Social choice with procedural preferences

Participants in an aggregation procedure have preferences not only over outcomes but also over procedural features (such as preferring consensus, preferring to be in the majority, preferring not having to compromise, etc.) Such procedural preferences can be expressed in a framework that, contrary to the traditional Arrovian framework, has voting patterns rather than outcomes as comparison classes. The extended framework helps us to resolve several of the puzzles of social choice theory. The (more or less anti-democratic) political conclusions that some author have been willing to draw from results in the Arrovian framework are shown to rely on formal restrictions that are present in that framework but not in the extended framework that is presented here.     

Social choice with analytic preferences

Arrow's axioms for social welfare functions are shown to be inconsistent when the set of alternatives is the nonnegative orthant in a multidimensional Euclidean space and preferences are assumed to be either the set of analytic classical economic preferences or the set of Euclidean spatial preferences. When either of these preference domains is combined with an agenda domain consisting of compact sets with nonempty interiors, strengthened versions of the Arrovian social choice correspondence axioms are shown to be consistent. To help establish the economic possibility theorem, an ordinal version of the Analytic Continuation Principle is developed. Received: 4 July 2000/Accepted: 2 April 2001     

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.     

Social choice in economic environments with dimensional variation

An argument for welfarist social evaluation is presented that replaces the independence axiom with a consistency axiom for social-evaluation functionals in economic environments. This axiom (consistency across dimension or COAD) requires that, if two allocations contain suballocations in common, and if individual utility functions are projected down to the smaller economy where allocations change, then these small allocations must be ranked in the same way that their ancestral allocations were.The basic result is applied to different information environments and a variety of ethical axioms appropriate to economic environments is investigated.We are indebted to Charles Blackorby, Erwin Diewert, Ed Morey, Bill Schworm and John Weymark for helpful discussions, and to the Social Sciences and Humanities Research Council, the Killiam Foundation and the National Science Foundation, for research support.     

Economic utility versus the attitudinal perspective of consumer choice

Consumer behavior has been extensively researched by economists and social psychologists under the labels of demand theory and attitude theory, respectively. These schools have historically ignored each other's contributions, largely because demand theory has focused on constrained choice while attitude theory has not. However, Warshaw, Sheppard and Hartwick have recently extended attitude theory so that constraints and choice are now endogenous to the model. The points of tangency and distinctiveness between this paradigm and that version of demand theory which is most pertinent to brand choice (i.e., Lancaster economics) are critically discussed, providing a frame of reference for future research at the boundary of economics and social psychology.     

Social structure and personal choice

A review of representative literature in the newly developing area of alternative lifestyle research suggests an antisocial structural bias. The origin of this trend and its implications for a theoretically based social science of alternative lifestyles are explored. The aged, women, and Black families are viewed as examples where social structural conditions affect the diversity of intimacy, marriage, and family alternative lifestyles chosen. Current definitions of alternative lifestyles, individual freedom, and choice are seen as reflecting and supporting the social, political, and economic status quo in American society. It is concluded that a social science of alternative lifestyles is only possible when we more fully understand the individual, institutional, and historical dynamics determining the availability and feasibility of alternatives in intimacy, marriage, and family life.     

Path independent choice and the ranking of opportunity sets

The indirect utility principle provides an instrumentalist basis for ranking opportunity sets, given an underlying preference ranking on alternatives. Opportunity set A is weakly preferred to B if A includes at least one preference-maximising element from $A\cup B$ . We introduce the Plott consistency principle as a natural extension of this logic to decision-makers who choose amongst alternatives according to a path independent choice function. Such choice functions need not be rationalisable by a preference order. Plott consistency requires that A is an acceptable choice from $\left\{ A, B\right\} $ if A includes at least one element from the set of acceptable choices from $A\cup B$ . We explore necessary and sufficient conditions (imposed on a choice function defined on collections of opportunity sets) for Plott consistency.     

Social choice and the indexing dilemma

This paper distinguishes an index ordering and a social ordering function as a simple way to formalize the indexing problem in the social choice framework. Two main conclusions are derived. First, the alleged dilemma between welfarism and perfectionism is shown to involve a third possibility, exemplified by the fairness approach to social choice. Second, the idea that an individual is better off than another whenever he has more (goods, functionings, etc.) in all dimensions, which is known to enter in conflict with the Pareto principle, can be partly salvaged by adopting the fairness approach. This paper has benefited very much from comments by M. Salles and from stimulating interactions with K. Basu, P. Pattanaik, B. Tungodden and the participants at the Philosophical Aspects of Social Choice conference in Caen.     

