Pairwise Strategy-Proofness and Self-Enforcing Manipulation

“Strategy-proofness” is one of the axioms that are most frequently used in the recent literature on social choice theory. It requires that by misrepresenting his preferences, no agent can manipulate the outcome of the social choice rule in his favor. The stronger requirement of “group strategy-proofness” is also often employed to obtain clear characterization results of social choice rules. Group strategy-proofness requires that no group of agents can manipulate the outcome in their favors. In this paper, we advocate “effective pairwise strategy-proofness.” It is the requirement that the social choice rule should be immune to unilateral manipulation and “self-enforcing” pairwise manipulation in the sense that no agent of a pair has the incentive to betray his partner. We apply the axiom of effective pairwise strategy-proofness to three types of economies: public good economy, pure exchange economy, and allotment economy. Although effective pairwise strategy-proofness is seemingly a much weaker axiom than group strategy-proofness, effective pairwise strategy-proofness characterizes social choice rules that are analyzed by using different axioms in the literature.     

Multi-profile intergenerational social choice

In an infinite-horizon setting, Ferejohn and Page showed that any social welfare function satisfying Arrow’s axioms and stationarity must be a dictatorship of the first generation. Packel strengthened this result by proving that no collective choice rule generating complete social preferences can satisfy unlimited domain, weak Pareto and stationarity. We prove that this impossibility survives under a domain restriction and without completeness. We propose an alternative stationarity axiom and show that a social welfare function on a specific domain satisfies this modified version and some standard social choice axioms if and only if it is a chronological dictatorship.     

On the multi-preference approach to evaluating opportunities

The purpose of the paper is to provide a general framework for analyzing “preference for opportunities.” Based on two simple axioms a fundamental result due to Kreps is used in order to represent rankings of opportunity sets in terms of multiple preferences. The paper provides several refinements of the basic representation theorem. In particular, a condition of “closedness under compromise” is suggested in order to distinguish the flexibility interpretation of the model from normative interpretations which play a crucial role in justifying the intrinsic value of opportunities. Moreover, the paper clarifies the link between the multiple preference approach and the “choice function” approach to evaluating opportunities. In particular, it is shown how the well-known Aizerman/Malishevski result on rationalizability of choice functions can be obtained as a corollary from the more general multiple preference representation of a ranking of opportunity sets. Received: 3 September 1996 / Accepted: 18 August 1997     

Anonymity in large societies

In a social choice model with an infinite number of agents, there may occur “equal size” coalitions that a preference aggregation rule should treat in the same manner. We introduce an axiom of equal treatment with respect to a measure of coalition size and explore its interaction with common axioms of social choice. We show that, provided the measure space is sufficiently rich in coalitions of the same measure, the new axiom is the natural extension of the concept of anonymity, and in particular plays a similar role in the characterization of preference aggregation rules.     

A graphical analysis of some basic results in social choice

We use a simple graphical approach to represent Social Welfare Functions that satisfy Independence of Irrelevant Alternatives and Anonymity. This approach allows us to provide simple and illustrative proofs of May's Theorem, of variants of classic impossibility results, and of a recent result on the robustness of Majority Rule due to Maskin (1995). In each case, geometry provides new insights on the working and interplay of the axioms, and suggests new results including a new characterization of the entire class of Majority Rule SWFs, a strengthening of May's Theorem, and a new version of Maskin's Theorem. Received: 31 July 1999/Accepted: 27 March 2001     

Characterizations of two power indices for voting games with r alternatives

In the first three sections of this paper we present a set of axioms which provide a characterization of an extension of the Banzhaf index to voting games with r alternatives, such as the United Nations Security Council where a nation can vote “yes”, “no”, or “abstain”. The fourth section presents a set of axioms which characterizes a power index based on winning sets instead of pivot sets. Received: 4 April 2000/Accepted: 30 April 2001     

Positional Independence in Preference Aggregation: A Remark

In a recent article, Quesada (Soc Choice Welfare 20 363–370, 2003) showed that if, for strict preferences, a unique strongly unanimous Choice Function (CF) is used to aggregate preferences position-wise then the resulting Social Welfare Function (SWF) is dictatorial. We show that this result is still true if one allows the use of different choice functions, one for each position. We also show that allowing choice functions not to be unanimous leads to SCW that are perm-dictatorial or imposed. We also show a way to set a dual problem to the one exposed in Que03, namely only perm-dictatorial and imposed SWFs can be decomposed into several Dual Choice Functions.An anonymous referee is thanked for his useful remarks.     

Strategy-proof resolute social choice correspondences

We qualify a social choice correspondence as resolute when its set valued outcomes are interpreted as mutually compatible alternatives which are altogether chosen. We refer to such sets as “committees” and analyze the manipulability of resolute social choice correspondences which pick fixed size committees. When the domain of preferences over committees is unrestricted, the Gibbard–Satterthwaite theorem—naturally—applies. We show that in case we wish to “reasonably” relate preferences over committees to preferences over committee members, there is no domain restriction which allows escaping Gibbard–Satterthwaite type of impossibilities. We also consider a more general model where the range of the social choice rule is determined by imposing a lower and an upper bound on the cardinalities of the committees. The results are again of the Gibbard–Satterthwaite taste, though under more restrictive extension axioms.     

