Intergenerational equity and an explicit construction of welfare criteria

Ranking infinite utility streams includes many impossibility results, most involving certain Pareto, anonymity, or continuity requirements. We introduce the concept of the future agreement extension, a method that explicitly extends orderings on finite time horizons to an infinite time horizon. The future agreement extension of the given orderings is quasi-transitive, complete, and pairwisely continuous. Furthermore, its asymmetric part is larger than that of any other pairwisely continuous extension of the orderings. In case of anonymous and strongly Paretian orderings, their future agreement extension is variable step anonymous and strongly Paretian. Characterizations of the future agreement extensions of the utilitarian and leximin orderings are obtained as applications.     

Dictatorial domains in preference aggregation

We call a domain of preference orderings “dictatorial” if there exists no Arrovian (Pareto optimal, IIA and non-dictatorial) social welfare function defined over that domain. In a finite world of alternatives where indifferences are ruled out, we identify a condition which implies the dictatoriality of a domain. This condition, to which we refer as “being essentially saturated”, is fairly weak. In fact, independent of the number of alternatives, there exists an essentially saturated (hence dictatorial) domain which consists of precisely six orderings. Moreover, this domain exhibits the superdictatoriality property, i.e., every superdomain of it is also dictatorial. Thus, given m alternatives, the ratio of the size of a superdictatorial domain to the size of the full domain may be as small as 6/m!, converging to zero as m increases.     

The Bordes-LeBreton exceptional case

Bordes and LeBreton have found a set D of weak orderings of X that includes all linear (strong) orderings of X but where there exists a social welfare function f on D ^N satisfying all of Arrow's (non-domain) conditions. In this paper we characterize all such D and f possibilities.     

Poverty orderings and welfare dominance

This paper examines the partial orderings of discrete distributions derived from various poverty indices and sets of welfare functions. The poverty ordering with respect to some indexP is the ordering obtained whenP ranks consistently over a range of admissible poverty lines. The poverty orderings derived from the headcount ratio, the per-capita income gap and another distribution-sensitive index are characterized in some detail when the poverty standard is allowed to take any positive value, and these orderings are shown to coincide with the natural interpretation of first, second and third degree welfare dominance, respectively. Additional results are then obtained for the situation in which the admissible poverty lines cannot exceed some finite upper bound.We are particularly indebted to Nick Kiefer for initial insights into the issues addressed in this paper. We have also had helpful comments from Amartya Sen, from an anomymous referee, and from many seminar audiences. Financial support from the Krannert Endowment Trust and the Leverhulme Trust is gratefully acknowledged.     

Single-peaked Compatible Preference Profiles: Some Combinatorial Results

This paper examines combinatorial problems in connection with single-peaked preference orderings on a unidimensional scale. A binary relation, dominance, is defined on the set of connected orderings. Relevant properties of the corresponding poset and cover graph are discussed. A formula for the number of pairs of connected orderings consistent with spatial single-peakedness is derived. The total number of such pairs is shown to be expressible in a simple form involving binomial probabilities. A possible application is a coalition formation process of the kind examined by Brams et al. (J Theor Polit 14:359–383, 2002), where actors have single-peaked preferences on a common scale.     

The Lorenz zonotope and multivariate majorizations

 The distribution of d commodities among n individuals is described by an n×d row stochastic matrix. We present a geometric approach to order such matrices. For a row stochastic matrix the Lorenz zonotope is investigated, which is a higher dimensional generalization of the Lorenz curve. The Lorenz zonotope is a convex polytope. The inclusion of Lorenz zonotopes defines an ordering between row stochastic matrices, which is a multivariate majorization. For a cone in nonnegative d-space, a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced. We study this class of orderings and establish equivalence with known majorizations. It is provided a finite set of inequalities to which the ordering is equivalent. Received: 16 February 1994/Accepted: 22 May 1996     