A case for cardinal utility and non-arbitrary choice of commodity units

With preference changes, cardinal utility is indispensable. For any necessity good, there exists an intermediate consumption level at which a change in preference intensity has no effect on utility, below/above which an increase in preference intensity decreases/increases utility. This is supported by an indicative empirical survey. At the intermediate consumption level, the utility from the relevant good is zero. For a Cobb-Douglas utility function, this intermediate consumption level equals one, making the choice of the unit of measurement non-arbitrary.We are grateful to a referee for some helpful comments     

浅谈"飞地经济"中"飞地"的选择

“飞地经济”是指发达地区与欠发达地区双方政府打破行政区划限制,把“飞出地”方的资金和项目放到行政上互不隶属的“飞人地”方的工业基地,通过规划、建设、管理和税收分配等合作机制,实现互利共赢的持续或跨越发展的经济模式。     

Social choice and the closed convergence topology

This paper revisits the aggregation theorem of Chichilnisky (1980), replacing the original smooth topology by the closed convergence topology and responding to several comments (N. Baigent (1984, 1985, 1987, 1989), N. Baigent and P. Huang (1990) and M. LeBreton and J. Uriarte (1990a, b). Theorems 1 and 2 establish the contractibility of three spaces of preferences: the space of strictly quasiconcave preferences P _SCO, its subspace of smooth preferences P _infSCO ^supS , and a space P ₁ of smooth (not necessarily convex) preferences with a unique interior critical point (a maximum). The results are proven using both the closed convergence topology and the smooth topology. Because of their contractibility, these spaces satisfy the necessary and sufficient conditions of Chichilnisky and Heal (1983) for aggregation rules satisfying my axioms, which are valid in all topologies. Theorem 4 constructs a family of aggregation rules satisfying my axioms for these three spaces. What these spaces have in common is a unique maximum (or peak). This rather special property makes them contractible, and thus amenable to aggregation. However, these aggregation rules cannot be extended to the whole space of preferences P which is not contractible and therefore does not admit continuous aggregation rules satisfying anonymity and unanimity, Chichilnisky (1980, 1982). The results presented here clarify an erroneous example in LeBreton and Uriarte (1990a, b) and respond to Baigent (1984, 1985, 1987) and Baigent and Huang (1990) on the relative advantages of continuous and discrete approaches to Social Choice.Comments from Geoffrey M. Heal, Andreu Mas Colell, Jean Francois Mertens and Maurice Salles are gratefully acknowledged. Research support was provided by NSF SES 8409857.     

Welfare, freedom of choice and composite utility in the logit model

Discrete choice models characterize the alternatives in the choice set by utilities/attributes. The decision making is described by a probability distribution over the choice set. In this paper we introduce a welfare measure based on expected payoff and expected freedom of choice for the simple one parameter logit model. In this case the welfare measure turns out to be the so called composite utility. This means that the composite utility can be interpreted as the combined benefit of expected payoff and expected freedom of choice. The proposed welfare measure can be extended to the linear-in-parameters logit model and nested logit models and others. The proposed welfare measure is formulated in terms of the choice probability distribution. It depends on the form of the probabilities, but not on any particular derivation of the distribution.     

Social choice,optimal inference and figure skating

We approach the social choice problem as one of optimal statistical inference. If individual voters or judges observe the true order on a set of alternatives with error, then it is possible to use the set of individual rankings to make probability statements about the correct social order. Given the posterior distribution for orders and a suitably chosen loss function, an optimal order is one that minimises expected posterior loss. The paper develops a statistical model describing the behaviour of judges, and discusses Markov chain Monte Carlo estimation. We also discuss criteria for choosing the appropriate loss functions. We apply our methods to a well-known problem: determining the correct ranking for figure skaters competing at the Olympic Games.     

Social choice with infinite populations: construction of a rule and impossibility results

 We provide a simple construction of social choice rules for economies with infinite populations. The rules are continuous, Pareto and non-dictatorial; they are constructed as limits of individual preferences when the limit exists, and otherwise as adequate generalizations. This contrasts with the impossibility results of Arrow (1951) and Chichilnisky (1980), which are valid on economies with finitely many individuals. Our social choice rules are, however, limits of dictatorial rules. This paper was written in 1979. Received: 30 October 1994/Accepted: 22 April 1996     

Social choice and individual values in the electronic republic

Voting rules and internet value-aggregation procedures are subtly different in their purposes and, as a result, in certain of their Arrovian properties. This article draws some fundamental contrasts and poses some questions for further investigation.     

