Utility and the individual: An analysis of internal conflicts

Herbert Simon has argued that economic agents do not maximise a transitive ordering but rather adopt what he calls satisficing behaviour. He argues that such behaviour is rational. This paper aims to provide a theory to support Simon's viewpoint. Because of social choice problems an individual with multiple objectives may find it impossible to construct a transitive ordering and hence may have to adopt satisficing type behaviour. We show that whether or not an individual adopts satisficing behaviour depends on the information available.I would like to thank Amartya Sen, the members of a seminar in Oxford, and an anonymous referee for their comments on previous drafts of this paper.     

Strategic behaviour and a notion of ex ante efficiency in a voting model

A person is said to prefer in the stochastic dominance sense one lottery-over-outcomes over another lottery-over-outcomes if the probability of his (at least) first choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, the probability of his at least second choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, and so on, with at least one strict inequality. This (partial) preference relation is used to define straightforwardness of a social choice function that maps profiles of ordinal preferences into lotteries over outcomes. Given a prior probability distribution on profiles this partial preference ordering (taking into account the additional randomness) is used to induce a partial preference ordering over social choice functions for each individual. These are used in turn to define ex ante Pareto undominated (efficient) social choice functions. The main result is that it is impossible for a social choice function to be both ex ante efficient and straightforward. We also extend the result to cardinal preferences and expected utility evaluations.This work was supported by Grant #SOC 77-27403 and #SES 80-26086 from the National Science Foundation. It has been prepared at the University of Illinois and the University of Pennsylvania. We want to thank Steve Matthews and an anonymous referee for helpful comments     

Essentially lexicographic aggregation

In the paper a new approach to lexicography is developed by which in the general framework of ordered blocks with a monotonic basis it is shown that a nontrivial ordering is translation-invariant if and only if it is essentially lexicographic of degree n. Here, the latter means that the ordering can be represented by an ordinary lexicographic ordering in n dimensions. As an application it is shown that a nontrivial social welfare ordering on Euclidean space possesses a useful invariance property (cardinality and non comparability) if and only if the ordering is essentially lexicographic of a strong kind in that it can be obtained from ordinary lexicography by permutation, cutting-off and order reversal with respect to components. This result generalizes the characterization of lexical individual dictatorship obtained by Gevers and d'Aspremont and it provides, within the social welfare approach, a strong version of Arrow's impossibility theorem by not invoking any Pareto principle at all.The author thanks K. Arrow, W. Gaertner, L. Gevers, and two anonymous referees for helpful hints and suggestions.     

Moral sentiments and social choice

We examine the implications, for social choice, of individuals having an intrinsic sense of fairness. Taking the viewpoint that social justice reflects the moral attitudes of the constituent members, we analyze the effect of the intensity of the individual sense of fairness on the solution of Nash bargaining over random allocation procedures. We use a stylized model of university admission policies to illustrate our approach. We show that even if social policies are ultimately determined by the bargaining power of the different groups, a society whose members have a common notion of fairness tends to implement fairer admission policies when the intensity of the sense of fairness of individual members increases. While working on the research that is summarized in this paper the authors visited several institutions. Edi Karni visited the Berglas School of Economics, Tel Aviv University and GRID, at Ecole Normale Superieur de Cachan. Zvi Safra visited CERMCEM and EUREQua, at the University of Paris I and LIP6, at the University of Paris 6. The hospitality of these institutions is gratefully acknowledged. We are also grateful to the editor and two anonymous referees for their very useful comments and suggestions. Zvi Safra thanks The Israel Science Foudation (grant 1299/05) for its support.     

