ANDREAS HEINRICH VOIGT AND THE HICKS‐ALLEN REVOLUTION IN CONSUMER THEORY

In 1893, Andreas Heinrich Voigt argued that utility admits only an ordinal characterization. We discuss the apparent impact of Voigt's now forgotten early argument for an ordinal approach to utility on later economists. Edgeworth cited Voigt's ordinal‐cardinal distinction several times in the Economic Journal, bringing both the concept and the terminology into Anglophone economics. In 1927, Rosenstein‐Rodan, too, cited Voigt's argument for ordinal utility. Since Hicks apparently learned the cardinal‐ordinal terminology from Edgeworth, and discussed utility theory and complementarity with Rosenstein‐Rodan, it appears that Voigt's 1893 article is the original source of ordinal utility in economics. (JEL B13, B21)     

A CRITICAL ASSESSMENT OF MEASURES OF CENTRAL BANK INDEPENDENCE

The methodology of measuring central bank independence suggested by Bade and Parkin three decades ago and inverse correlations between the measures and inflation have been widely accepted. The measurement literature has made important contributions identifying elements of institutional design that establish the relationship between the central bank and the government and the measurements from an ordinal perspective provide some useful insights about the major institutional redesigns of central banks during the past several decades. At the same time, the measurement literature is problematic. First, a dummy variable bifurcating central banks into groups of independent and less independent central banks can duplicate the standard correlations suggesting the information content of the specific measures is limited; second, the correlations between inflation and measures of independence are not as stable as claimed; and most important, the measurements are subject to classification problems that have not been fully appreciated. Review of the institutional design and history of the Bank of Korea, Bank of Japan, and the Federal Reserve provide evidence the classification problems are important. The measures of independence are more appropriately regarded as ordinal rankings of central bank independence rather than considered cardinal measures suitable for econometric modeling. (JEL E50, E58, E65)     

Equitable opportunities in economic environments

 In this paper, we extend the axiomatic analysis of equitable opportunities developed in Kranich [6] from finite to continuous opportunity sets. This extended framework is amenable to economic applications. The main results establish conditions under which an ordinal ranking of profiles of opportunity sets can be represented by a cardinal advantage function which describes both the extent of inequality and the distribution of advantage among the agents. Received: 3 November 1993/Accepted: 18 December 1995     

Condorcet choice functions and maximal elements

Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Moreover, we compare these choice functions with those that already exist in the literature.Thanks are due to José Alcalde, J.V. Llinares and M.C. Sánchez, for helpful comments. The comments and suggestions of a referee’s report have improved the work; we are most grateful to her/him. Financial support from the Spanish DGICYT, under project BEC2001-0781, Fundación Séneca (PI74/00826/FS/01) and from the IVIE is acknowledged.     

Manipulating an aggregation rule under ordinally fuzzy preferences

It is well known that many aggregation rules are manipulable through strategic behaviour. Typically, the aggregation rules considered in the literature are social choice correspondences. In this paper the aggregation rules of interest are social welfare functions (SWFs). We investigate the problem of constructing a SWF that is non-manipulable. In this context, individuals attempt to manipulate a social ordering as opposed to a social choice. Using techniques from an ordinal version of fuzzy set theory, we introduce a class of ordinally fuzzy binary relations of which exact binary relations are a special case. Operating within this family enables us to prove an impossibility theorem. This theorem states that all non-manipulable SWFs are dictatorial, provided that they are not constant. This theorem uses a weaker transitivity condition than the one in Perote-Peña and Piggins (J Math Econ 43:564–580, 2007), and the ordinal framework we employ is more general than the cardinal setting used there. We conclude by considering several ways of circumventing this impossibility theorem.     

