Ranking opportunity sets in the space of functionings

We develop a ranking of compact, convex and comprehensive opportunity sets defined in the evaluative space of individual functionings. We suppose the existence of a target, that is a multi-dimensional bliss point in terms of functionings. This leads us to define concepts such as essentiality and freedomin a novel way. As a main result, we give an axiomatic characterization of the ranking obtained by minimizing the Euclidean distance between each opportunity set and the target.     

Opportunity sets and individual well-being

 An opportunity set ranking rule assigns an ordering of opportunity sets to each individual utility function (defined on the universal set of alternatives) within the domain of this rule. Using an axiomatic approach, this paper characterizes a general class of opportunity set ranking rules which are based on the utilities associated with the elements of an opportunity set. It is argued that the addition of an alternative to a given opportunity set is not necessarily desirable in terms of overall well-being, and this position is reflected in replacing a commonly used monotonicity axiom with an alternative condition. Received: 15 May 1995/Accepted: 14 December 1995     

Consistency between tastes and values: A universalization approach

The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that transform individuals ‘tastes’– which reflect the self-interested view point of the individuals – into (social) ranking of alternatives. In addition to her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of income inequality aversion, the so-called ‘ethics of responsibility’ and the aggregation of individual ranking of opportunity sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of ‘laundering’ individual preferences is also provided. Received: 25 June 1998/Accepted: 16 March 1999     

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     

Extending an order to the power set: The Leximax Criterion

This work analyzes the issue of ranking the levels of well-being enjoyed by an agent when dealing with her opportunity set in a freedom of choice context. We try to propose a natural extension of a preference relation over a (possibly) infinite set X to its power set, compatible with the finite Leximax criterion. This research has been supported by Comisión Interministerial de Ciencia y Tecnología, SEC2000-0838 (Ballester), and Dirección General de Enseñanza Superior e Investigación Científica, PB98-0551 (De Miguel).     

Path independent choice and the ranking of opportunity sets

The indirect utility principle provides an instrumentalist basis for ranking opportunity sets, given an underlying preference ranking on alternatives. Opportunity set A is weakly preferred to B if A includes at least one preference-maximising element from $A\cup B$ . We introduce the Plott consistency principle as a natural extension of this logic to decision-makers who choose amongst alternatives according to a path independent choice function. Such choice functions need not be rationalisable by a preference order. Plott consistency requires that A is an acceptable choice from $\left\{ A, B\right\} $ if A includes at least one element from the set of acceptable choices from $A\cup B$ . We explore necessary and sufficient conditions (imposed on a choice function defined on collections of opportunity sets) for Plott consistency.     

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     

Essential alternatives and freedom rankings

We study the problem of ranking opportunity sets in terms of freedom of choice. The analysis is based on the notion of essential alternatives introduced in Puppe (J Econ Theory 68:174–199, 1996). An alternative in an opportunity set is called essential if by deleting it, the reduced opportunity set offers less freedom than the original set. We provide an axiomatic characterization of the ranking according to which an opportunity set offers more freedom than another opportunity set if its share of essential elements in their union is larger.     

Ranking linear budget sets

We consider the problem of ranking linear budget sets. After discussing a difference between two approaches suggested by Xu (Soc Choice Welf 22:281–289, 2004) and Kolm (Soc Choice Welf 2009), we introduce three axioms which are motivated by Kolm’s approach. Using the three axioms, we characterize a ranking rule named the pointed distance rule proposed by Kolm (Soc Choice Welf 2009).     

Entrepreneurial Motivations and Capabilities of Migrant Entrepreneurs in Australia

This article presents findings on immigrant entrepreneurship in Australia. The relationship between the entrepreneurial start‐up motivation, co‐ethnic preferences and entrepreneurial capabilities of established immigrant businesses are explored. We analyse data collected with a self‐administered survey questionnaire from 157 immigrant entrepreneurs in Melbourne's suburbs. Our findings show that immigrant entrepreneurs who report a high level of individual achievement as their start‐up motivation also report high levels of entrepreneurial capabilities in terms of opportunity recognition, managerial innovativeness and proactiveness. Immigrant entrepreneurs who are highly influenced by co‐ethnic preferences on staff employment and customer targeting report higher opportunity recognition than those who have a co‐ethnic preference on suppliers. We provide important insights and explanations for these findings and their implications for Australian immigrant entrepreneurs and policymakers.     

