A revealed preference analysis of solutions to simple allocation problems

We interpret solution rules on a class of simple allocation problems as data on the choices of a policy maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well-known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction independent and other-c monotonic rule is transitive-rational; and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function.     

Stochastic revealed preference and rationalizability

This article explores rationalizability issues for finite sets of observations of stochastic choice in the framework introduced by Bandyopadhyay et al. (Journal of Economic Theory, 84(1), 95–110, 1999). It is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity bundles. A new rationalizability condition for stochastic choices, “rationalizable in terms of stochastic orderings on the normalized price space” (rsop), is defined. rsop is satisfied if and only if there exists a solution to a linear feasibility problem. The existence of a solution also implies rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here.     

A graph-theoretical approach to the aggregation of individual preference orderings

A graph-theoretical approach as first outlined by Harary et al. is developed for solving the problem of aggregating a given set of individual preference orderings provided that no individual preferential judgment is inconsistent with the collective preference ordering obtained by aggregation.

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Set and revealed preference axioms for multi-valued choice

Theory and Decision - We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We...     

The choice axiom,revealed preference,and the theory of demand

The paper relates the classical economic theory of consumer demand to Luce's well-known general theory of choice behaviour. After discussing some fundamental similarities between the two theories, a simplified variant of Luce's probabilistic theory is used as an aid to construct, by analogy, a generalization of the classical theory of demand. In the light of Luce's theory it is then examined in what sense the representative demand of the uncertain consumer will coincide with the demand that maximizes utility, and in what sense it will coincide with classical demand.     

A new approach to care proceedings

A new approach to care proceedings, introduced in April 2008 with revised Children Act 1989 Guidance Volume 1 and the Public Law Outline (PLO), a procedural guide for the courts, adds a semi‐formal pre‐proceedings stage. This paper critiques the aims and objectives of the pre‐proceedings process in the light of what is known about the families who become subject to care proceedings. Drawing on the Care Profiling Study, the analysis of a random sample of 386 court files for care proceedings brought in 2004 and the Ministry of Justice's preliminary study of the operation of care proceedings under the PLO, it questions whether formalizing communication between the local authority and the parents immediately before proceedings can produce the intended benefits of diverting cases from the courts and improving the preparation of court applications. It considers how the new processes fit with existing safeguarding and planning procedures, the impact on workers and families, and whether the procedures will help produce good, long‐term arrangements for children at risk of significant harm more quickly.     

A subjectivist approach to consecutive conflict

An easily applied approach is developed to provide one participant in a sequence of conflicts with an optimal strategy. A goal of this article is to demonstrate that it is mathematically feasible to incorporate a decision maker's subjective distributions over the effects his actions will have on the outcomes of future conflicts. Unlike many other approaches, the model of this article does not restrict the beliefs that the participant is allowed to express. The participant, not the decision theorist, decides on what is relevent. Model assumptions required for updating rules, such as Bayesian updating, are not required unless they really are appropriate for the situation.Thanks are due to J. B. Kadane for suggesting the problem and for many helpful discussions.     

A unified approach to restricted games

There have been two main lines in the literature on restricted games: the first line was started by Myerson (1977) that studied graph-restricted games an the second one was initiated by Faigle (1989). The present paper provides a unified way to look on the literature and establishes connections between the two different lines on restricted games. The strength and advantages of this unified approach becomes clear in the study of the inheritance of the convexity from the game to the restricted game where an interesting result by Nouweland and Borm (1991) on the convexity of graph-restricted games is turned into a direct consequence of the corresponding result by Faigle (1989), by means of this relation. This revised version was published online in June 2006 with corrections to the Cover Date.     

A variational model of preference under uncertainty

A familiar example devised by Daniel Ellsberg to highlight the effects of event ambiguity on preferences is transformed to separate aleatory uncertainty (chance) from epistemic uncertainty. The transformation leads to a lottery acts model whose states involve epistemic uncertainty; aleatory uncertainty enters into the statedependent lotteries. The model proposes von Neumann-Morgenstern utility for lotteries, additive subjective probability for states, and the use of across-states standard deviation weighted by a coefficient of aversion to variability to account for departures from Anscombe-Aumann subjective expected utility. Properties of the model are investigated and a partial axiomatization is provided.     