INCIDENCE AND CONSEQUENCES OF RISK‐TAKING BEHAVIOR IN TOURNAMENTS—EVIDENCE FROM THE NBA

We empirically explore the relevance and efficiency of risk‐taking behavior in tournaments. We use data from the National Basketball Association (NBA) and measure risk‐taking by the fraction of three‐point shots in basketball games. We examine how point differences between teams during games affect their subsequent risk‐taking behavior. It is found that teams that are trailing are more likely to increase their use of three‐point shots. We additionally analyze the consequences of this change in behavior. Enhanced risk‐taking is inefficient in the vast majority of cases and is only beneficial if a team is trailing by a rather large margin. We discuss possible explanations for these decision errors. (JEL M5, D81, J30)     

Monotonicity of ‘ranking by choosing’: A progress report

Procedures designed to select alternatives on the basis of the results of pairwise contests between them have received much attention in literature. The particular case of tournaments has been studied in depth. More recently weak tournaments and valued generalizations thereof have been investigated.The purpose of this paper is to investigate to what extent these choice procedures may be meaningfully used to define ranking procedures via their repeated use, i.e. when the equivalence classes of the ranking are determined by successive applications of the choice procedure. This is what we call ranking by choosing. As could be expected, such ranking procedures raise monotonicity problems. We analyze these problems and show that it is nevertheless possible to isolate a large class of well-behaved choice procedures for which failures of monotonicity are not overly serious. The hope of finding really attractive ranking by choosing procedures is however shown to be limited. Our results are illustrated on the case of tournaments.I am grateful to Hervé Raynaud and Jean-Claude Vansnick for stimulating discussions. Jean-François Laslier, Thierry Marchant, Bernard Monjardet, Xavier Juret and an anonymous referee made very helpful comments on earlier drafts of this text. Special thanks go to Patrice Perny who introduced me to the subject and to Olivier Hudry for his help with Slater orders. The usual caveat applies. Part of this work was accomplished while I was visiting the Service de Mathématiques de la Gestion at the Université Libre de Bruxelles (Brussels, Belgium). I gratefully acknowledge the warm hospitality of the Service de Mathématique de la Gestion as well as the support from the Belgian Fonds National de la Recherche Scientifique and the Brussels-Capital Region through a Research in Brussels action grant.     

THE OPTIMAL ALLOCATION OF PRIZES IN TOURNAMENTS OF HETEROGENEOUS AGENTS

Tournaments are widely used in organizations, explicitly or implicitly, to reward the best‐performing employees, for example, by promotion or bonuses, and/or to penalize the worst‐performing employees, for example, by demotion, withholding bonuses, or unfavorable job assignments. These incentive schemes can be interpreted as various prize allocations based on the employees' relative performance. While the optimal prize allocation in tournaments of symmetric agents is relatively well understood, little is known about the impact of the allocation of prizes on the effectiveness of tournament incentive schemes for heterogeneous agents. We show that while multiple prize allocation rules are equivalent when agents are symmetric in their ability, the equivalence is broken in the presence of heterogeneity. Under a wide range of conditions, loser‐prize tournaments, that is, tournaments that award a low prize to relatively few bottom performers, are optimal for the firm. The reason is that low‐ability agents are discouraged less in such tournaments, as compared to winner‐prize tournaments awarding a high prize to few top performers, and hence can be compensated less to meet their participation constraints. (JEL M52, J33, J24)     

Comparison functions and choice correspondences

In this paper, we introduce the concept of a comparison function, which is a mapping g that assigns numbers to ordered pairs of alternatives (x,y) with the property that g(x,y)=−g(y,x). The paper discusses how some well-known choice correspondences on tournaments such as the uncovered set, the minimal covering set and the bipartisan set can be extended to this general framework. Axiomatic characterizations and properties are studied for these correspondences. Received: 4 November 1996/Accepted: 13 April 1998     

A DESIGNER'S CHOICE BETWEEN SINGLE‐PRIZE AND PARALLEL TOURNAMENTS

In this article, I theoretically and experimentally compare a designer's profits from two tournament designs. The first design is a standard winner‐take‐all tournament with a single prize. The second design features two winner‐take‐all (parallel) tournaments with different prizes where individuals choose which tournament to enter before competing. I develop a simple model that illustrates how the relative performances of these designs change as contestants' abilities differ. The theoretical model shows that the designer's profit is higher (lower) in the parallel tournament when contestants' abilities differ greatly (are similar). I complement these findings with experimental evidence. The experiments show that the parallel tournament is more profitable under high heterogeneity, whereas under low heterogeneity, the designer is better off with the single‐prize tournament. Furthermore, high‐ability agents under‐participate and low‐ability agents over‐participate in the high‐prize tournament relative to the theoretical prediction. (JEL C72, D82, J33, M51, M52)     