The structure of continuous-valued neutral monotonic social functions

This article consists of several results characterizing neutral monotonic social functions over alternative sets that are compact, convex subsets of Euclidean space. One major result is that a neutral monotonic social function is continuous-valued (i.e., does not make abrupt reversals) for all profiles of continuous-valued weak orderings if and only if it is simple (i.e., completely determined by a single set of decisive coalitions). A second major result is that a continuous-valued neutral monotonic social function will guarantee the existence of a socially undominated alternative for all profiles of continuousvalued, almost convex weak orderings if and only if the smallest empty intersection within the set of decisive coalitions is at least m+2 in size where m is the dimension of the alternative set.Associate Professor of Law, University of Southern California and Assistant Professor of Law and Economics, California Institute of Technology.This article is taken almost directly from a chapter of my Ph.D. dissertation (Strnad 1982). That chapter itself is substantially the same as an earlier paper, Strnad (1981). I have profited greatly from the suggestions, guidance and encouragement of Donald Brown in this work. Strnad (1981) was presented at the California Institute of Technology Theory Workshop in January 1982 and at the annual Public Choice Society Meetings in San Antonio, Texas on March 5–7, 1982. I am grateful to participants at both the Workshop and the Meetings for their comments. Comments by the referee and by Jerry Kramer, the editor, also were very helpful. Any remaining errors are solely my responsibility.Substantial financial support for this work has been provided by Summer Research Grants for 1981 and 1982 from the University of Southern California Law Center     

Rational choice and revealed preference without binariness

 This paper attempts to provide a unified account of the rationalization of possibly non-binary choice-functions by “Extended Preference Relations” (relations between sets and elements). The analysis focuses on transitive EPRs for which three choice-functional characterizations are given, two of them based on novel axioms. Transitive EPRs are shown to be rationalizable by sets of orderings that are “closed under compromise”; this novel requirement is argued to be the key to establish a canonical relationship between sets of orderings and choice-functions. The traditional assumption of “binariness” on preference relations or choice functions is shown to be analytically unhelpful and normatively unfounded; non-binariness may arise from “unresolvedness of preference”, a previously unrecognized aspect of preference incompleteness. Received: 28 August 1995/Accepted: 14 February 1996     

Generalized Gini Indices of Equality of Opportunity

This article considers the ranking of profiles of opportunity sets on the basis of their equality. A version of the Pigou–Dalton transfer principle that is appropriate for the measurement of opportunity inequality is introduced and used to axiomatize the class of generalized Gini equality of opportunity orderings. A characterization of the class of generalized Gini social preference orderings for opportunity profiles is also provided.     

Bergson social welfare functions in applied welfare analysis

Characterizations of the orderings induced on a set of alternatives by often-used Bergson Social Welfare Functions are provided. The characterizations are particularly useful in applied welfare analysis, because they are formulated entirely in terms of orderings of alternatives, rather than orderings of utilities, as is typically done.Helpful comments from Charles Blackorby, Ake Blomqvist, John Broome, Sam Bucovetsky, Mike Hoy, Glenn MacDonal, John Weymark and three referees are gratefully acknowledged, but the usual disclaimer applies.     

Covering relations,closest orderings and hamiltonian bypaths in tournaments

We show that the Slater's set of a tournament, i.e. the set of the top elements of the closest orderings, is a subset of the top cycle of the uncovered set of the tournament. We also show that the covering relation is related to the hamiltonian bypaths of a strong tournament in that if x covers y, then there exists an hamiltonian bypath from x to y.We thank B. Monjardet and an anonymous editor for helpful suggestions.     

The probability of the paradox of voting for weak preference orderings

In this paper the probability of the voting paradox for weak orderings is calculated analytically for the three-voter-three-alternative case. It appears that the probability obtained this way is considerably smaller than in the corresponding case for linear orderings. The probability of intransitive majority relations for weak orderings in the 3 × 3 case is calculated as well, both with unconcerned and with concerned voters. Basic in the calculations are three theorems which are formulated in the field of domain conditions and restricted preferences. Received: 18 February 1997 / Accepted: 21 October 1997     

From Arrow to cycles, instability, and chaos by untying alternatives

From remarkably general assumptions, Arrow's Theorem concludes that a social intransitivity must afflict some profile of transitive individual preferences. It need not be a cycle, but all others have ties. If we add a modest tie-limit, we get a chaotic cycle, one comprising all alternatives, and a tight one to boot: a short path connects any two alternatives. For this we need naught but (1) linear preference orderings devoid of infinite ascent, (2) profiles that unanimously order a set of all but two alternatives, and with a slightly fortified tie-limit, (3) profiles that deviate ever so little from singlepeakedness. With a weaker tie-limit but not (2) or (3), we still get a chaotic cycle, not necessarily tight. With an even weaker one, we still get a dominant cycle, not necessarily chaotic (every member beats every outside alternative), and with it global instability (every alternative beaten). That tie-limit is necessary for a cycle of any sort, and for global instability too (which does not require a cycle unless alternatives are finite in number). Earlier Arrovian cycle theorems are quite limited by comparison with these. Received: 31 July 1999/Accepted: 15 October 1999     

