Extension of Preferences to an Ordered Set

If a decision maker prefers x to y to z, would he choose orderd set [x;z] or [y;x]? This article studies extension of preferences over individual alternatives to an ordered set which is prevalent in closed ballot elections with proportional representation and other real life problems where the decision maker is to choose from groups with an associated hierarchy inside. I introduce ve ordinal decision rules: highest-position, top-q, lexicographic order, max-best, highest-of-best rules and provide axiomatic characterization of them. I also investigate the relationship between ordinal decision rules and the expected utility rule. In particular, whether some ordinal rules induce the same (weak) ranking of ordered sets as the expected utility rule

Generalized Decision Rule Approximations for Stochastic Programming via Liftings

Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations that result in loose bounds. To address this problem, we propose a lifting technique that maps a given stochastic program to an equivalent problem on a higherdimensional probability space. We prove that solving the lifted problem in primal and dual linear decision rules provides tighter bounds than those obtained from applying linear decision rules to the original problem. We also show that there is a one-to-one correspondence between linear decision rules in the lifted problem and families of non-linear decision rules in the original problem. Finally, we identify structured liftings that give rise to highly flexible piecewise linear decision rules and assess their performance in the context of a stylized investment planning problem.

Optimal sequential procedures with Bayes decision rules

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect decision and the cost of observations.Comment: Shortened version for print publication, 17 page

Methodological Background of Decision Rules and Feedback Tools for Outcomes Management in Psychotherapy

Systems to provide feedback regarding treatment progress have been recognized as a promising method for the early identification of patients at risk for treatment failure in outpatient psychotherapy. The feedback systems presented in this article rely on decision rules to contrast the actual treatment progress of an individual patient and his or her expected treatment response (ETR). Approaches to predict the ETR on the basis of patient intake characteristics and previous treatment progress can be classified into two broad classes: Rationally derived decision rules rely on the judgments of experts, who determine the amount of progress that a patient has to achieve for a given treatment session to be considered “on track.” Empirically derived decision rules are based on expected recovery curves derived from statistical models applied to aggregated psychotherapy outcomes data. Examples of each type of decision rule and of feedback systems based on such rules are presented and reviewed

Welfarism and the Assessments of Social Decision Rules

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Forecasting and Evaluating Network Growth

This research assesses the implications of existing trends on future network investment, comparing alternative scenarios concerning budgets and investment rules across a variety of performance measures. The main scenarios compare 'stated decision rules';, processes encoded in flowcharts and weights developed from official documents or by discussion with agency staff, with 'revealed decision rules', weights estimated statistically based on observed historical behavior. This research specifies the processes necessary to run the network forecasting models with various decision rules. Results for different scenarios are presented including adding additional constraints for the transportation network expansion and calibration process details. We find that alternative decision rules make only small differences in overall system performance, though they direct investments to very different locations. However, changes in total budget can make a significant difference to system-wide performance.