Technology Asymmetries, Group Algebra, and Multiplant Cost Minimization

For a homogeneous good, this article studies firm-level production activities when the firm controls a plural number of plants. Through careful construction of cost function technology asymmetries, we inquire into the ordinal structure of the production vector for multiplant cost minimizers. When Schur-convexity of a reference pseudo-cost technology is the principal functional assumption, then ordinal concepts of technical asymmetries map into rank order on the equilibrium production vector. Under a more generalized characterization of the technical asymmetries a multiplant firm encounters, group theory is used to map a cardinal concept of asymmetries into cardinal bounds on the optimum allocation.     

INEQUALITY OF SUBJECTIVE WELL‐BEING AS A COMPREHENSIVE MEASURE OF INEQUALITY

The link between happiness and overall inequality is best studied using an index that incorporates different aspects of inequality, and is measured consistently in different countries. One such index is the degree to which happiness itself varies among individuals. Its correlation with both happiness levels and social trust is substantially stronger than the corresponding correlation for income inequality. This remains so after allowing for bounded scale reporting, including a purely ordinal measure of dispersion. Moreover, the correlation is stronger for individuals who profess to care most about inequality. The link between happiness and inequality may thus be stronger than previously appreciated. (JEL I31, D6, D63, D31)     

A note on contestation-based tournament solutions

In tournaments, one alternative contests another if is a “winner” among only alternatives that beat it. This paper examines the consequences and limitations of the contestation relation by considering a procedure in which alternatives that are contested are iteratively eliminated from consideration. In doing so, a new family of tournament solutions are introduced and related to existing refinements of the Banks set. Findings show that iterated removal of contested alternatives a limited device for choosing from tournaments. These results contrast with results regarding the top-set of the contestation relation. Results highlight the role of the top-set operator for choice from tournaments.     

AN EXPERIMENTAL INVESTIGATION OF RESEARCH TOURNAMENTS

Research tournaments are predicted to encourage R&D. Recent theoretical developments in research tournaments are grounded in search theory. Although the economic intuition behind tournaments is straightforward, computing equilibrium strategies is complex. The participants compute a stopping rule based on the number of participants, the prize and the cost of research. It is an empirical question whether agents will behave as predicted or will employ simple "rule of thumb" strategies such as taking a predetermined number of draws. This paper reports the results of a series of laboratory experiments designed to test the predictions of the search model of tournaments. ( JEL C9, D8)     

The direct social preference relation in the theory of public expenditure

It is shown that if there is a finite number of private goods, a single public good, and the individual preferences satisfy certain monotonicity and separability conditions then there is a unique and complete social preference relation defined on the set of allocations by the requirement that the relation is individualistic in terms of the individual ordinal preferences. This relation, called the direct social preference relation, is derived without imposing interpersonal welfare comparisons and all its ordinal properties are inherited directly from those of the individual preferences. However, an allocation which is maximal in terms of the direct social preference relation on the set of feasible allocations is in general not Pareto optimal and the relation may therefore not be suitable as a guide to optimizing social choice.This version of the paper has benefitted from J. Weymark's insightful and detailed comments. In addition, valuable suggestions have been received from G. C. Archibald, C. Blackorby, D. Donaldson and D. Primont. All remaining errors are the sole responsibility of the author     

AFTER THE TOURNAMENT: OUTCOMES AND EFFORT PROVISION

Outcomes of workplace competitions may themselves influence subsequent behavior—particularly if employees feel wronged. In a laboratory experiment, we find that—consistent with inequity aversion—tournament losers supply less postcompetition effort than winners when doing so reduces their tournament opponent's earnings. Consistent with procedural fairness concerns, subjects who lose arbitrarily decided tournaments that disregard tournament effort choices supply even less post‐tournament effort than other losers. While losers' effort reductions consistent with inequity aversion persist, effort reductions following arbitrarily decided tournaments fade over time. Finally, we show that effort reductions related to inequity aversion could potentially be mitigated through workplace rotations. (JEL C90, J30, D03)     

