Extended preferences and freedom of choice

The common choice theory in economics is based on the assumption that an individual is defined in terms of a binary preference relation. This preference relation is defined over alternatives without taking into account menu dependence and, in particular, freedom of choice or, more generally, the set that contains the alternatives. In this study we clarify the nature and the significance of freedom of choice which may positively or negatively affect the individual's welfare. Our proposed extended preference relation of the individual takes into account both the particular alternative and the opportunity set that he faces. This extended relation does not induce ranking of opportunity sets. Its restriction to a particular opportunity set is the paradigmatic preference relation and it can capture the dependence of preferences on freedom of choice. Our main result establishes the inconsistency between dependence of extended preferences on freedom of choice and the existence of a utility that represents the paradigmatic preference relation and any of its restrictions. Received: 30 December 1997/Accepted: 6 September 1999     

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).     

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     

Freedom of choice and expected compromise

This article develops a new measure of freedom of choice based on the proposal that a set offers more freedom of choice than another if, and only if, the expected degree of dissimilarity between a random alternative from the set of possible alternatives and the most similar offered alternative in the set is smaller. Furthermore, a version of this measure is developed, which is able to take into account the values of the possible options.     

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     

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.     

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.     

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.     

Freedom of choice and rational decisions

The paper formalizes a notion of preference-based freedom and examines to which extent such a notion is consistent with otherwise standard conditions of rational decision making. The central result is as follows. Suppose that a preference-based ranking of opportunity sets satisfies a very mild condition of preference for freedom of choice. Then, either the ranking is degenerate in being discontinuous, or the underlying preference relation among the basic alternatives is incomplete. Hence, in any case preference-based rankings of freedom will violate at least some of the basic assumptions of traditional choice modelling. This conclusion is enhanced if the conditions on preference-based freedom are slightly strengthened.I would like to thank the participants of seminars held at the Universities of Karlsruhe and Vienna for valuable comments and stimulating discussions. I am especially indebted to Thomas Christ, Egbert Dierker, Georg Kirchsteiger, Dieter Puppe and anonymous referees for helpful comments. The research has been made possible by a fellowship of the DFG (Deutsche Forschungsgemeinschaft) which is also gratefully acknowledged.     

Ranking opportunity sets on the basis of their freedom of choice and their ability to satisfy preferences: A difficulty

This paper examines a possibility of enlarging the domain of definition of individual preferences suggested by the recent literature on freedom of choice. More specifically, the possibility for an individual to have preferences that depend upon both the opportunity set that she faces and the particular alternative that she chooses from that set is considered. Even more specifically, the possibility for these preferences to value freedom of choice, as defined by the set theoretic relation of inclusion, while being consistent, in a certain sense, with the existence of a preference ordering over the options contained in opportunity sets is investigated. It is shown in the paper that a necessary condition for the existence of any transitive extended preferences of this type is for freedom of choice to be given no intrinsic importance. Received: 22 November 1995 / Accepted: 11 January 1997     

On real economic freedom

Among the various concepts of freedom important for economics, ranking or measuring the freedom of choice provided by budget sets has an important place. The volume ranking has strange properties and cannot be justified by unit invariance and symmetry. The pointed distance (of the budget hyperplane from the origin along some line) provides a measure or ranking that coincides with the standard “purchasing power” or real income. The linear price index is practically unavoidable for measuring or ranking freedom. This is applied to the determination of income distribution and taxation implied by the equal freedom of choice of different domains. Concepts of equal or compared potential freedoms and utility-freedom relate freedom analysis to the basic classical concepts of fair allocation (equity-no-envy, egalitarian equivalence, etc.). The crucial difference between the two opposite concepts of invariance in comparisons is emphasized.     

Lexicographic measurement of the information contained in opportunity sets

An individual who has to choose one item from an opportunity set or menu may lack complete information about the final consequences attached to her choice. This problem has been modeled by Bossert (2000) who introduces an axiomatic approach to the ranking of menus according to their informational content. We propose a different ranking based on the lexicographic ordering on the vectors of numbers of consequences for each item and characterize it axiomatically. Received: 12 June 1998/Accepted: 5 September 2000     

The value of opportunities over time when preferences are unstable

Most work on measuring opportunity is directed at ranking opportunity sets. This paper addresses the more general issue of assessing the opportunity provided by multi-period decision problems, focusing on the dynamic inconsistencies that can occur if agent’s preferences are unstable. A principle is proposed by which a dominance relation among outcomes iteratively induces a dominance relation among multi-period problems. This principle implies that opportunities to make sequences of individually reasonable actions have positive value, even if, because of dynamic inconsistency, those sequences lead to unambiguous loss. Opportunities which allow an agent to constrain herself are shown to have zero value.     

