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.     

INFORMATION ACQUISITION UNDER RISKY CONDITIONS ACROSS REAL AND HYPOTHETICAL SETTINGS

I collect data on how subjects acquire information about risky choices in both real and hypothetical settings using process‐tracing software called Mouselab. On average, there are no significant differences across settings in the amount of time subjects take to make a choice or the completeness of the information they acquire. Subjects also acquire information in sequences consistent with an integration model of decision‐making, such as expected utility theory or prospect theory. I do not find significant differences in risk preferences across settings, on average, but I do find that subjects' risk preferences are related to the completeness of the information that they acquire and where they start their information acquisition. (JEL C91, D80, D83)     

Almost all social choice rules are highly manipulable,but a few aren't

Explores, for several classes of social choice rules, the distribution of the number of profiles at which a rule can be strategically manipulated. In this paper, we will do comparative social choice, looking for information about how social choice rules compare in their vulnerability to strategic misrepresentation of preferences.I am indebted to Universidad Internacional Menendez Pelayo for an invitation to present an early version of this paper at a June, 1989 conference at Valencia, Spain. Thanks for comments go to the participants of that conference, especially Salvador Barbera; also for comments at seminars at Syracuse University and the University of Rochester.     

The common will

This paper discusses the formation of a common will among a group of people from two separate points of view: that of social choice theory and that of discourse ethics. The paper evaluates the formation of a common will by “silent” mechanisms for aggregating individual wishes and preferences, traditionally the domain of social choice theory, from a procedural perspective. I will consider—and answer in the negative—the question of whether or not there exists a mechanism for aggregating individual preferences that is perfectly reflective—in the sense that it can be applied recursively in order to justify or legitimate its own application. I will then consider discourse ethics from a consequentialist standpoint—rather than the traditional, process-oriented perspective from which it usually advanced and defended—and show that its insistence on dialogue as a means for the formation of a common will is based on underlying assumptions about the nature of preferences—such as the discussability of tastes and the malleability of time scales—which run counter to the view of preferences normally associated with standard economic theory. I conclude that, although neither approach to the formation of a common will fares well by the standards normally used to justify the other, proponents of either approach have much to learn from a dialogue with proponents of the other.     

Topological aggregation of preferences: the case of a continuum of agents

 This paper studies the topological approach to social choice theory initiated by G. Chichilnisky (1980), extending it to the case of a continuum of agents. The social choice rules are continuous anonymous maps defined on preference spaces which respect unanimity. We establish that a social choice rule exists for a continuum of agents if and only if the space of preferences is contractible. We provide also a topological characterization of such rules as generalized means or mathematical expectations of individual preferences. Received: 30 November 1994/Accepted: 22 April 1996     

Self-selective social choice functions

It is not uncommon that a society facing a choice problem has also to choose the choice rule itself. In such situations, when information about voters’ preferences is complete, the voters’ preferences on alternatives induce voters’ preferences over the set of available voting rules. Such a setting immediately gives rise to a natural question concerning consistency between these two levels of choice. If a choice rule employed to resolve the society’s original choice problem does not choose itself, when it is also used for choosing the choice rule, then this phenomenon can be regarded as inconsistency of this choice rule as it rejects itself according to its own rationale. Koray (Econometrica 68: 981–995, 2000) proved that the only neutral, unanimous universally self-selective social choice functions are the dictatorial ones. Here we introduce to our society a constitution, which rules out inefficient social choice rules. When inefficient social choice rules become unavailable for comparison, the property of self-selectivity becomes more interesting and we show that some non-trivial self-selective social choice functions do exist. Under certain assumptions on the constitution we describe all of them.     

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     

On the informational basis of social choice

The notion of informational basis in social choice can be broadened so as to cover not only the standard notions related to interpersonal utility comparisons, but also information about utilities or preferences at (ir)relevant alternatives, non-utility features of alternatives, personal responsibility, unconcerned subpopulations, and feasibility constraints. This paper proposes a unified conceptual framework for all these notions, and analyzes the kind of information retained in each case. This new framework yields a deeper understanding of the difficulties and possibilities of social choice. New welfarism theorems are also obtained.I am indebted to W. Bossert, W. Gaertner, F. Gaspart, L. Gevers, N. Gravel, S. Kolm, M. Le Breton, Ph. Mongin, P. Hammond, K. Suzumura, K. Tadenuma, A. Trannoy and J. Weymark for many conversations on topics related to this paper. I have benefited from reactions of the audience at the conference in honor of Louis Gevers, Namur 1999, and at a seminar at the LSE, and from comments by two referees and the editor, F. Maniquet. None of them is responsible for the shortcomings of the paper.     

