An axiomatic characterization of the Theil inequality ordering

We axiomatically characterize the Theil ordering of income inequality. In addition to the uncontroversial axioms of anonymity, homogeneity, replication invariance, strong directedness, and a standard continuity property, we appeal to both an independence and a decomposability axioms. These two axioms are ordinal implications of Theil decomposability, the central axiom in previous characterizations of the Theil index. To the best of our knowledge, the present is the first fully ordinal characterization of this index.     

An axiomatic characterization of the Theil measure of income inequality

This paper provides a characterization of a frequently used measure of income inequality. It has been known for some time that the Theil measure of income inequality (1) is consistent with the Lorenz criterion, when it applies, and (2) exhibits a simple and empricically useful decomposition by population subgroup into within-group and between-group terms. The major theorem establishes the converse: the decomposability property defines the Theil measure uniquely (up to a positive multiple) among all Lorenz-consistent measures.     

An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom

The independence axiom used to derive the expected utility representation of preferences over lotteries is replaced by requiring only convexity, in terms of probability mixtures, of indifference sets. Two axiomatic characterizations are proven, one for simple measures and the other continuous and for all probability measures. The representations are structurally similar to expected utility, and are unique up to a generalization of affine transformations. First-order stochastic dominance and risk aversion are discussed using a method which finds an expected utility approximation to these preferences without requiring differentiability of the preference functional.     

Feasible elimination procedures in social choice: An axiomatic characterization

Feasible elimination procedures (Peleg, 1978) play a central role in constructing social choice functions which have the following property: in the associated game form, for any preference profile there exists a strong Nash equilibrium resulting in the sincere outcome. In this paper we provide an axiomatic characterization of the social choice correspondences resulting from applying feasible elimination procedures. The axioms are anonymity, Maskin monotonicity, and independent blocking. We also show that these axioms are logically independent.     

The measurement of structural differences between economies: An axiomatic characterization

Summary. In empirical studies concerning comparison of economic structures and/or structural changes of economies, it is quite useful to employ an aggregate index to describe the structural difference (similarity). This paper offers an axiomatic characterization of the measurement of structural difference between economies that leads to some difference (similarity) index which is practically useful in empirical studies. Received: September 3, 1999; revised version: November 9, 1999     

An axiomatic definition of the leximin

For a class of multicriterion decision making problems the set of lexicographic minimax in a set of alternatives with regard to the given criterion functions is characterized by six axioms: symmetry, independence of irrelevant alternatives, domination, separability, convexity, and monotone transformation. Each of the axioms is independent of the rest.     

An axiomatic characterization of skew-symmetric bilinear functionals,with applications to utility theory

Axioms for two generalizations of von Neumann-Morgenstern linear utility are described. The first represents preferences between risky prospects by the positive part of a skew-symmetric bilinear functional; the second is based on quotients of linear functionals.     

Median-based extensions of an ordering over a set to the power set: An axiomatic characterization

In this paper we consider the problem of inducing an ordering over the set of all non-empty subsets of a finite set X of alternatives, given an ordering R over X. Assuming R to be antisymmetric and X to have at least six elements, we provide a set of independent, necessary, and sufficient conditions for the induced ordering to be “median-based” (so that every non-empty subset of X is “indifferent” to its own median set defined in terms of R).     

An axiomatic theory of political representation

We discuss the theory of gerrymandering-proof voting rules. Our approach is axiomatic. We show that, for votes over a binary set of alternatives, any rule that is unanimous, anonymous, and gerrymandering-proof must decide a social outcome as a function of the proportions of agents voting for each alternative, and must either be independent of this proportion, or be in one-to-one correspondence with the proportions. In an extended model in which the outcome of a vote at the district level can be a composition of a governing body (with two possible parties), we discuss the quasi-proportional rules (characterized by unanimity, anonymity, gerrymandering-proofness, strict monotonicity, and continuity). We show that we can always (pointwise) approximate a single-member district quota rule with a quasi-proportional rule. We also discuss a more general environment, where there may be more than two parties.     

An efficiency characterization of plurality rule in collective choice problems

We consider the problem of selecting alternatives from a set of feasible alternatives over which each agent is endowed with a strict preference. We show that there is one and only one rule that satisfies anonymity, neutrality, efficiency, tops-only, and reinforcement. The rule is known as plurality rule, which selects the alternative(s) most preferred by the largest number of agents. I would like to thank William Thomson for helpful suggestions and discussions. I am grateful to Biung-Ghi Ju, Hyungjun Kim, and Yan-An Hwang for detailed comments. I am also indebted to the Editor and an anonymous referee for valuable suggestions. As usual, I am responsible for any remaining deficiency.     

A simple characterization of majority rule

Summary. Assuming an odd number of voters, E. S. Maskin recently provided a characterization of majority rule based on full transitivity. This paper characterizes majority rule with a set of axioms that includes two of Maskin's, dispenses with another, and contains weak versions of his other two axioms. It allows the number of voters to be odd or even. Received: December 23, 1998; revised version: May 10, 1999     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

Efficiency properties of strategies market games: An axiomatic approach

The paper investigates the conditions under which an abstractly given market game will have the property that if there is a continuum of traders then every noncooperative equilibrium is Walrasian. In orther words, we look for a general axiomatization of Cournot's well-known result. Besides some convexity, continuity, and nondegeneracy hypotheses, the crucial axioms are: anonymity (i.e., the names of traders are irrelevant to the market) and aggregation (i.e., the net trade received by a trader depends only on his own action and the mean action of all traders). It is also shown that the same axioms do not guarantee efficiency if there is only a finite number of traders. Some examples are discussed and a notion of strict noncooperative equilibrium for anonymous games is introduced.     

Modelling change in individual characteristics: An axiomatic framework

Economic models describe individuals by underlying characteristics, such as the degree to which they like music, have sympathy, want success, need recognition, etc. In reality, such characteristics change through experiences: taste for Mozart changes through attending concerts, sympathy through meeting people, etc. Models typically ignore change, partly because it is unclear how to incorporate it. I develop a general axiomatic framework for defining, analysing and comparing rival models of change. Seemingly basic postulates on modelling change have strong implications, like irrelevance of the order in which someone has his experiences and ‘linearity’ of change. This paper is a step towards placing the modelling of change on axiomatic grounds and enabling non-arbitrary incorporation of change into economic models.     

An axiomatic approach to choice under uncertainty with catastrophic risks

This paper analyses decision under uncertainty with catastrophic risks, and is motivated by problems emerging from global environmental risks. These are typically low-probability events with major irreversible consequences. For such risks, the Von Neumann–Morgenstern (NM) axioms for decision making under uncertainty are not appropriate, since they are shown here to be insensitive to low-probability events. The paper introduces an alternative set of axioms requiring sensitivity to both low- and large-probability events. Through a new representation theorem in functional analysis, the results characterize all the operators whose maximization leads to the fulfillment of these axioms. They involve a convex combination of expected utility and a criterion based on the desire to avoid low probability and potentially catastrophic events. It is shown that the new axioms help resolve the Allais paradox. Open questions about risk aversion, games under uncertainty and calculus of variations are discussed.     

Directional measurement of technical efficiency of production: An axiomatic approach

This contribution revisits the debate on the axiomatic properties satisfied by various radial versus non-radial measures of technical efficiency in production. This issue arises whenever isoquant and efficient subset of technology diverge and hence traditional radial measurement does not comply with Koopmans' definition of technical efficiency. This axiomatic approach to technical efficiency measurement is revisited within the framework of the more recently introduced directional distance function. This analysis provides the opportunity to define some new directional efficiency measures.