Euclidean individual preference and continuous social preference

Assume a finite society, a standard space of allocations of public goods, and an open and connected domain of profiles of Euclidean individual preferences. (There is an additional technical restriction on the domain.) If a social welfare function f satisfies Arrow's independence axiom and generates social preferences that are continuous and transitive, then f is constant or dictatorial or inversely dictatorial.     

Neutrality in arrow and other impossibility theorems

Summary. Although not assumed explicitly, we show that neutrality plays an important role in Arrow and other impossibility theorems. Applying it to pivotal voters we produce direct proofs of classical impossibility theorems, including Arrow's, as well as extend some of these theorems. We further explore the role of neutrality showing that it is equivalent to Pareto or reverse Pareto, and to effective dictatorship for non-null social welfare functions satisfying the principle of independence of irrelevant alternatives. It is also equivalent to Wilson's Citizens' Sovereignty--which is related to the intuition that symmetry over alternatives makes social preference depend only on citizens' preferences. We show that some of these results are more fundamental than others in that they extend both to infinite societies and to considerably smaller domains of preferences. Finally, as an application of Arrow's theorem, we provide a simple proof of the Gibbard-Satterthwaite theorem.Received: 13 April 2000, Revised: 6 December 2002, JEL Classification Numbers: D71, C70.I thank Salvador Barberá, Luis Corchón, Cesar Martinelli, Eric Maskin, Tomas Sjöström, Ricard Torres, José Pedro Ubeda, and an anonymous referee for feedback. The proofs of Arrow's theorem and two Wilson's theorems come from a note I wrote in 1987 at Universitat Autónoma de Barcelona (Ubeda [16]). In 1996 Geanakoplos [7] wrote a proof of Arrow's theorem similar but not identical to mine. All work in this paper is independent of his.     

Arrow's Possibility Theorem for one-dimensional single-peaked preferences

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow's requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2^N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave.     

Aggregation of binary evaluations with abstentions

A general model of aggregation of binary evaluations over interrelated issues, introduced by Wilson and further studied by Rubinstein and Fishburn and by the authors, is extended here to allow for abstentions on some of the issues. It is shown that the same structural conditions on the set of feasible evaluations that lead to dictatorship in the model without abstentions, lead to oligarchy in the presence of abstentions. Arrow's impossibility theorem for social welfare functions, Gibbard's oligarchy theorem for quasi-transitive social decision functions, as well as some apparently new theorems on preference aggregation, are obtained as corollaries.     

Information Invariance in Variable-Population Social-Choice Problems

We examine the possibilities of extending Sen's taxonomy of fixed-population information assumptions regarding the measurability and interpersonal comparability of individual utilities to social-choice problems where the population may vary. It is shown that in order to avoid impossibility results, informationally more demanding assumptions than in the fixed-population framework are required. We provide characterizations of variable-population social-welfare orderings based on information assumptions, and we suggest a way of generating the required informational environment by means of norms that impose a domain restriction on the set of possible utility profiles.     

Social welfare orderings for ratio-scale measurable utilities

Summary. This article characterizes all of the continuous social welfare orderings which satisfy the Weak (resp. Strong) Pareto principle when utilities are ratio-scale measurable. With Weak Pareto, on both the nonnegative and positive orthants the social welfare ordering must be representable by a weakly increasing Cobb-Douglas social welfare function while on the whole Euclidean space the social welfare ordering must be strongly dictatorial. With Strong Pareto, on the positive orthant the social welfare ordering must be representable by a strictly increasing Cobb-Douglas social welfare function but on the other two domains an impossibility theorem is obtained. Received: July 31, 1995; revised version August 7, 1996     

Factoring out the impossibility of logical aggregation

According to a theorem recently proved in the theory of logical aggregation, any nonconstant social judgment function that satisfies independence of irrelevant alternatives (IIA) is dictatorial. We show that the strong and not very plausible IIA condition can be replaced with a minimal independence assumption plus a Pareto-like condition. This new version of the impossibility theorem likens it to Arrow's and arguably enhances its paradoxical value.     

On measurability and comparability: Comment on Pauwels's “the implicit welfare weights used when maximizing aggregate surplus”

The note demonstrates that the unweighted sum of the Hicksian equivalent variations is not a reasonable welfare indicator if consumers have different wages. It recommends the unweighted sum of the individual money metrics, all evaluated at thesame reference pricesand reference wage. For this measure the comparability and necessary measurability of utility functions and welfare changes can be guaranteed. In contrast to Pauwels's measure the indicator proposed possesses the properties one expects.     

Unequal uncertainties and uncertain inequalities: an axiomatic approach

In this paper, we provide an axiomatic characterization of social welfare functions for uncertain incomes. Our most general result is that a small number of reasonable assumptions regarding welfare orderings under uncertainty rule out pure ex ante as well as pure ex post evaluations. Any social welfare function that satisfies these axioms should lie strictly between the ex ante and the ex post evaluations of income distributions. We also provide an axiomatic characterization of the weighted average of the minimum and the maximum of ex post and ex ante evaluations.     