Axiomatic foundations for fairness-motivated preferences

Much work in social choice theory takes individual preferences as uninvestigated inputs into aggregation functions designed to reflect considerations of fairness. Advances in experimental and behavioural economics show that fairness can also be an important motivation in the preferences of individuals themselves. A proper characterisation of how fairness concerns enter such preferences can enrich the informational basis of many social choice exercises. This paper proposes axiomatic foundations for individual fairness-motivated preferences that cover most of the models developed to rationalise observed behaviour in experiments. These models fall into two classes: Outcome-based models, which see preferences as defined only over distributive outcomes, and context-dependent models, which allow rankings over distributive outcomes to change systematically with non-outcome factors. I accommodate outcome-based and context-sensitive fairness concerns by modelling fairness-motivated preferences as a reference-dependent preference structure. I first present a set of axioms and two theorems that generate commonly used outcome-based models as special cases. I then generalise the axiomatic basis to allow for reference-dependence, and derive a simple functional form in which the weight on each person’s payoff depends on a reference vector of how much each person deserves.     

Market arbitrage, social choice and the core

 This paper establishes a clear connection between equilibrium theory, game theory and social choice theory by showing that, for a well defined social choice problem, a condition which is necessary and sufficient to solve this problem – limited arbitrage – is the same as the condition which is necessary and sufficient to establish the existence of an equilibrium and the core. The connection is strengthened by establishing that a market allocation, which is in the core, can always be realized as a social allocation, i.e. an allocation which is optimal according to an ordering chosen by a social choice rule. Limited arbitrage characterizes those economies without Condorcet triples, and those for which Arrow’s paradox can be resolved on choices of large utility values. Received: 30 December 1994/Accepted: 12 August 1996     

Manipulating an aggregation rule under ordinally fuzzy preferences

It is well known that many aggregation rules are manipulable through strategic behaviour. Typically, the aggregation rules considered in the literature are social choice correspondences. In this paper the aggregation rules of interest are social welfare functions (SWFs). We investigate the problem of constructing a SWF that is non-manipulable. In this context, individuals attempt to manipulate a social ordering as opposed to a social choice. Using techniques from an ordinal version of fuzzy set theory, we introduce a class of ordinally fuzzy binary relations of which exact binary relations are a special case. Operating within this family enables us to prove an impossibility theorem. This theorem states that all non-manipulable SWFs are dictatorial, provided that they are not constant. This theorem uses a weaker transitivity condition than the one in Perote-Peña and Piggins (J Math Econ 43:564–580, 2007), and the ordinal framework we employ is more general than the cardinal setting used there. We conclude by considering several ways of circumventing this impossibility theorem.     

The informational basis of the theory of fair allocation

The theory of fair allocation is often favourably contrasted with the social choice theory in the search for escape routes from Arrow’s impossibility theorem. Its success is commonly attributed to the fact that it is modest in its goal vis-à-vis social choice theory, since it does not aspire for a full-fledged ordering of options, and settles with a subset of ‘fair’ options. We show that its success may rather be attributable to a broadened informational basis thereof. To substantiate this claim, we compare the informational basis of the theory of fair allocation with the informational requirements of social choice theory.This paper is derived from a part of an earlier draft of our paper entitled ‘Informational requirements for social choice in economic environments’. The authors thank A. Trannoy, an associate editor and three referees for comments, and participants at seminars in University of Cergy-Pontoise, University of Rochester, Hitotsubashi University, and Waseda University, and the 5th International Meeting of the Society for Social Choice and Welfare in Alicante. Financial support from the Ministry of Education of Japan through Grant-in-Aid No. 10045010 (‘Economic Institutions and Social Norms: Evolution and Transformation’) and the 21st Century Center of Excellence Project on the Normative Evaluation and Social Choice of Contemporary Economic Systems is gratefully acknowledged.     

