Equity, continuity, and myopia: A generalization of Diamond’s impossibility theorem

 We consider social preferences over infinite horizon intergenerational consumption paths. We use the Mackey topology to define continuity of social preferences. Our main objective is to generalize one of Diamond’s impossibility theorems. First, we show that the trivial preference relation is the only asymmetric social preference relation satisfying equity and continuity. Second, we compare Campbell’s impossibility theorem with ours. Finally we use an order-based notion of myopia and establish another impossibility result. Received: 26 August 1994/Accepted: 5 June 1996     

Rational Choice and von Neumann– Morgenstern’s Stable Set: The Case of Path-dependent Procedures

Describing a procedure in which choice proceeds in a sequence, we propose two alternative ways of resolving the decision problem whenever the outcome is sequence sensitive. One way yields a rationalizable choice set, and the other way produces a weakly rationalizable choice set that is equivalent to von Neumann–Morgenstern’s stable set. It is shown that for quasi-transitive rationalization, the maximal set must coincide with its stable set.     

Arrow’s theorem in judgment aggregation

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using “systematicity” and “independence” conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model.     

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.     

Arrow's theorem for economic environments and effective social preferences

Arrow's impossibility theorem has been proved for the realm of private goods and economic preferences by Border and by Bordes and Le Breton. However, their proofs require the exclusion of the zero vector from the commodity space. This paper proves the impossibility theorem for the entire allocation space and the classical domain of economic preferences by adding effectiveness to Arrow's hypothesis. Social preference is effective if every nonempty compact set contains at least one socially optimal allocation.Financial support from the Social Sciences and Humanities Research Council (Canada) is gratefully acknowledged. The comments of an anonymous referee were much appreciated. The author assumes responsibility for any errors.     

Wilson's theorem for economic environments and continuous social preferences

Wilson's generalization of Arrow's impossibility theorem has been proved for the realm of private goods and economic preferences by Border and by Bordes and Le Breton. However, their proofs require the exclusion of the zero vector from the commodity space. This paper assumes continuity of social preference to obtain the impossibility theorem for the entire allocation space, even if the society is infinite. A simple corollary reveals that there is some individual who is assigned the zero consumption vector at every social optimum whenever the social welfare function is nonnull and nonimposed, and satisfies Arrow's independence axiom and continuity and transitivity of social preference.Financial support from the Social Sciences and Humanities Research Council is gratefully acknowledged, as are the suggestions of Charles Plott and an anonymous referee. The author assumes responsibility for any errors.     

Consequences,opportunities, and Arrovian impossibility theorems with consequentialist domains

We examine the possibility of Arrovian social choice when alternatives consist of outcomes and opportunity sets from which they are chosen. Consequentialism is a choice attitude towards outcomes and opportunities for choice and prioritizes outcomes rather than opportunities for choice. We first propose a sufficient condition for a restricted domain on which Arrow’s impossibility theorem holds. A domain such that there exists a similarity of choice attitudes within consequentialism satisfies the proposed domain condition. We observe that a diversity of choice attitudes within consequentialism is crucial to resolve an Arrovian impossibility, but this resolution is restricted in plausibility.     

A note on continuous social choice

 We discuss continuous social choice functions defined on the set of the equivalence classes induced by profiles of individual preferences corresponding to anonymity. It is shown that we can at best obtain the equivalent result of Chichilnisky’s impossibility theorem when the set of an equivalence classes is endowed with various reasonable topologies. Received: 28 February 1994/Accepted: 22 April 1996     

Social aggregators

This paper proposes a general framework for analyzing a class of functions called social aggregators, which map profiles of linear orders to a set of binary relations. This class of aggregators includes aggregators that yield a preference relation (social welfare functions) and those which yield a choice of an alternative (social choice functions). Equipped with this framework, I identify a property called Preference Reversal (PR) such that any Pareto efficient aggregator having this property must be dictatorial. This allows me to state a general impossibility theorem, which includes Arrows Theorem and the Gibbard Satterthwaite Theorem as two special examples. Furthermore, I show that monotonicity and IIA are closely linked, by demonstrating that both are actually special cases of PR in specific environments.Received: 15 October 2001     