The measurement of opportunity inequality: a cardinality-based approach

We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on a given ranking of individual opportunity sets, we define the notion of an equalizing transformation. Then, assuming that the opportunity sets are ranked according to the cardinality ordering, we formulate the analogues of the notions of the Lorenz partial ordering, equalizing (Dalton) transfers, and inequality averse social welfare functions – concepts which play a central role in the literature on income inequality. Our main result is a cardinality-based analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of rank preserving equalizations, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functions. In addition, we characterize the smallest monotonic and transitive extension of our cardinality-based Lorenz inequality ordering. Received: 2 May 1995 / Accepted: 11 October 1996     

Mutual dependency between capabilities and functionings in Amartya Sen’s capability approach

Amartya Sen’s capability approach has recently been widely discussed as a theoretical basis for making resource allocation decisions in health care. The purpose of this paper is to analyze the relationship between capabilities and functionings in the capability approach. The paper shows that some functionings are not only the result of capabilities, but also their prerequisite. That is, there is a dual role of some functionings as both ends and instruments, resulting in a mutual dependency between capabilities and functionings. Functionings may be a direct requirement for capabilities, but also an indirect one because they ensure the absence of mental disorders or negative thoughts, both of which are relevant constraints on freedom. This has important implications. It supports a policy that ensures for everyone an initial endowment of (1) mental and physical health, (2) education, and (3) other functionings with a direct or indirect impact on capabilities.     

Some startling inconsistencies when electing committees

We generalize the idea of a Condorcet winner to committee elections to select a Condorcet committee of size m. As in the case of a Condorcet winner, the Condorcet committee need not exist. We adapt two methods to measure how far a set of m candidates is from being the Condorcet committee. In particular, we generalize a procedure proposed by Lewis Carroll for selecting the candidate that is closest to being the Condorcet winner to allow the selection of a committee. We also generalize Kemenys method, which gives a complete transitive ranking, to the selection of committees and show that it is closely related to the first method.We show that these methods lead to some surprising inconsistencies. For example, the committee of size k may be disjoint from the committee of size j or they may overlap in any manner, the committee arising from Carrolls method may appear at any locations in the Kemeny ranking, and except for two highly restrictive cases, the members of the committee arising from Kemenys method may appear at any location in the Kemeny ranking. The author wishes to express his thanks to Don Saari for his conversations and suggestions for the paper and to the Institute for Mathematical Behavioral Sciences at the University of California at Irvine where the initial work for this paper took place. He also wishes to thank the anonymous reviewer whose careful reading and suggestions greatly improved the paper.     

Ranking profiles of capability sets

In this paper, we present an innovative approach for ranking profiles of capability sets on the basis of equity. An interesting way of capturing the notion of equity is to take into account the extent to which each of the different functioning vectors is shared by the population under consideration (of size n). This is done by defining the ‘common capability sets’ enjoyed by k individuals as the set of functioning vectors simultaneously available to at least k individuals (1 ≤ k ≤ n). These sets are closely related to the original capability sets and have some interesting properties that are examined throughout the paper. We define and axiomatically characterize a capability profile ranking that lexicographically compares the different common capability sets. We would like to thank for helpful discussion and comments to Jorge Alcalde-Unzu, Ritxar Arlegi, Miguel A. Ballester, Jose Enrique Galdón, Antonio Nicolò, Jorge Nieto, Prasanta Pattanaik, John Weymark and the anonymous referees of this paper. The project is supported by Spanish’ Comision Interministerial de Ciencia y Technologia (SEC2003-08105) and by the European Commission (MRTN-CT-2003-504796).     