VOTING EXPRESSIVELY

We address a common criticism directed toward models of expressive voting that they are ad hoc in nature. To that end, we propose a foundation for expressive behavior that is based on a novel theory of social preferences under risk. Under our proposal, expressive considerations in behavior arise from the particular way in which risky social prospects are assessed by decision‐makers who want to interpret their choices as moral. To illustrate the scope of our framework, we use it to address some key questions in the literature on expressive voting: why, for expressive considerations, might voters vote against their self‐interest in large elections and why might such elections exhibit a moral bias. Specifically, we consider an electoral set‐up with two alternatives and explain why, when the size of the electorate is large, voters may want to vote for the alternative they deem morally superior even if this alternative happens to be strictly less preferred, in an all‐inclusive sense, than the other. (JEL D01, D03, D81, D72, A13)     

Uncertainty with ordinal likelihood information

We present a model that is closely related to the so-called models of choice under complete uncertainty, in which the agent has no information about the probability of the outcomes. There are two approaches within the said models: the state space-based approach, which takes into account the possible states of nature and the correspondence between states and outcomes; and the set-based approach, which ignores such information, and solves certain difficulties arising from the state space-based approach. Kelsey (Int Econ Rev 34:297–308, 1993) incorporates into a state space-based framework the assumption that the agent has ordinal information about the likelihood of the states. This paper incorporates this same assumption into a set-based framework, thus filling a theoretical gap in the literature. Compared to the set-based models of choice under complete uncertainty we introduce the information about the ordinal likelihood of the outcomes while, compared to Kelsey’s approach, we incorporate the advantages of describing uncertainty environments from the set-based perspective. We present an axiomatic study that includes adaptations of some of the axioms found in the related literature and we characterize some rules featuring different combinations of information about the ordinal likelihood of the outcomes and information about their desirability.     

Measurement theory and the foundations of utilitarianism

This article reconsiders the Harsanyi–Sen debate concerning whether Harsanyi is justified in interpreting his Aggregation and Impartial Observer Theorems as providing axiomatizations of utilitarianism. Sen's criticism and its formalization by Weymark are based on the claim that von Neumann–Morgenstern utility theory is ordinal, whereas Harsanyi's utilitarian conclusions require cardinal utility. Proposals for overcoming Sen's objection that appeal to formal measurement theory are considered. It is argued that one of these proposals due to Broome and Risse rightly points to a feature of expected utility theory that was ignored by Sen and Weymark, but that this proposal does not provide a normatively compelling justification for cardinal utility. The other proposal due to Broome is shown to make use of a strength of preference relation in addition to the axioms of expected utility theory.     

The weakest link and the commodification of subjectivity by the means of play

Abstract

This article considers the process of commodification (the extension of the realm of money, the spread of typically capitalist mechanisms like competition and consumption) as a cultural means of the reproduction of subjectivity. The particular aim is to highlight the psychic processes that are tempted by commodification. Thus, at the background of this essay, there is a psychoanalytical notion of the self that has been developed in an examination of subjectivity and play, a notion based especially on the thinking of D.W. Winnicott and Jessica Benjamin. These analysts see an ambivalent self‐destructiveness of the self reformulated in relation to the ‘potential space’ of play. In relation to this analysis, the influence of advanced capitalism on the self is discussed in some of its more competitive scenes of consumptions. The quiz show The Weakest Link, for example, is considered as a pale, commodified form of play. It is argued that the main seduction of the show is the dwindled and distorted potential space offered by its ultimate, destructive, and in the last analysis sado‐masochistic logic of exchange. In addition to The Weakest Link, a couple of relevant thematisations of commodified culture by contemporary Finnish literature are brought out. Moreover, the commodification of subjectivity by the means of play is loosely related to some general characterisations concerning the prevailing cultural situation (see Jameson 1999 and Rifkin, 2000).