$${\mathcal{Q}}$$-anonymous social welfare relations on infinite utility streams

This paper studies a class of social welfare relations (SWRs) on the set of infinite utility streams. In particular, we examine the SWRs satisfying -Anonymity, an impartiality axiom stronger than Finite Anonymity, as well as Strong Pareto and a certain equity axiom. First, we characterize the extension of the generalized Lorenz SWR by combining -Anonymity with Strong Pareto and Pigou–Dalton Equity. Second, we replace Pigou–Dalton Equity with Hammond Equity for characterizing the extended leximin SWR. Third, we give an alternative characterization of the extended utilitarian SWR by substituting Incremental Equity for Pigou–Dalton Equity.     

On the Extension of the Utilitarian and Suppes–Sen Social Welfare Relations to Infinite Utility Streams

Extensions of a utilitarian and a Suppes–Sen grading principle defined on infinite utility streams are characterized with a stronger notion of Anonymity and without any consistency postulate. The relative merits of the Extended Utilitarian relation are discussed and its rankings are compared with those of the overtaking criterion and the Basu–Mitra Utilitarian relation.I am indebted to Tapan Mitra for several insightful discussions on the subject matter of this paper and on intertemporal social choice theory in general. I thank a Managing Editor for meticulously reading through two versions of the paper and two anonymous referees of this journal for providing detailed comments, pointing out errors and suggesting expositional changes. I also thank Kaushik Basu for his comments. I am responsible for any remaining errors.     

The inverse Banzhaf problem

Let ${\mathcal{F}}Let F{\mathcal{F}} be a family of subsets of the ground set [n] = {1, 2, . . . , n}. For each i ? [n]{i \in [n]} we let p(F,i){p(\mathcal{F},i)} be the number of pairs of subsets that differ in the element i and exactly one of them is in F{\mathcal{F}}. We interpret p(F,i){p(\mathcal{F},i)} as the influence of that element. The normalized Banzhaf vector of F{\mathcal{F}}, denoted B(F){B(\mathcal{F})}, is the vector (B(F,1),...,B(F,n)){(B(\mathcal{F},1),\dots,B(\mathcal{F},n))}, where B(F,i)=\fracp(F,i)p(F){B(\mathcal{F},i)=\frac{p(\mathcal{F},i)}{p(\mathcal{F})}} and p(F){p(\mathcal{F})} is the sum of all p(F,i){p(\mathcal{F},i)}. The Banzhaf vector has been studied in the context of measuring voting power in voting games as well as in Boolean circuit theory. In this paper we investigate which non-negative vectors of sum 1 can be closely approximated by Banzhaf vectors of simple voting games. In particular, we show that if a vector has most of its weight concentrated in k < n coordinates, then it must be essentially the Banzhaf vector of some simple voting game with n − k dummy voters.     

A complete and strongly anonymous leximin relation on infinite streams

Various extensions of the leximin order to the infinite dimensional setting have been suggested. They relax completeness and strong anonymity. Instead, by removing sensitivity to generations at infinite rank this paper defines a complete and strongly anonymous leximin relation on infinite streams. The order is axiomatized, and it is shown to be the limit of extended rank-discounted utilitarianism for any utility function, as the discount factor approaches zero.     

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.     

Liberal approaches to ranking infinite utility streams: when can we avoid interference?

In this work we analyse social welfare relations on sets of finite and infinite utility streams that satisfy various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that verify non-interference axioms together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani (2011) prove that a fully liberal non-interfering view of a finite society leads to dictatorship if the weak Pareto principle is imposed. We first prove that this impossibility result vanishes when we extend the horizon to infinity. Then we investigate a related problem: namely, the possibility of combining “standard” semicontinuity with efficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between relaxed forms of continuity and non-interference principles, both under ordinal and cardinal views of the problem.     

On the continuity of ethical social welfare orders on infinite utility streams

In this paper we study the extent to which ethical social welfare orders on infinite utility streams can be continuous. For a class of metrics, we show that ethical preferences can be continuous if and only if the continuity requirement is in terms of a metric which satisfies a simplex condition. This condition requires that the distance from the origin to the unit simplex in the space of utility streams be positive. We use this characterization result to establish that the metric used by Svensson (Econometrica 48:1251–1256, 1980) induces the smallest topology for which there exist continuous ethical preferences. We thank an associate editor and two referees of this journal for their comments and suggestions.     