Objective measures of well-being and the cooperative production problem

 The concern for measuring well-being objectively (as opposed to subjectively, that is, relying only on preferences) is found in modern political philosophy, especially in J. Rawls’s, A. Sen’s and G. Cohen’s writings. This paper explains the implications of using an objective well-being index as equalisandum or, close to the so-called “safety net preoccupation”, to guarantee a well-being lower bound. In the simple production model studied here, five characterization results and two related theorems prove the convergence of both approaches. We come to the conclusion that the Proportional Solution is the dominant solution according to “objectivist” axioms. Received: 5 September 1994/Accepted: 29 June 1996     

The Separability Principle in Economies with Single-Peaked Preferences

We investigate the implications of the “separability principle” for the class of problems allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. The separability principle requires that for two problems with the same population, but possibly different social endowments, in which the preferences of agents may change, if there is a subgroup of agents whose preferences are the same and the total amounts awarded to them are the same, then the amount awarded to each agent in the subgroup should be the same. First, we investigate the logical relations between separability and other axioms. As it turns out, consistency implies separability. Then, we present characterizations of the uniform rule on the basis of separability and also on the basis of other axioms.     

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     

Sophisticated voting and equilibrium refinements under plurality rule

In this paper we show in the context of voting games with plurality rule that the “perfect” equilibrium concept does not appear restrictive enough, since, independently of preferences, it can exclude at most the election of only one candidate. Furthermore, some examples show that there are “perfect” equilibria that are not “proper”. However, also some “proper” outcome is eliminated by sophisticated voting, while Mertens' stable set fully satisfies such criterium, for generic plurality games. Moreover, we highlight a weakness of the simple sophisticated voting principle. Finally, we find that, for some games, sophisticated voting (and strategic stability) does not elect the Condorcet winner, neither it respects Duverger's law, even with a large number of voters. Received: 16 March 1999/Accepted: 25 September 1999     

An axiomatization of the Nash bargaining solution

I prove that ‘Disagreement Point Convexity’ and ‘Midpoint Domination’ characterize the Nash bargaining solution on the class of two-player bargaining problems and on the class of smooth bargaining problems. I propose an example to show that these two axioms do not characterize the Nash bargaining solution on the class of bargaining problems with more than two players. I prove that the other solutions that satisfy these two properties are not lower hemi-continuous. These different results refine the analysis of Chun (Econ Lett 34:311–316, 1990). I also highlight a rather unexpected link with the result of Dagan et al. (Soc Choice Welfare 19:811–823, 2002).     

Negatively interdependent preferences

We develop a theory of representation of interdependent preferences that reflect the widely acknowledged phenomenon of keeping up with the Joneses (i.e. of those preferences which maintain that well-being depend on “relative standing” in the society as well as on material consumption). The principal ingredient of our analysis is the assumption that individuals desire to occupy a (subjectively) better position than their peers. This is quite a primitive starting point in that it does not give any reference to what is actually regarded as “status” in the society. We call this basic postulate negative interdependence, and study its implications. In particular, combining this assumption with some other basic postulates that are widely used in a number of other branches of the theory of individual choice, we axiomatize the relative income hypothesis, and obtain an operational representation of interdependent preferences. Received: 7 December 1998/Accepted: 24 August 1999     

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.     

Characterizing best–worst voting systems in the scoring context

An increasing body of theoretical and empirical work on discrete choice considers a choice design in which a person is asked to select both the best and the worst alternative in an available set of alternatives, in contrast to more traditional tasks, such as where the person is asked to: select the best alternative; select the worst alternative; rank the alternatives. Here we consider voting systems motivated by such “best–worst” choice; characterize a class of “best–worst” voting systems in terms of a set of axioms in the context of scoring rules; and discuss briefly possible extensions to approval–disapproval systems.     

New places — New identities: Settings in the lives of the old

This paper addresses the relationship between meaning attached to settings by social actors and their self-identities. In the context of research on the social worlds of old widows the author identifies “ideal type” self-designated identities, namely that of “resident” vs. “newcomer” in a setting. These self-identities are considered in light of the bearing upon them of the non-human or physical aspects of settings as well as of the people who share the settings. Finally, strategies for maintaining “resident” status are shown to be more limited for the old than for the younger members of society. I would like to thank Juanita B. Wood, Stephen G. Wieting, Ellen Horgan Biddle, Harold B. Freshley, and an anonymous reviewer forQualitative Sociology for their instructive comments on earlier drafts of this paper. This research was supported in part by a grant from the Administration on Aging, Department of Health, Education, and Welfare. Researchers undertaking such projects are encouraged to express freely their professional judgment. Therefore, points of view or opinions stated in this document do not necessarily represent the official position or policy of the Department of Health, Education, and Welfare.     

The case of the “unfair” review: Ethical issues from an editor’s file

This narrative traces the life and fate of a paper submitted to the journalSocial Problems and ultimately rejected, with the author claiming that the review was “unfair.” It is an editor’s story and seeks to specify various “ethical” dilemmas that help to define such work. He currently is completing a three-year team as editor ofSocial Problems.     

Strategy-proofness and efficiency in a simple production economy

We consider an economy with two agents, “firm” and “worker.” The firm owns a technology which transforms a single input into a single output and the worker owns a limited amount of input good, for example, leisure. The firm is interested in profit measured in terms of output and the worker's preferences are defined over the input-output space. Manipulability comes not only from a lack of information about the (worker's) preferences but also about the technology. With a possibility for manipulation, can we still obtain efficient allocations? We show that there is no allocation mechanism which is Pareto efficient, strategy-proof, and non-dictatorial. Received: 30 March 1998/Accepted: 06 July 1999