Confidence in preferences

Indeterminate preferences have long been a tricky subject for choice theory. One reason for which preferences may be less than fully determinate is the lack of confidence in one’s preferences. In this paper, a representation of confidence in preferences is proposed. It is used to develop and axiomatise an account of the role of confidence in choice which rests on the following intuition: the more important the decision to be taken, the more confidence is required in the preferences needed to take it. This theory provides a natural account of when an agent should defer a decision; namely, when the importance of the decision exceeds his confidence in the relevant preferences. Possible applications of the notion of confidence in preferences to social choice are briefly explored.     

Assent-maximizing social choice

We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population’s preferences and on the probability distribution over the sets of feasible alternatives that the society will face. Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule, it is known a priori that the subset of feasible alternatives will be a pair. We define a distinct social choice function for each distribution over the feasible subsets. Our rules can be interpreted as distance minimization—selecting the order closest to the population’s preferences, using a metric on the orders that reflects the distribution over the possible feasible sets. The distance is the probability that two orders will disagree about the optimal choice from a randomly selected available set. We provide an algorithmic method to compute these metrics in the case where the probability of a given feasible set is a function only of its cardinality.     

Toward a theory of choice: Socially embedded preference construction

We present a boundedly rational model of choice that makes room for individual values and social influences in a process of preference construction. It takes from the subjective expected utility model the notion that people assess their options in terms of expected outcomes, referenced to personal values, but it presumes that individuals assess sharply truncated lists of relevant options, outcomes and values and apply a classification logic rather than a calculative one. Such a model is consistent with the nature of evolved human cognitive abilities. The model treats cognitive heuristics and various forms of social influence as determinants of selection of the truncated lists and it treats moral norms as classification rules activated when certain actions and outcomes become salient. The model has implications for understanding how political rhetoric affects individual and social preferences and how “hot cognitions” fit into human choice and for developing improved methods of collective decision making.     

Testing models of information avoidance with binary choice dictator games

Standard social choice experiments generally force subjects to make decisions about giving money to another person, but the ability to avoid information outside of the lab could lead to less altruistic or fair behavior than such experiments tend to suggest. I expand on the design of Dana, Weber, and Kuang (2007) to better study information avoidance in an experimental setting. Subjects are given the chance to avoid information about a recipient’s payoffs in a dictator game. I vary the probability that a dictator’s payoffs will be aligned with the recipient’s in order to assess the role of beliefs on avoidance and test contradictory models. The within-subjects approach shows that even people who are generous in a stark choice will make self-serving decisions when they can avoid knowing the recipient’s outcome. People avoid information more often when the self-serving choice is unlikely to hurt the recipient, which supports Rabin’s model (1995) of moral rules and moral preferences.     

Bayesian implementation in exchange economies with state dependent preferences and feasible sets

This paper considers Bayesian and Nash implementation in exchange economic environments with state dependent preferences and feasible sets. We fully characterize Bayesian implementability for both diffuse and non-diffuse information structures. We show that, in exchange economic environments with three or more individuals, a social choice set is Bayesian implementable if and only if closure, non-confiscatority, Bayesian monotonicity, and Bayesian incentive compatibility are satisfied. As such, it improves upon and contains as special cases previously known results about Nash and Bayesian implementation in exchange economic environments. We show that the individual rationality and continuity conditions, imposed in Hurwicz et al. [12], can be weakened to the non-confiscatority and can be dropped, respectively, for Nash implementation. Thus we also give a full characterization for Nash implementation when endowments and preferences are both unknown to the designer. Received: 4 March 1996 / Accepted: 8 September 1997     

Nash Implementation with Lottery Mechanisms

Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin in Rev Econ stud 66: 23–38, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackon and Palfrey in J Econ Theory 98: 1–25, 2001).I thank Toyo Sakai for his comments on a previous draft. I also thank two anonymous referees and an editor of this journal for helpful comments that improved this paper. A previous version circulated as “A note on Maskin monotonicity”. After the results presented here were obtained, I became aware of a new unpublished paper by Benoit and Ok (2004). The result of Theorem 2 and the discussion that follows is partially similar to their Theorem 1.     

Fair social orderings when agents have unequal production skills

We develop an approach which escapes Arrows impossibility by relying on information about agents indifference curves instead of utilities. In a model where agents have unequal production skills and different preferences, we characterize social ordering functions which rely only on ordinal non-comparable information about individual preferences. These social welfare functions are required to satisfy properties of compensation for inequalities in skills, and equal access to resources for all preferences.We thank participants of the SCW conference in Vancouver (July 1998), of workshops at Cergy and Osnabrück, and of seminars at Tokyo (Hitotsubashi U.) and Caen. We are also grateful to an Associate Editor and two referees for their very helpful comments. Financial Support from European TMR Network FMRX-CT96-0055 is gratefully acknowledged.     