Veto in fixed agenda social choice correspondences

In this paper we analyze the relationship between social decision functions (SDF) and fixed agenda social choice correspondences (fixed agenda SCC), satisfying some rationality conditions (such as Pareto, Independence, Monotonicity, Neutrality or Anonimity), with the aim of translating known results on the existence of individuals with veto power into the fixed agenda framework (e.g., Blair and Pollak [2], Blau and Deb [3], …). In order to do this, a new independence condition (which we call Pseudo-Independence), as well as a notion of veto power, are introduced in the context of fixed agenda SCC. The conclusion is that, by fixing the agenda, under Independence and Pareto assumptions, the existence of individuals with veto power cannot be avoided. Received: 6 November 1995 / Accepted: 9 September 1997     

Welfarist-consequentialism,similarity of attitudes,and Arrow’s general impossibility theorem

Two features of Arrows social choice theory are critically scrutinized. The first feature is the welfarist-consequentialism, which not only bases social judgements about right or wrong actions on the assessment of their consequences, but also assesses consequences in terms of peoples welfare and nothing else. The second feature is a similarity of peoples attitudes towards social outcomes as a possible resolvent of the Arrow impossibility theorem. Two extended frameworks, one consequentialist and the other non-consequentialist, are developed. Both frameworks are shown to admit some interesting resolutions of Arrows general impossibility theorem, which are rather sharply contrasting with Arrows own perspective.     

Acyclicity and the dispersion of the veto power

Blair and Pollak (Econometrica (1982) 50: 931–943) prove that, if there are more alternatives than individuals, then, for every arrovian binary decision rule that is acyclic, there is at least one individual who has a veto power over a critical number of pairs of alternatives. If the number of individuals is larger than the number of alternatives, there need not be single vetoers but there could be small coalitions endowed with a similar power. Kelsey (Soc Choice Welfare (1985) 2: 131–137) states precise results in this respect. In this paper, we first give a new and much simpler proof of the main result of Blair and Pollak and complete proofs of the generalization of this result by Kelsey. Then we give a precise answer as to the minimum size of the coalitions that must have a veto power under any acyclic binary decision rule and the minimum number of pairs of alternatives on which these coalitions may exercise their power. We also show that, if the veto power of the coalitions of the minimal size attainable under the last objective is limited to the minimum number of pairs of alternatives, then all larger coalitions have a veto power on all pairs. All the results are obtained by appealing to an acyclicity condition found by Ferejohn and Fishburn (J Econ Theory (1979) 21: 28–45). In the case of symmetric and monotonic binary decision rules, proofs are even easier and illustrate clearly the reasons for the veto power.     

On the social stability of coalitional property rights regimes

We present a model of coalitional property rights (CPR) regimes– regimes in which ownership of a good is attributable to coalitions of various sizes. Specifically, for each good, we define a legal structure that specifies the legal coalitions of individuals that share a communal claim to that good. Generally, each legal coalition may use exclusionary rules to allocate its holdings internally. These rules allow eligible subcoalitions to recontract by expropriating some fraction of the legal coalition's endowment. We then ask: what types of CPR regimes are socially stable in the sense of having a nonempty core? We give conditions on the legal structure and the primitives of the economy that achieve social stability in this sense. We emphasize two cases of particular interest. ( I ) Unanimity. Unanimity is required for a legal coalition to recontract against (block) the status quo. In this case, the core is nonempty under standard assumptions. Each agent's ability to veto an alternative allocation allows a partial characterization in terms of the economies that are privatized by dividing up the communal endowment among the members of each legal coalition. We show that in some economies' collective vs private ownership matters in terms of social stability. ( II ) Exclusion. Many eligible subcoalitions can expropriate the legal coalition's entire endowment. An example is the collection of simple majorities. The presence of cycles can easily lead to social instability. We show that if endowment holdings are sufficiently “specialized” and each agent's “veto power” sufficiently large, then stability can be achieved despite the presence of cycles in some goods. Received: 30 June 1993/Accepted: 28 February 1998     

