An axiomatic characterization of the Baker-Thompson rule

The airport problem is a widely studied allocation problem, with the aim of providing simple and fair sharing rule for the landing fees. In this note we introduce some fairness criteria and characterize the classical Baker-Thompson allocation rule.     

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.     

Proportional concessions and the leximin solution

In this note we introduce a new axiom for bargaining solutions, named Proportional Concession Monotonicity (PCM), which imposes that no player benefits when all players collectively make proportional concessions with respect to their respective utopia values. We reconsider the leximin solution (Imai, 1983), and obtain an alternative characterization on the basis of PCM.     

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.     

Individual monotonicity and the leximin solution

Summary. Most axiomatic treatments of bargaining do not give a substantive role to individually irrational points. We show in this paper that it can matter greatly whether axioms and solutions are formulated with respect to the entire feasible set or with respect to only the individually rational portion. In particular, a principle of individual monotonicity becomes much more powerful when all feasible points are considered. We characterize the n-person Leximin solution as the only solution that satisfies Pareto efficiency, symmetry, individual monotonicity, and independence of individually irrational points.     

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.     

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.     

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.     

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.     

Growth-equity decomposition of a change in poverty: An axiomatic approach

This paper studies a class of subgroup decomposable poverty measures whose changes may be decomposed into a growth component and a redistribution component. A set of reasonable axioms leads inexorably to a combination of the Watts measure and the poverty gap measure.     

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.     

An axiomatic approach to \boldsymbol{\varepsilon}-contamination

Summary.  Suppose that an economic agent is 100% certain that uncertainty she faces is characterized by a particular probability measure, but that she has a fear that, with 100% chance, her conviction is completely wrong and she is left perfectly ignorant about the true measure in the present as well as in the future. This situation is often called -contamination of confidence. The purpose of this paper is to provide a simple set of behavioral axioms under which the decision-makers preference is represented by the Choquet expected utility with the -contamination of confidence.Received: 25 November 2002, Revised: 15 November 2004, JEL Classification Numbers:   D81. Correspondence to: Hiroyuki OzakiWe are grateful to an anonymous referee. The referees comments greatly improved the exposition of the paper. The work reported here is partially supported by a grant from the Economic and Social Research Insitute, the Cabinet Office, the Government of Japan.     

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     

A leximin characterization of strategy-proof and non-resolute social choice procedures

Summary. We characterize strategy-proof social choice procedures when choice sets need not be singletons. Sets are compared by leximin. For a strategy-proof rule g, there is a positive integer k such that either (i) the choice sets g(r) for all profiles r have the same cardinality k and there is an individual i such that g(r) is the set of alternatives that are the k highest ranking in i's preference ordering, or (ii) all sets of cardinality 1 to k are chosen and there is a coalition L of cardinality k such that g(r) is the union of the tops for the individuals in L. There do not exist any strategy-proof rules such that the choice sets are all of cardinality to k where . Received: November 8, 1999; revised version: September 18, 2001     

An axiomatic basis for the three objective social welfare function within a poverty context

This article argues that numbers of uncompensated losers, here equated with numbers below the poverty line, should accompany distribution and efficiency as a third element in the SWF. No constant weights, efficiency and distribution SWF can satisfy two simple axioms.