COMPARATIVE JUDGMENTS AS A FUNCTION OF THE DIRECTION OF COMPARISON VERSUS WORD ORDER

Previous findings showed that comparative judgments in surveyquestions are largely affected by the direction of comparison,that is, whether the question asks respondents to compare A(subject) to B (referent) or B to A. These asymmetry effectswere attributed to the dynamics that respondents attend differentlyto the features of an object depending on whether it functionsas the subject or the referent of a comparison. Most researchon direction-of-comparison effects, however, confounded directionof comparison and word order so that the subject is typicallypresented first and the referent second. This article disentanglesthis confound and investigates the separate impact of the directionof comparison and word order. The results replicate earlierfindings regarding direction-of-comparison effects and foundno evidence for a systematic impact of word order. Even whenthe referent of the comparison is presented first and the subjectis presented last, direction-of-comparison effects are observed.The findings are discussed in terms of applied and theoreticalsignificance.     

PRODUCER AND CONSUMER RESPONSES TO GREEN HOUSING LABELS

We find “green” labels increase residential property values by an average of 5%. This premium varies by label stringency and across market segments. Builders respond to the stringency of labels by strategically incorporating green features to achieve higher ratings. This strategy seems reasonable as there is no market premium for green features that lead to scores between label rating cutoff values. These results raise important questions as to how green label policies should be designed in order to foster the supply of green features. Gradations of green attributes are influential, particularly for highly rated homes. The most stringent labels have the greatest role at the high price end of the market. (JEL Q20, Q40, R31)     

Social welfare,inequality, and poverty when needs differ

The paper examines income distributions of a finite population consisting of households which may differ with respect to needs. Since observed incomes are not directly comparable, income distributions have to be adjusted. Incomes are transformed to equivalent incomes interpreted as living standards and measured for a reference type, and the latter are supplemented by weights depending on needs. A general class of social welfare orderings (being based on adjusted rank-ordered income distributions) is characterized by a set of properties. Severe limitations for the form of the adjustment process are implied. The consequences for the measurement of inequality and poverty are demonstrated, and corresponding orderings are derived.     

Lorenz non-consistent welfare and inequality measurement

Typical welfare and inequality measures are required to be Lorenz consistent which guarantees that inequality decreases and welfare increases as a result of a progressive transfer. We explore the implications for welfare and inequality measurement of substituting the weaker absolute differentials and deprivation quasi-orderings for the Lorenz quasi-ordering. Restricting attention to distributions of equal means, we show that the utilitarian model - the so-called expected utility model in the theory of risk - does not permit one to make a distinction between the views embedded in the differentials, deprivation and Lorenz quasi-orderings. In contrast it is possible within the dual model of M. Yaari (Econometrica 55 (1987), 99–115) to derive the restrictions to be placed on the weighting function which guarantee that the corresponding welfare orderings are consistent with the differentials and deprivation quasi-orderings respectively. Finally we drop the equal mean condition and indicate the implications of our approach for the absolute ethical inequality indices.     

Aggregation of coarse preferences

We consider weak preference orderings over a set A _n of n alternatives. An individual preference is of refinement?≤n if it first partitions A _n into ? subsets of `tied' alternatives, and then ranks these subsets within a linear ordering. When ?<n, preferences are coarse. It is shown that, if the refinement of preferences does not exceed ?, a super majority rule (within non-abstaining voters) with rate 1− 1/? is necessary and sufficient to rule out Condorcet cycles of any length. It is argued moreover how the coarser the individual preferences, (1) the smaller the rate of super majority necessary to rule out cycles `in probability'; (2) the more probable the pairwise comparisons of alternatives, for any given super majority rule. Received: 29 June 1999/Accepted: 25 February 2000     

A fair solution to the compensation problem

We deal with a fair division model concerning compensation among individuals endowed with different, non transferable, personal talents. We construct social orderings over all conceivable allocations based on efficiency, fairness, and robustness properties. Relying on orderings gives us the possibility of deriving the appropriate public policy even if incentive constraints arise.