A psychosocial approach to supporting injured dancers

Professional dancers experience injury as a crisis and threat to identity that often leads to numerous psychosocial concerns. This article describes a group model designed to help injured dancers recover. As a program of The Actors Fund, this 10-week Support Group for Injured Dancers reduces unwanted isolation caused by injury and provides dancers with strategies for stress reduction and healing. The purpose of this article is to aid practitioners in mitigating emotional distress among injured dancers by providing the history and rationale behind the group, an overview of the group’s structure and methods, and suggestions for further research and growth.     

A simplified axiomatic approach to ambiguity aversion

This paper takes the Anscombe–Aumann framework with horse and roulette lotteries, and applies the Savage axioms to the horse lotteries and the von Neumann–Morgenstern axioms to the roulette lotteries. The resulting representation of preferences yields a subjective probability measure over states and two utility functions, one governing risk attitudes and one governing ambiguity attitudes. The model is able to accommodate the Ellsberg paradox and preferences for reductions in ambiguity.     

A multidisciplinary approach to treating child neglect

Although the multidisciplinary team approach is useful in treating child abuse and neglect, it is underutilized in the first instance and rarely employed in the second. The authors discuss the rationale, process, function, and effectiveness of such a team in dealing with child neglect.     

A differential approach to the repeated prisoner's dilemma

The repeated prisoner's dilemma game is converted into a differential game by assuming that the players, instead of making decisions individually for each repetition of the prisoner's dilemma game, make decisions on the ratio of cooperative and noncooperative games that they wish to play over the next few moves, and that the actual plays are then determined using this ratio and a randomizing procedure. Although it sounds like a significant departure, this assumption is probably not too different from reality.Since each player can always obtain by his own action at least the payoff which he would receive from the noncooperative-noncooperative pair of strategies, that part of the differential game which is dominated by such a dual noncooperative strategy for either player is an unlikely outcome. This dominated area can be readily computed for any game, including those with more than two players.Formal testing with empirical data was impossible because of uncertainty about the proper null hypothesis. Nevertheless, experimental results reported by Rapoport are consistent with the theory.The authors are, respectively, Graduate Research Asistant in Economics and Professor of Economics and Public Choice at Virginia Polytechnic Institute and State University.     

A rational approach to pricing of catastrophe insurance

A methodology for rational pricing of catastrophe insurance is described. The methodology has two components: a solvency- and stability-based pricing framework, and an engine to quantify the loss variability that drives solvency and stability. Generalization to account for contagious effects of catastrophes and multiple occurrence of peril is presented in detail.     

A Diamond-Stiglitz approach to the demand for self-protection

The existing research concerning the relationship between risk aversion and prudence and the demand for self-protection assumes that the loss variable follows a Bernoulli distribution, and that changes in the level of self-protection are mean preserving. The analysis here replaces these two very strong conditions with ones which are more general. When doing this, the method of analysis is also significantly modified. This modification includes representing a change in the level of self-protection using the procedure developed by Diamond and Stiglitz (Journal of Economic Theory 8:337-360, 1974) for representing a change in risk. This alternate representation allows the existing findings to be generalized considerably, and also simplifies the analysis.     

A dual approach to Bayesian inference and adaptive control

Probability updating via Bayes' rule often entails extensive informational and computational requirements. In consequence, relatively few practical applications of Bayesian adaptive control techniques have been attempted. This paper discusses an alternative approach to adaptive control, Bayesian in spirit, which shifts attention from the updating of probability distributions via transitional probability assessments to the direct updating of the criterion function, itself, via transitional utility assessments. Results are illustrated in terms of an adaptive reinvestment two-armed bandit problem.     

A grass roots approach to influencing child welfare policy

This paper provides a brief review of child welfare issues identified by a Canadian Task Force convened for the 1979 Year of the Child. Project experience with the use of Looking After Children is linked to the issues identified in 1979. A fairly extensive discussion of legal considerations is presented to provide a context for the challenge of influencing policy. Finally, the possibility of influencing policy from a grass roots approach that can transcend jurisdictional boundaries is presented as offering hope for change in a child‐centred direction.