Subjective probabilities and utility with event-dependent preferences

This article generalizes Savage's theory to include event-dependent preferences. The state space is partitioned into finitely many events. The induced preferences over consequences are assumed independent of the underlying states within, but not across, these events. This results in an additively separable representation of preferences over acts. The dependence of the preference relation over consequences on the events is represented by event-dependent mappings of the set of consequences onto itself. Given these mappings, the preferences on acts are represented by the expectation of event-dependent utilities on the consequences with respect to unique subjective probabilities on the states.Helpful discussions with David Schmeidler are gratefully acknowledged.     

A LOWER BOUND FOR THE SINGLE-LEVEL DYNAMIC HORIZON LOT-SIZING PROBLEM

Conventional production planning methods assume the existence of a medium- or longrange demand horizon. However, demand usually is known over a much shorter range; scheduling decisions must be made within this “decision window,” which rolls forward in time. This paper presents a new lower bound for lot-sizing heuristics in a rolling-horizon framework and compares it to the well-known Wagner-Whitin bound. The new bound indicates heuristic schedules that have costs close to the optimum. Rolling-horizon schedule costs are compared to corresponding static-horizon schedule costs (assuming the whole horizon is known in advance), using the ratio of decision-window size to the natural order cycle as a parameter. For values below unity, the rolling-horizon policy is significantly more costly. For values above one, the two policies have similar costs and actually converge as the parameter value increases.     

On nonlinear multi-covering problems

In this paper we define the exact k-coverage problem, and study it for the special cases of intervals and circular-arcs. Given a set system consisting of a ground set of n points with integer demands \(\{d_0,\dots ,d_{n-1}\}\) and integer rewards, subsets of points, and an integer k, select up to k subsets such that the sum of rewards of the covered points is maximized, where point i is covered if exactly \(d_i\) subsets containing it are selected. Here we study this problem and some related optimization problems. We prove that the exact k-coverage problem with unbounded demands is NP-hard even for intervals on the real line and unit rewards. Our NP-hardness proof uses instances where some of the natural parameters of the problem are unbounded (each of these parameters is linear in the number of points). We show that this property is essential, as if we restrict (at least) one of these parameters to be a constant, then the problem is polynomial time solvable. Our polynomial time algorithms are given for various generalizations of the problem (in the setting where one of the parameters is a constant).     

Does the Person‐of‐the‐Therapist Training (POTT) Promote Self‐Care? Personal Gains of MFT Trainees Following POTT: A Retrospective Thematic Analysis

As we recognize how taxing our profession can be, therapist's self‐care has become a salient topic in mental health. However, we are still discerning how to promote self‐care in our practice and in training. In this paper, we present a study on the personal gains that MFT students experienced after participating in the Person‐of‐the‐Therapist Training (POTT). We propose that the reported changes (better understanding of self, change to self, relational changes, and change as a process) constitute improvements in the trainees’ well‐being, and can therefore be considered self‐caring behaviors and practices. We state that models like POTT, that focus on embracing our vulnerability, can help clinicians be more caring toward ourselves. We conclude this paper by presenting clinical and training recommendations.     

Moral sentiments and social choice

We examine the implications, for social choice, of individuals having an intrinsic sense of fairness. Taking the viewpoint that social justice reflects the moral attitudes of the constituent members, we analyze the effect of the intensity of the individual sense of fairness on the solution of Nash bargaining over random allocation procedures. We use a stylized model of university admission policies to illustrate our approach. We show that even if social policies are ultimately determined by the bargaining power of the different groups, a society whose members have a common notion of fairness tends to implement fairer admission policies when the intensity of the sense of fairness of individual members increases. While working on the research that is summarized in this paper the authors visited several institutions. Edi Karni visited the Berglas School of Economics, Tel Aviv University and GRID, at Ecole Normale Superieur de Cachan. Zvi Safra visited CERMCEM and EUREQua, at the University of Paris I and LIP6, at the University of Paris 6. The hospitality of these institutions is gratefully acknowledged. We are also grateful to the editor and two anonymous referees for their very useful comments and suggestions. Zvi Safra thanks The Israel Science Foudation (grant 1299/05) for its support.     

Unbounded behaviorally consistent stopping rules

In this article we study behaviorally consistent stopping rules in an unbounded search from a known distribution with no recall and with positive search cost. We show that if the searcher's preferences are quasi-convex in the probabilities, then behaviorally consistent search strategies in the unbounded case are obtained as limits of the corresponding bounded search strategies and are characterized by reservation levels property. Unlike optimal stopping rules under expected utility theory, however, the reservation levels may not be monotonically increasing in the number of permissible stages of the search process, and, in the unbounded case, may not be unique.     

David Schmeidler’s contributions to decision theory

Theory and Decision -     

Helping patients and physicians reach individualized medical decisions: theory and application to prenatal diagnostic testing

This paper presents a procedure designed to aid physicians and patients in the process of making medical decisions, and illustrates its implementation to aid pregnant women, who decided to undergo prenatal diagnostic test choose a physician to administer it. The procedure is based on a medical decision-making model of Karni (J Risk Uncertain 39: 1–16, 2009). This model accommodates the possibility that the decision maker’s risk attitudes may vary with her state of health and incorporates other costs, such as pain and inconvenience, associated with alternative treatments. The medical decision problem was chosen for its relative simplicity and the transparency it affords.     

“If I Can Grapple With This I Can Truly Be Of Use In The Therapy Room”: Using The Therapist's Own Emotional Struggles To Facilitate Effective Therapy

This study premises that self‐of‐the‐therapist work is pivotal in the development of effective therapists. However, therapy models vary in their goals for this work and the means of accomplishing them. This study presents the perspective of the person‐of‐the‐therapist Training (POTT) model that prioritizes the ability to consciously and purposefully use the self‐as‐is at the moment of contact with the client over the traditional goal of therapists working to resolve their issues. A key underlying assumption of the model proposes that therapists' core issues (referred to as “signature themes”) are potent resources that can be tapped into to connect, assess and intervene effectively with clients. The study presents the model and illustrates the use of signature themes in clinical work.     

On the Representation of Beliefs by Probabilities

This paper explores two axiomatic structures of subjective expected utility assuming a finite state-space and state-dependent, connected, topological outcome-spaces. Building on the work of Karni and Schmeidler (1981) the analytical framework includes, in addition to the preference relation on acts, introspective preferences on hypothetical lotteries that are linked to the preference relation on acts by consistency axioms. The two models accommodate state-dependent preferences and yield subjective probabilities that correctly represent the decision-maker's beliefs. State-independent preferences are a special case.