The structure of coalitional power under probabilistic voting procedures

We consider probabilistic voting procedures which map each feasible set of alternatives and each utility profile to a social choice lottery over the feasible set. It is shown that if we impose: (i) a probabilistic collective rationality condition known as regularity; (ii) probabilistic counterpart of Arrow's independence of irrelevant alternatives and citizens' sovereignty; (iii) a probabilistic positive association condition called monotonicity; then the coalitional power structure under a probabilistic voting procedure is characterized by weak random dictatorship. Received: 1 March 1999/Accepted: 21 May 2001     

Continuity and equity with infinite horizons

 In an infinite dimensional space, e.g. the set of infinite utility streams, there is no natural topology and the content of continuity is manipulable. Different desirable properties induce different topologies. We consider three properties: effectiveness. l ₁-summability and equity. In view of effectivity, the product topology is the most favourable one. The strict topology is the largest topology for which all the continuous linear maps are l ₁-summable. However, both topologies are myopic and conflict with the principle of equity. In case equity is desirable, the sup topology comes forward. Received: 15 April 1993 / Accepted: 22 April 1996     

An axiomatic approach to sustainable development

The paper proposes two axioms that capture the idea of sustainable development and derives the welfare criterion that they imply. The axioms require that neither the present nor the future should play a dictatorial role.Theorem 1 shows there exist sustainable preferences, which satisfy these axioms. They exhibit sensitivity to the present and to the long-run future, and specify trade-offs between them. It examines other welfare criteria which are generally utilized: discounted utility, lim inf. long run averages, overtaking and catching-up criteria, Ramsey's criterion, Rawlsian rules, and the criterion of satisfaction of basic needs, and finds that none satisfies the axioms for sustainability.Theorem 2 gives a characterization of all continuous independent sustainable preferences. Theorem 3 shows that in general sustainable growth paths cannot be approximated by paths which approximate discounted optima. Proposition 1 shows that paths which maximize the present value under a standard price system may fail to reach optimal sustainable welfare levels, and Example 4 that the two criteria can give rise to different value systems.This paper was prepared for a presentation on Reconsideration of Values at the Stanford Institute for Theoretical Economics, organized by K.J. Arrow in July 1993. It was also presented at Intergovernmental Panel on Climate Change Seminar in Montreux, Switzerland, March 1994, at a Seminar on Inconmensurability and Values at Château du Baffy, Normandy, April 1994, and at the Graduate School of Business of Stanford University in May 1994. e mail gc@columbia.edu.     

Invariance axioms for preferences: applications to social choice theory

I investigate the role played by the combination of two invariance axioms for preferences in utility theory; namely, those of zero-independence and scale-independence, respectively. I provide a characterization of the preference relations on ${\mathbb{R}^{n}}$ that satisfy these two axioms as those which are either trivial, or what I call a two-serial total preorder on ${\mathbb{R}^{n}}$ . This result is then applied in social choice theory to characterize those social welfare functions that satisfy IIA and PI. Other characterizations involving the usual Pareto concepts are also provided.     

Alienation,indifference and the choice of ideological position

In this paper we describe a simple model of individual voting behavior and present its implications for the candidate positioning problem under both vote and plurality maximization. Under our assumptions, some voters at the extremes of the ideological spectrum typically will not vote because they are alienated by the equilibrium location of candidates. There will also be some voters in the middle of the ideological spectrum who will not vote because they are indifferent between the equilibrium locations of the candidates. Both the abstention from alienation and from indifference arise explicitly from utility maximization. Once we allow for alienation and indifference, the two alternative candidate objective functions (vote maximization and plurality maximization) yield different outcomes. In particular, we show that under vote maximization the Median Voter (or Minimum Differentiation) outcome will not arise. On the other hand, under plurality maximization, the Median Voter outcome may or may not hold, depending on the distribution of voter preferences.We should like to thank Jerry Fusselman, Jon Hamilton, Mel Hinich, Charlie Holt and participants at seminars at the University of Virginia, Northwestern University and the 1989 Meetings of the Public Choice Society and the Economic Science Association for their helpful comments.     

