that an individual is defined in terms of a binary preference relation. This preference relation is defined over alternatives without taking into account menu dependence and, in particular, freedom of choice or, more generally, the set that contains the alternatives. In this study we clarify the nature and the significance of freedom of choice which may positively or negatively affect the individual's welfare. Our proposed extended preference relation of the individual takes into account both the particular alternative and the opportunity set that he faces. This extended relation does not induce ranking of opportunity sets. Its restriction to a particular opportunity set is the paradigmatic preference relation and it can capture the dependence of preferences on freedom of choice. Our main result establishes the inconsistency between dependence of extended preferences on freedom of choice and the existence of a utility that represents the paradigmatic preference relation and any of its restrictions. Received: 30 December 1997/Accepted: 6 September 1999     

Distribution-neutral provision of public goods

The paper describes a normative approach to budget incidence, given the provision of a public good. The objective is to balance the budget by an income tax such that the budget is distribution-neutral. This property requires that every consumer’s net welfare gain, i.e. the benefit from consuming the public good and the tax burden in financing it, does not change the inequality inherent in the income distribution. The properties of the distribution-neutral tax are investigated and completely determined. The marginal willingness to pay for the public good is decisive for the degree of progression of the tax schedule. My co-author Georg Tillmann passed away in March 2006, much too soon. He was my friend, more than a colleague. I dedicate this paper to his memory.     

Ranking intersecting Lorenz curves

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At the limit the systems of dominance criteria appear to depend solely on the income share of either the worst-off or the best-off income recipient. This result suggests two alternative strategies for increasing the number of Lorenz curves that can be strictly ordered; one that places more emphasis on changes that occur in the lower part of the income distribution and the other that places more emphasis on changes that occur in the upper part of the income distribution. Both strategies turn out to depart from the Gini coefficient; one requires higher degree of downside and the other higher degree of upside inequality aversion than what is exhibited by the Gini coefficient. Furthermore, it is demonstrated that the sequences of dominance criteria characterize two separate systems of nested subfamilies of inequality measures and thus provide a method for identifying the least restrictive social preferences required to reach an unambiguous ranking of a given set of Lorenz curves. Moreover, it is demonstrated that the introduction of successively more general transfer principles than the Pigou–Dalton principle of transfers forms a helpful basis for judging the normative significance of higher degrees of Lorenz dominance. The dominance results for Lorenz curves do also apply to generalized Lorenz curves and thus provide convenient characterizations of the corresponding social welfare orderings.     

On Preference, Freedom and Diversity

We study the problem of ranking sets of options in terms of freedom of choice. We propose a framework in which both the diversity of the options and the preferences of the agent over the options do play a role. We formulate some axioms that reflect these two aspects of freedom and we study their logical implications. Two different criteria for ranking sets are characterized, which generalize some of the rankings proposed so far in the literature.     

The sensitivity of income polarization

This study looks at polarization and its components’ sensitivity to assumptions about equivalence scales, income definition, ethical income distribution parameters, and the income accounting period. A representative sample of Danish individual incomes from 1984 to 2002 is utilised. Results show that polarization has increased over time, regardless of the applied measure, when the last part of the period is compared to the first part of the period; primary causes being increased inequality (alienation) and faster income growth among high incomes relative to those in the middle of the distribution. Increasing the accounting period confirms the reduction in inequality found for shorter periods, but polarization is virtually unchanged, because income group identification increases. Applying different equivalence scales does not change polarization ranking for different years, but identification ranks are affected. The welfare state considerably reduces income polarization and inequality, but at the expense of some more identification.      

Exclusive representation in public employment: A public choice perspective

Public sector unionization has grown rapidly in recent years, and research has suggested that among the reasons for such growth is legislation granting special privileges to public employee unions. This paper examines one form of legislative privilege, exclusive representation, from a public choice perspective. It is shown that exclusivity reduces employees’ freedom of choice, increases the welfare of union leaders at the expense of union members, limits employment opportunities to “outsiders,” entrenches the monopoly provision of public services, and generates conflict and instability in labor relations.     

Intersecting Lorenz Curves, the Degree of Downside Inequality Aversion, and Tax Reforms

This paper clarifies the conceptual distinction of downside inequality aversion (or transfer sensitivity) as a normative criterion for judging income distributions from the Pigou-Dalton principle of transfers. We show that when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting downside inequality aversion often depends on the relative strengths of its downside inequality aversion and inequality aversion. For additive inequality indices or their monotonic transformations, a measure characterizing the strength of an index’s downside inequality aversion against its inequality aversion is shown to determine the ranking by the index of two distributions whose Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz curves is also identified. The results are particularly useful in understanding the distributional impact of tax reforms. I received exceptionally helpful comments from Mike Hoy, Peter Lambert, the Editor, Buhong Zheng, and an anonymous referee. The remaining errors and shortcomings are my own – W.H. Chiu     

The labor supply of married women and spousal tax deductions in Japan—a structural estimation

The Japanese tax system offers an opportunity to investigate the labor supply response of married women to the income tax and the intrahousehold resource allocation mechanism, since the deductible amount from the husband’s income decreases as the wife’s earnings increase. Using cross-section data, I structurally estimate the labor supply of married women under the piece-wise linear budget constraint created by the Japanese tax and social security system. I find that the wife’s labor supply response to her husband’s decreasing deduction tends to be greater than the response to her own income tax. This suggests that not only the unitary model is rejected but also that female labor is allocated inefficiently within a family. Finally, this study shows that the choice of household model affects the predicted effect of policy reform and that the currently proposed reforms will have less of an effect on the labor supply of married women than previous studies claim.

The possibility of group choice: pairwise comparisons and merging functions

Preferences in Arrow’s conditions are ordinal. Here we show that when intensity of preference represented by reciprocal pairwise comparisons is considered, it is always possible to construct an Arrowian social welfare function using a two-stage social choice process. In stage 1, the individual pairwise relations are mapped into a social pairwise relation. In stage 2, the social pairwise relation is used to generate a cardinal ranking and this ranking is then used to select a particular member of the choice set.     

Freedom of choice

Inspired by the discussion of different functions of freedom of choice (instrumental versus intrinsic value) by Sen and others and an axiomatic characterization of an intrinsic aspect by Pattanaik and Xu, we compare unique axiomatic characterizations of three classes of rankings of opportunity sets in terms of freedom of choice: First, we investigate the simple cardinality-based ranking proposed by Pattanaik and Xu and a generalization of this. Secondly, we propose a new criterion that is based on the comparison of the ranges of sets of options. Thirdly, we solve possibly occuring conflicts between these two criteria.I am indebted to Wulf Gaertner, Yongsheng Xu, Walter Bossert, the participants of the Economic Theory Workshop of the University of Rochester, and anonymous referees for helpful discussions and comments. Financial support by Deutsche Forschungsgemeinschaft is gratefully acknowledged.