Demographic,organizational and economic determinants of work satisfaction: An assessment of work attitudes of females in academic settings

Using a sample of females employed in nonindustrial settings, a model of work satisfaction was proposed and tested using nonlinear iterative partial least squares (PLS). Included in the final model were three demographic variables (age, hierarchical level, and education); two organizational variables (routinization and size); and two economic variables (objective and perceptual measures of opportunity). Positive relationships were observed between age and work satisfaction and hierarchical level and work satisfaction. An inverse relationship between education and work satisfaction was detected also. Both of the organizational variables were negatively correlated with work attitudes. Objective measures of opportunity (e.g., the unemployment rate) were negatively related to perceived opportunity, and perceived opportunity was inversely related to work satisfaction. The model explained almost 33% of the variance in job satisfaction, although the objective measures of opportunity accounted for less than 2% of the variance in perceived opportunity. The best predictor of work attitudes was routinization. Perceived opportunity and size were the second and third best predictors, respectively. The implications of this research for organizational theorists and managers are discussed.     

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.     

Inequality of opportunity in the land of opportunities, 1968–2001

We measure inequality of opportunity for earnings acquisition in the U.S. between 1968 and 2001. Following recent theories of social justice, earnings determinants are divided into two parts: Circumstances, which are characteristics outside individual control and effort representing factors impacting earnings but under individuals’ responsibility. Equality of opportunity requires that inequality of circumstances must be corrected while differences of effort must remain unaltered. Circumstances are represented by parental education and occupation, ethnic origin, place of birth and age. Effort is modeled with schooling choices and labour supply decisions. Using the PSID from 1968 to 2001, we provide two alternative assessments of inequality of opportunity using counterfactual distributions. The statistical framework is semi-parametric and builds on duration models. Finally, we conclude that inequality of opportunity represents between 20 and 43% of earnings inequality, but decreases all over the period reaching around 18% in 2001.     

The Borda dictionary

Forn candidates, a profile of voters defines a unique Borda election ranking for each of the 2 ⁿ – (n + 1) subsets of two or more candidates. The Borda Dictionary is the set of all of these election listings that occur for any choice of a profile. As such, the dictionary contains all positive features, all flaws, and all paradoxes that can occur with single profile, sincere Borda elections. After the Borda Dictionary is characterized, it is used to show in what ways the Borda Count (BC) is an improvement over other positional voting methods and to derive several new BC properties. These properties include several new characterizations of the BC expressed in terms of axiomatic representations of social choice functions, as well as showing, for example, that the BC ranking ofn candidates can be uniquely determined by the BC rankings of all sets ofk <n candidates for any choice ofk between 2 andn.This research was supported, in part, by NSF grants IRI8415348, IRI-8803505 and a Fellowship from the Guggenheim Memorial Foundation.     

Rationality,external norms,and the epistemic value of menus

Ever since Sen’s criticism of internal consistency properties of choice, there exists a perception that the standard rational choice approach has difficulties in coping with the existence of external norms, or the information a menu of choice might convey to a decision maker. This article provides a brief survey of possible responses to these criticisms of traditional rational choice theory. We review approaches to the internalization of external norms as well as ways to formulate norm-conditional rationalizability. Furthermore, we illustrate how the epistemic value of an opportunity set can be incorporated into rational choice theory.     

YOUR RIGHT ARM FOR A PUBLICATION IN AER?

The time tradeoff (TTO) method is popular in medical decision making for valuing health states. We use it to elicit economists' preferences for publishing in top economic journals and for living without limbs. The economists value journal publications highly and have a clear preference among them, with the American Economic Review (AER) the most preferred. Their responses imply they would sacrifice more than half a thumb for an AER publication. These TTO results are consistent with ranking and willingness to pay results, and indicate that journal preferences are not entirely determined by impact factors or by expectations of a salary increase following a publication in a prestigious journal. (JEL A10, B41, I10)