Identification of domain restrictions over which acyclic, continuous-valued, and positive responsive social choice rules operate

We consider a social choice problem in various economic environments consisting of n individuals, 4≤n<+∞, each of which is supposed to have classical preferences. A social choice rule is a function associating with each profile of individual preferences a social preference that is assumed to be complete, continuous and acyclic over the alternatives set. The class of social choice rules we deal with is supposed to satisfy the two conditions; binary independence and positive responsiveness. A new domain restriction for the social choice rules is proposed and called the classical domain that is weaker than the free triple domain and holds for almost all economic environments such as economies with private and/or public goods. In this paper we explore what type of classical domain that admits at least one social choice rule satisfying the mentioned conditions to well operate over the domain. The results we obtained are very negative: For any classical domain admitting at least one social choice rule to well operate, the domain consists only of just one profile.     

Nonmanipulable decision mechanisms for economic environments

In the social choice literature studying the problem of designing institutions for collective decision making, it is customary to (implicitly) assume that each dimension of the social outcome is of public interest (i.e., that each individual's welfare depends on every dimension of the outcome). Thus, the scope of the conclusions obtained is very limited. Here social decision problems with and without that public character are considered and it is shown that the same negative results arise in most cases; namely, that only dictatorial mechanisms are immune to the participants' manipulations. These results are obtained without requiring that the mechanisms produce Pareto optimal outcomes (they must simply be minimally responsive to the participants' preferences), which deepens their pessimistic character.I am deeply grateful to my advisor, Mark Walker, for his continuous guidance and encouragement. I wish also to thank Salvador Barberà, John Weymark, and two anonymous referees for helpful comments.     

Rights and the liberal paradoxes

Traditional social choice theory does not distinguish between the choices and the preferences of an individual. However, it is often rational for an individual to make choices that do not follow his preferences, e.g. when he makes compromises with other individuals. A social choice format is introduced with separate representations for choice and preference. It is shown how different types of rights and other legal positions can be expressed in this format. Definitions are given of what it means for rights to be compatible and for a set of rights to be respected. Further, it is shown that much weaker (and fully plausible) conditions are needed to avoid Sen's paradox (the impossibility of a Paretian liberal) in this social choice format than in a traditional format that does not distinguish between choices and preferences. As an example of this, Sen's paradox can be avoided if each individual, ceteris paribus, prefers that her choices be respected in matters that belong to her own personal sphere.An earlier version of this paper has been discussed at a Swedish-English Symposium on Rights and Rationality. I would like to thank the participants, Peter Gärdenfors, William Hart, Stig Kanger, David Kelsey, Prasanta Pattanaik, and Robert Sugden for valuable comments.     

Equivalence of Nash implementability and robust implementability with incomplete information

This paper is concerned with the design of robust mechanisms which are applicable to a wide class of possible information structures of agents. We examine a society consisting of several groups such that (i) there are at least three agents in each group; and (ii) each agent knows the preferences of the agents in his group but has incomplete information about the preferences of the agents outside his group. We show that for a large class of information structures, a social choice set (SCS) is implementable for each possible information structure if and only if it is Nash implementable. In other words, the class of robustly implementable SCS's is identical to the class of implementable SCS's in the complete information setting.This paper is a substantially revised version of a chapter of my dissertation submitted to the University of Rochester (Yamato [25]). I thank Professor William Thomson for his invaluable advice and suggestions. Detailed comments and suggestions of an anonymous referee were very helpful for further revision of the paper. I also acknowledge comments from Professors Randall Calvert, Luis Corchon, Glenn MacDonald, Eric Maskin, Lionel McKenzie, Ryo-Ichi Nagahisa, Koji Okuguchi, Ignacio Ortuño-Ortin, Tatsuyoshi Saijo, Ken-Ichi Shimomura, Tomas Sjöström, Yoshikatsu Tatamitani, and seminar participants at Harvard University, the 1992 Meeting of Kobe Summer Seminar in Economics of Organization and Game Theory, Tokyo Metropolitan University, and Toyama University. This work was supported in part by the Ministry of Education in Japan, the Nomura Foundation for the Social Sciences, and the Tokyo Center for Economic Research.     

Risky social choice with incomplete or noisy interpersonal comparisons of well-being

In this study, we develop a model of social choice over lotteries, where people’s psychological characteristics are mutable, their preferences may be incomplete, and incomplete or noisy interpersonal comparisons of well-being are possible. Formally, we suppose individual preferences are described by a von Neumann-Morgenstern (vNM) preference order on a space of lotteries over psychophysical states; the social planner must construct a vNM preference order on lotteries over social states. First, we consider a model where the individual vNM preference order is incomplete (so not all interpersonal comparisons are possible). Then, we consider a model where the individual vNM preference order is complete, but unknown to the planner, and thus modelled by a random variable. In both cases, we obtain characterizations of a utilitarian social welfare function.