Preferential trade areas, multinational enterprises, and welfare

Abstract.  The effects of preferential trade areas (PTAs) on the investments by multinational enterprises and their implications for the welfare of members and non‐members are studied in a model with two types of firms: national firms and multinational firms. In the presence of multinational activity PTAs can create new investment as well as divert investment from non‐members to members. Both affect the welfare of members positively. More interestingly, if the investment creation effect of a PTA is sufficiently strong, then the PTA could be welfare enhancing for non‐members as well. JEL classification: F2, L1     

Unemployment and the welfare effects of trade policy

Abstract.  In this paper the welfare effects of tariffs and import quotas in the presence of involuntary unemployment are derived and compared. The framework used is the standard model of a competitive small open economy with many goods and factors. Optimum levels of the respective trade policy instruments are derived, as well as welfare increasing reform strategies. In all cases, the labour intensity of the import‐competing sectors turns out to be a crucial variable for deriving the welfare effects. JEL classification: F13, F16     

On the impossibility of complete Non-Interference in Paretian social judgements

We study a principle of ‘Non-Interference’ in social welfare judgements. Non-Interference captures aspects of liberal approaches (particularly a Millian approach) to social decision making. In its full generality, Non-Interference produces an impossibility result: together with Weak Pareto Optimality, it implies that a social welfare ordering must be dictatorial. However, interesting restricted versions of Non-Interference are compatible with standard social welfare orderings.     

Zero-sum condition: A necessary and sufficient condition for a transitive voting system

A simple and quick way to ascertain whether or not any given majority voting system can always produce a transitive social preference orderings without imposing any restriction on the distribution of diverse individual preference orderings is to examine whether all individual voting (preference) vectors satisfy the Addition Rule or not. This conclusion was obtained by first reformulating the voting mechanism into that of a linear mapping from T^m defined by q = Σp_i. It was found that the subset P of T that can accommodate all possible individual preference ordering profiles and such that every sum vector q = Σ p_i of its member vectors p_i is contained in T can be expressed as P = {p: p∈ T, s(p) = 0}. It was also pointed out that this is equivalent to the requirement that all individual preference (voting) functions must satisfy the Addition Rule. Finally, Borda's Rule and Saposnik's Contributive Rule were shown to be examples of transitive voting rules which satisfy these necessary and sufficient conditions.     

On the impossibility of representing infinite utility streams

We introduce a new Pareto-type criterion for social welfare functions over infinite utility streams that is not necessarily sensitive to increments in just a finite number of components. We show that there is no social welfare function that satisfies both this criterion and Diamond’s equity condition simultaneously. With our result, we extend the impossibility theorem of Basu and Mitra. Moreover, we show that, even under a weaker version of equity related to Zame’s intergenerational equity condition, the impossibility results are obtained as well.     

Health investment, saving, and public policy

Abstract.  This paper develops an overlapping‐generations model in which agents invest in health to prolong life in both working and retirement periods. It explores how unfunded social security with or without health subsidies affects life expectancy, economic growth, and welfare. In particular, by extending life at a possible cost of capital accumulation, health subsidies and a pay‐as‐you‐go pension can improve welfare, especially in the short run. JEL classification: I12, J14, J18, O11     

Arrovian aggregation in economic environments: how much should we know about indifference surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference surfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes “within the Edgeworth box” is not enough, and knowledge of substantially non-local information is necessary.     

Living Standard,Social Welfare,and the Redistribution of Income in a Heterogeneous Population

The paper considers the redistribution of income in a population of households which may differ by type. The redistribution is based on (differences in) living standard and a principle of between‐type‐progressive transfers (BTPT). We characterize the relationship between a social welfare ordering satisfying the BTPT principle and the concept of living standard the principle is based on. It turns out that there is a close link: The ordering of living standard can be derived from the social welfare ordering. Conversely, the class of welfare orderings fulfilling the BTPT principle for a given concept of living standard can be completely described.     

Independence of irrelevant alternatives and consistency of choice

Summary. We show that Arrow's condition of independence of irrelevant alternatives is logically related to conditions of consistency of choice (in particular, to Arrow's choice axiom). The relation, however, is indirect. The link is provided by an independence condition due to Hansson (Synthese, 1969) which applies to fixed agenda social choice rules.     

INSUFFICIENT ENTRY OF EMPLOYEE‐CONTROLLED FIRMS IN A FREE‐ENTRY OLIGOPOLY

This study is a theoretical examination of whether employee‐controlled firms (ECFs) enter a free‐entry oligopolistic market excessively or insufficiently, from the viewpoint of welfare maximization. The excess entry theorem is well known in oligopoly theory. According to this theorem, a greater number of profit‐maximizing firms enter a free‐entry oligopolistic market than is optimal for welfare maximization. We demonstrate the possibility that insufficient entry arises when ECFs compete in a free‐entry market. In particular, we show that if both the demand and cost functions are convex, insufficient ECF entry necessarily occurs. Our results suggest that competition among firms seeking purposes other than profit might lead to insufficient entry because differences in competing firms’ objectives affect the intensity of market competition.