Axiomatization of ratio equilibria in public good economies

Using consistency properties, we characterize the cost-sharing scheme arising from the ratio equilibrium concept for economies with public goods. The characterization turns out to be surprisingly simple and direct. In contrast to most axiomatic characterizations based on reduced games and consistency properties, our characterization requires that in the reduced game, the players take as given the proportions of the costs paid by the members of the complementary player set, rather than their utility levels. Received: 4 July 1996/Accepted: 28 March 2001     

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.     

Agreement, separability, and other axioms for quasi-linear social choice problems

A quasi-linear social choice problem is concerned with choosing one among a finite set of public projects and determining side payments among agents to cover the cost of the project, assuming each agent has quasi-linear preferences. We first investigate the logical relations between various axioms in this context. They are: agreement, separability, population solidarity, consistency, converse consistency, and population-and-cost solidarity. Also, on the basis of these axioms, we present alternative characterizations of egalitarian solutions; each solution assigns to each agent an equal share of the surplus derived from the public project over some reference utility level, but uses a different method to compute the reference utility level. Received: 18 May 1998/Accepted: 1 July 1999     

Partially monotonic bargaining solutions

The purpose of the paper is to study partially monotonic solutions for two-person bargaining problems. Partial monotonicity relates to the uncertainty a player has about the solution before bargaining. If the minimum utility a player can expect is greater in game T than in game S, and if T contains more alternatives than S, this may bring him to expect that his utility at the solution is greater in T than in S. Partially monotonic solutions reflect these expectations.One partially monotonic solution is axiomatized. The axioms of symmetry and independence of linear transformations are not explicitly assumed, although the solution has also these properties. The Kalai-Smorodinsky solution is shown to be the only continuous partially monotonic solution.This study was financed by the Yrjö Jahnsson Foundation, which is gratefully acknowledged. I like to thank an associate editor and a referee for their valuable suggestions, and the Yrjö Jahnsson Foundation Study Group on Public Economics for useful discussions     

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A _k is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B _l . If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained.     

DOMESTIC OR U.S. NEWS: WHAT DRIVES CANADIAN FINANCIAL MARKETS?

Using a generalized autoregressive conditional heteroscedasticity (GARCH) model, we study the effects of Canadian and U.S. central bank communication and macroeconomic news on Canadian bond, stock, and foreign exchange market returns and volatility. First, Canadian central bank communication is more relevant than its U.S. counterpart, whereas in the case of macro news, that originating from the United States dominates. Second, we find evidence that the impact of Canadian news reaches its maximum when the Canadian target rate departs from the U.S. target rate (2002–2004) and thereafter. The introduction of fixed announcement dates initially does not cause a noticeable break in the data. (JEL E52, G14, G15)     

THEORIES OF RISK: TESTING INVESTOR BEHAVIOR ON THE TAIWAN STOCK AND STOCK INDEX FUTURES MARKETS

This article considers four utility functions—concave, convex, S‐shaped, and reverse S‐shaped—to analyze the behavior of different types of investors on the Taiwan stock index and its corresponding index futures. Using stochastic dominance (SD) rules, we show that the existence of all four investor types is plausible. Risk averters prefer spot to futures, whereas risk seekers prefer futures to spot. Investors with S‐shaped utility functions prefer spot (futures) to futures (spot) when markets move upward (downward). Investors with reverse S‐shaped utility functions prefer futures (spot) to spot (futures) when markets move upward (downward). We show that both spot and futures markets can exist when only risk averters are present, but futures can dominate spot only if there is some risk‐seeking behavior. These results are robust with respect to subperiods, spot returns including dividends, and diversification. (JEL C14, G12, G15)     

Bargaining over a finite set of alternatives

We analyze bilateral bargaining over a finite set of alternatives. We look for "good" ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued. Professor Sertel passed away on January 25, 2003.