Is fairness in the eye of the beholder? An impartial spectator analysis of justice

A popular sentiment is that fairness is inexorably subjective and incapable of being determined by objective standards. This study, on the other hand, seeks to establish evidence on unbiased justice and to propose and demonstrate a general approach for measuring impartial views empirically. Most normative justice theories associate impartiality with limited information and consensus. In both the normative and positive literature, information is usually seen as the raw material for self-serving bias and disagreement. In contrast, this paper proposes a type of impartiality that is associated with a high level of information and that results in consensus. The crucial distinction is the emphasis here on the views of impartial spectators, rather than implicated stakeholders. I describe the quasi-spectator method, i.e., an empirical means to approximate the views of impartial spectators. Results of a questionnaire provide evidence on quasi-spectator views and support this approach as a means to elicit moral preferences. By establishing a relationship between consensus and impartiality, this paper helps lay an empirical foundation for welfare analysis, social choice theory and practical policy applications.

“There is no objective standard of ‘fairness.’ ‘Fairness’ is strictly in the eye of the beholder... To a producer or seller, a ‘fair’ price is a high price. To the buyer or consumer, a ‘fair’ price is a low price. How is the conflict to be adjudicated?” – Milton Friedman, Newsweek, July 4, 1977.

     

Lexicographic measurement of the information contained in opportunity sets

An individual who has to choose one item from an opportunity set or menu may lack complete information about the final consequences attached to her choice. This problem has been modeled by Bossert (2000) who introduces an axiomatic approach to the ranking of menus according to their informational content. We propose a different ranking based on the lexicographic ordering on the vectors of numbers of consequences for each item and characterize it axiomatically. Received: 12 June 1998/Accepted: 5 September 2000     

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 expanding definition of framing and its particular impact on economic experimentation

In both experimental economics and psychology, framing research has focused primarily on the reflection effect. Recently, however, economic research on framing has employed a broader definition which incorporates context and institutional factors in a more general and productive way-a way which is also more consistent with the goals of socio-economics. This paper explores this expanding definition of framing and its particular impact on economic experimentation. A wide range of studies are reviewed to illustrate the influence on economics of the changes in understandings of framing, and to examine some of the evidence for context-dependent choice. Research concerning fairness and institutional framing, social norms, reference points, and non-rational choice is considered. Because of the complementarity between economic experimentation and economic theory, these advances in framing research are viewed as further positive signs of the opening of neoclassical economics to socio-economic premises.     

Social choice by majority rule with rational participation

This paper explores the social choice properties of majority rule when voters rationally participate in elections. Employing the basic model of voter behavior developed originally by Ledyard (1984) and Palfrey and Rosenthal (1985), we show that when the electorate is sufficiently large, a participation equilibrium exists and is unique. The main result of the paper shows that under these conditions the social preference ordering induced by majority rule is identical to that given by the expected utility of a randomly selected voter, implying the existence of a Condorcet point in the proposal space. A final section provides intuition for the main theorems and relates the equilibrium of this majority rule game to the median voter result.     

An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set

The lexicographic maximin extension of an ordering is an important and widely used tool in social choice theory. We provide an axiomatization of it by means of five axioms. When the basic ordering is linear the following four (independent) axioms are sufficient: (1) Gärdenfors principle; (2) Neutrality; (3) Strong Fishburn monotonicity; and (4) Extension. Our result may also have applications in the theory of individual choice under uncertainty.     

Rationalizable solutions to pure population problems

In pure population problems, a single resource is to be distributed equally among the agents in a society, and the social planner chooses population size(s) and per-capita consumption(s) for each resource constraint and set of feasible population sizes within the domain of the solution. This paper shows that a weak condition regarding the possible choice of a zero population is necessary and sufficient for the rationalizability of a solution by a welfarist social ordering. In addition, solutions that are rationalized by critical-level generalized utilitarianism are characterized by means of a homogeneity property. Received: 1 December 1997/Accepted: 26 February 1998     

On fairness and welfare analysis under uncertainty

This paper investigates the role of fairness, uncertainty, and a “veil of ignorance” in efficient resource allocation. It focuses on the choice of private and public goods, the method of financing, as well as the choice of information available for public decision-making. A fair-equivalent and Pareto efficient allocation is presented using a maximin criterion defined in terms of individual willingness-to-pay. The paper investigates the role of information in public decision making in terms of its implications for both efficiency and fairness. While better information typically generates improved efficiency, it can also contribute to unfair allocations. The effects of asymmetric information are discussed. Received: 4 May 1998/Accepted: 28 February 2002 We would like to thank two anonymous referees for very useful comments on an earlier draft of the paper. The research was supported in part by a Hatch grant from the University of Wisconsin, Madison.     