Freedom of choice and diversity of options: Some difficulties

This paper explores the possibility for a (non-preference-based) freedom ranking of opportunity sets that is sensitive to the diversity of the options. It turns out that how distances between sets and alternatives are measured is crucial to the derivation of such a ranking. Several proposals are examined, each of which is shown to lead to impossibility results. Earlier versions of this paper were presented at conferences in Kortrijk, Osnabrück, Oisterwijk, Caen and Pavia. I thank the participants at these conferences for their comments. I would also like to thank Steven Hartkamp, Theo Kuipers, Clemens Puppe and especially Kotaro Suzumura for their helpful comments. Furthermore, I am very grateful to Somdeb Lahiri for pointing out a mistake in a previous version of this paper.     

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     

Freedom of choice

Inspired by the discussion of different functions of freedom of choice (instrumental versus intrinsic value) by Sen and others and an axiomatic characterization of an intrinsic aspect by Pattanaik and Xu, we compare unique axiomatic characterizations of three classes of rankings of opportunity sets in terms of freedom of choice: First, we investigate the simple cardinality-based ranking proposed by Pattanaik and Xu and a generalization of this. Secondly, we propose a new criterion that is based on the comparison of the ranges of sets of options. Thirdly, we solve possibly occuring conflicts between these two criteria.I am indebted to Wulf Gaertner, Yongsheng Xu, Walter Bossert, the participants of the Economic Theory Workshop of the University of Rochester, and anonymous referees for helpful discussions and comments. Financial support by Deutsche Forschungsgemeinschaft is gratefully acknowledged.     

On Preference, Freedom and Diversity

We study the problem of ranking sets of options in terms of freedom of choice. We propose a framework in which both the diversity of the options and the preferences of the agent over the options do play a role. We formulate some axioms that reflect these two aspects of freedom and we study their logical implications. Two different criteria for ranking sets are characterized, which generalize some of the rankings proposed so far in the literature.     

Justifiable preferences over opportunity sets

In this paper we say that a preference over opportunity sets is justifiable if there exists a reflexive and complete binary relation on the set of alternatives, such that one opportunity set is at least as good as a second, if and only if the there is at least one alternative from the first set which is no worse than any alternative of the two sets combined together, with respect to the binary relation on the alternatives. In keeping with the revered tradition set by von Neumann and Morgenstern we call a reflexive and complete binary relation, an abstract game (note: strictly speaking von Neumann and Morgenstern refer to the asymmetric part of a reflexive and complete binary relation as an abstract game; hence our terminology though analytically equivalent, leads to a harmless corruption of the original meaning). In this paper we obtain a necessary and sufficient condition for the justifiability of transitive and quasi transitive preferences over opportunity sets. I would like to thank Prasanta Pattanaik for motivation in this research. I would also like to thank Maurice Salles and an anonymous referee of this journal for useful suggestions leading to considerable improvement in the presentation. An earlier version of this paper was presented at the Sixth Annual Conference on Econometric Modeling for Africa, held at Pretoria from July 4–6, 2001. I would like to thank all the conference participants for their observations on my paper. However, the sole responsibility for errors that do remain is my own.     

The Extramarital Affair: A Language of Yearning and Loss

This paper presents an extramarital relationship as an experience of self-enhancement, not of pathological conflict. It will suggest that the simultaneous relationship with the lover AND an empathically attuned therapist can be healing for the patient. It is seen as often an opportunity for essential developmental needs to be fulfilled when damaging failures in the bond between child and caretaker have restricted the vitalizing atmosphere of mutual influence that results in unrecognized subjectivity. Rather than viewed as a reality-escaping midlife enactment, these relationships can be better thought of as efforts to revisit the traumatic experiences that have created the organizing patterns that have limited a patient's self-development. An extramarital affair is often about yearning and loss and the freedom to enact one's own desire.     

Paired comparisons analysis: an axiomatic approach to ranking methods

In this paper we present an axiomatic analysis of several ranking methods for general tournaments. We find that the ranking method obtained by applying maximum likelihood to the (Zermelo-)Bradley-Terry model, the most common method in statistics and psychology, is one of the ranking methods that perform best with respect to the set of properties under consideration. A less known ranking method, generalised row sum, performs well too. We also study, among others, the fair bets ranking method, widely studied in social choice, and the least squares method.