Independent Decisiveness and the Arrow theorem

I show that the condition of Independence of Irrelevant Alternatives in Arrow's impossibility theorem can be weakened into Relational Independent Decisiveness. The condition of Relational Independent Decisiveness is essentially a translation of Sen's Independent Decisiveness into the traditional Arrovian framework. I also show by example that Relational Independent Decisiveness is indeed weaker than Arrow's Independence of Irrelevant Alternatives. Received: 30 October 1996 / Accepted: 22 May 1997     

Arrovian impossibilities in aggregating preferences over non-resolute outcomes

Let A be a set of alternatives whose power set is . Elements of are interpreted as non-resolute outcomes. We consider the aggregation of preference profiles over into a (social) preference over . In case we allow individuals to have any complete and transitive preference over , Arrow’s impossibility theorem naturally applies. However, the Arrovian impossibility prevails, even when the set of admissible preferences over is severely restricted. In fact, we identify a mild “regularity” condition which ensures the dictatoriality of a domain. Regularity is compatible with almost all standard extension axioms of the literature. Thus, we interpret our results as the strong prevalence of Arrow’s impossibility theorem in aggregating preferences over non-resolute outcomes. This paper is part of a project entitled “Social Perception—A Social Choice Perspective”, supported by Istanbul Bilgi University Research Fund. It has been completed while Remzi Sanver was visiting Ecole Polytechnique, Paris. We are grateful to both institutions. We thank Nick Baigent, two anonymous referees and an anonymous associate editor for their valuable comments.     

Rational budgeters in the theory of social choice

The purpose of this paper is to explore duality in the theory of social choice. As application Arrow's Impossibility Theorem and another impossibility theorem using the notion of positive responsiveness are chosen. It will be seen that we can establish notions and theorems which are symmetric to the original ones. However, if we establish impossibility theorems when rational behaviour is described by budget correspondences and not by choice correspondences, we need not assume that every subset of X (a family of alternatives) with cardinality 2 is a budget set. Therefore the dual theorems also may hold for families of competitive budget sets. It will also be shown that although the underlying preferences on X need not be acyclic, local decisiveness on budget sets may lead to global decisiveness on these sets.     

Arrovian theorems for economic domains. The case where there are simultaneously private and public goods

We prove that Arrow's theorem and, with quasi-transitive social preferences, a version of Mas-Colell and Sonnenschein's theorem, hold when there are simultaneously private and public goods, and the individuals are supposed to have selfish, continuous, convex and strictly increasing preferences. We first prove the results in an abstract general setting, and show that the above-mentioned economic domain is a model for this setting.We thank Donald Campbell and two anonymous referees for helpfull suggestions.     

Coalitionally strategyproof functions depend only on the most-preferred alternatives

In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy “tops only.” That is, they depend only on which alternative each individual prefers the most, not on which alternative she prefers the second most, the third,…, or the least. The functions are defined on the domain of profiles measurable with respect to a Boolean algebra of coalitions. The unrestricted domain of profiles is an example of such a domain. I also prove an extension theorem. Received: 10 August 1998/Accepted: 3 May 1999     

重新思考群己权界:帕累托自由不可能性定理考辩

阿马蒂亚·森所证明的帕累托自由不可能性定理证明:两个似乎是不证自明的原则——最小自由原则和帕累托原则——之间是会存在冲突的。这一定理所蕴含的是一个元问题:确定自由边界的理据是什么?消解森定理中的悖论,需要形成某种合理的偏好。偏好的合理性、自由和权利边界是在历史过程中动态形成的,在不同的社会历史阶段是动态调整的。理解森定理,对于分析当下中国面对的种种权利冲突具有重要的现实意义。     

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.