From Contract to Status: Perspectives on Employment Seniority*

Length of service as a criterion governing personnel decisions is a widely applied normative principle. Contractual agreements that provide that employees' status with respect to promotion and layoff be based on seniority serve to limit discrimination and favoritism, remove an element of competition among workers, and provide a form of social insurance against the contingencies of aging. This status variable is sometimes erroneously perceived as “job ownership.” Decline of labor turnover, the aging of the labor force, and growth of pension programs reinforce concern about seniority. Expectations based on seniority have been challenged under the Civil Rights Act by former discriminatees who question the fairness of the rank ordering. In times of declining opportunity seniority as an allocative device assumes greater importance, while in a utopia, where all jobs are equally satisfying and there is full employment, seniority would be irrelevant.     

Fairness and self-interest: An assessment

This paper provides an assessment of some fairness notions that are particularly relevant to economics of the marketplace. Motivations of fairness are also discussed. In this vein, three sources of fairness are outlined: moral precepts, stable convention, and reciprocity. Some suitable theoretical and empirical evidence are presented in support of these views. Economic models based on the view that man is purely selfish have performed poorly in some areas, particularly game theory and voluntary contributions to public goods. In other social sciences, notably in psychology, political science, and sociobiology researchers have also encountered systematic deviations from purely selfish behavior. There is ample evidence that both fairness and self-interest matter. It is hoped that this paper will provide a better comprehension of the tensions and complementarities between fairness and self-interest and improve our understanding of human behavior.     

A tractable model of process fairness under risk

This paper proposes a social utility model of individual preferences for process fairness that complements the Fehr–Schmidt model for outcome fairness. The model assumes that the outcome generating process rather than the actual outcomes influences fairness perceptions, and that process fairness is evaluated through comparison of expected payoffs. The process model successfully predicts data from bargaining games involving risky payoffs that neither outcome-based nor reciprocity models can explain. In a theoretical application, Machina’s parental example for non-expected utility in a distributional problem (Machina’s Mom) is analyzed by incorporating individual level process fairness preferences under expected utility.     

Lives and well-being

This article attempts to use the analytical framework of social choice theory for exploring the ethical foundations of population policies. It is argued that non-existence is not a state and therefore that different numbers problems are conceptionally different from same numbers problems that concern much theoretical welfare economics. By means of examples it is argued that we should not expect to find an overall ethical ordering of social states when the size of future generations is subject to choice.This is a totally revised version of a paper (Dasgupta 1983) prepared for Professor Menahem Yaari's workshop on Social Choice Theory and Welfare Economics at the Hebrew University, Jerusalem, in the Spring of 1983. It was also presented at the meeting of the Working Group of the US National Academy of Science Committee on Population Growth and Economic Development held during August 2–4, 1984 at Woods Hole, Massachusetts. One strand of this earlier version, with extensions, was subsequently published in the volume of the Working Group: D. Gale Johnson and R. D. Lee (eds) (1987). I have benefitted greatly from discussions over the past several years with Kenneth Arrow, Robert Aumann, Simon Blackburn, Charles Blackorby, John Broome, David Donaldson, George Garnett, Peter Hammond, John Harsanyi, David Kelsey Marc Nerlove, Derek Parfit, John Rawls, Tim Scanlon, Paul Seabright, Amartya Sen, Robert Sugden, and Menahem Yaari. While preparing this eassay I received an extended letter from Jan Graaff in which he reflected on some of the issues discussed in the earlier paper.This present version bears the impact of his comments.