The structure of fuzzy preferences: Social choice implications

It has been shown that, with an alternative factorization of fuzzy weak preferences into symmetric and antisymmetric components, one can prove a fuzzy analogue of Arrow's Impossibility Theorem even when the transitivity requirements on individual and social preferences are very weak. It is demonstrated here that the use of this specification of strict preference, however, requires preferences to also be strongly connected. In the absence of strong connectedness, another factorization of fuzzy weak preferences is indicated, for which nondictatorial fuzzy aggregation rules satisfying the weak transitivity requirement can still be found. On the other hand, if strong connectedness is assumed, the fuzzy version of Arrow's Theorem still holds for a variety of weak preference factorizations, even if the transitivity condition is weakened to its absolute minimum. Since Arrow's Impossibility Theorem appeared nearly half a century ago, researchers have been attempting to avoid Arrow's negative result by relaxing various of his original assumptions. One approach has been to allow preferences – those of individuals and society or just those of society alone – to be “fuzzy.” In particular, Dutta [4] has shown that, to a limited extent, one can avoid the impossibility result (or, more precisely, the dictatorship result) by using fuzzy preferences, employing a particularly weak version of transitivity among the many plausible (but still distinct) definitions of transitivity that are available for fuzzy preferences. Another aspect of exact preferences for which the extension to the more general realm of fuzzy preferences is ambiguous is the factorization of a weak preference relation into a symmetric component (indifference) and an antisymmetric component (strict preference). There are several ways to do this for fuzzy weak preferences, all of them equivalent to the traditional factorization in the special case when preferences are exact, but quite different from each other when preferences are fuzzy (see, for example, [3]). A recent paper in this journal [1], by A. Banerjee, argues that the choice of definitions for indifference and strict preference, given a fuzzy weak preference, can also have “Arrovian” implications. In particular, [1] claims that Dutta's version of strict preference presents certain intuitive difficulties and recommends a different version, with its own axiomatic derivation, for which the dictatorship results reappear even with Dutta's weak version of transitivity. However, the conditions used to derive [1]'s version of strict preference imply a restriction on how fuzzy the original weak preference can be, namely, that the fuzzy weak preference relation must be strongly connected. Without this restriction, I will show that the rest of [1]'s conditions imply yet a third version of strict preference, for which Dutta's possibility result under weak transitivity still holds. On the other hand, if one accepts the strong connectedness required in order for it to be valid, I show that [1]'s dictatorship theorem can in fact be strengthened to cover any version of transitivity for fuzzy preferences, no matter how weak, and further, that this dictatorship result holds for any “regular” formulation of strict preference, including the one originally used by Dutta. Received: 13 May 1996 / Accepted: 13 January 1997     

Social choice theory in the case of von Neumann-Morgenstern utilities

Part I of this paper offers a novel result in social choice theory by extending Harsanyi's well-known utilitarian theorem into a multi-profile context. Harsanyi was contented with showing that if the individuals' utilities u _i are von Neumann-Morgenstern, and if the given utility u of the social planner is VNM as well, then the Pareto indifference rule implies that u is affine in terms of the u _i. We provide a related conclusion by considering u as functionally dependent on the u _i, through a suitably restricted social welfare functional (u ₁,...,u _n)u=f(u ₁,...,u _n). We claim that this result is more in accordance with contemporary social choice theory than Harsanyi's single-profile theorem is. Besides, harsanyi's initial proof of the latter was faulty. Part II of this paper offers an alternative argument which is intended to be both general and simple enough, contrary to the recent proofs published by Fishburn and others. It finally investigates the affine independence problem on the u _i discussed by Fishburn as a corollary to harsanyi's theorem.The authors are indebted to L. Haddad, A. Sen and two anonymous referees for useful written comments. They also benefited from stimulating remarks in seminars and helpful conversations with their colleagues. The usual caveat of course applies. One of the authors acknowledges partial financial support from the ARI Communication of the C.N.R.S., Paris.     

Social choice without the Pareto principle: a comprehensive analysis

This article provides a systematic analysis of social choice theory without the Pareto principle, by revisiting the method of Murakami Yasusuke. This article consists of two parts. The first part investigates the relationship between rationality of social preference and the axioms that make a collective choice rule either Paretian or anti-Paretian. In the second part, the results in the first part are applied to obtain impossibility results under various rationality requirements of social preference, such as S-consistency, quasi-transitivity, semi-transitivity, the interval-order property, and acyclicity.