Lexicographic order preservation and stochastic dominance

Stochastic dominance concerns conditions on outcome probabilities that are necessary and sufficient for one act to be (strictly) preferred to another according to all preference relations that share certain properties, one of which customarily is an Archimedean property sufficient to entail existence of real-valued representations. We relax this assumption to permit linear lexicographic utility of finite and known dimensionality. In some situations, levels of the lexicographic hierarchy could correspond to explicit criteria or attributes. In our model, subjective probabilities emerge as matrix premultipliers of the outcome utility vectors. We thus obtain matrix probability generalizations of the familiar cumulative probability conditions for stochastic dominance.     

Stochastic Dominance and Opaque Sweetening

This paper addresses the problem of opaque sweetening and argues that one should use stochastic dominance in comparing lotteries even when dealing with incomplete orderings that allow for non-comparable outcomes.     

Rough approximation of pairwise comparisons described by multi‐attribute stochastic dominance

Given a finite set A of actions evaluated by a set of attributes, preferential information is considered in the form of a pairwise comparison table including pairs of actions from subset B⊂A described by stochastic dominance relations on particular attributes and a total order on the decision attribute. Using a rough sets approach for the analysis of the subset of preference relations, a set of decision rules is obtained, and these are applied to a set A\B of potential actions. The rough sets approach of looking for the reduction of the set of attributes gives us the possibility of operating on a multi‐attribute stochastic dominance for a reduced number of attributes. Copyright © 1999 John Wiley & Sons, Ltd.     

Decomposition of multivariate utility functions in non-additive expected utility theory

In expected utility many results have been derived that give necessary and/or sufficient conditions for a multivariate utility function to be decomposable into lower-dimensional functions. In particular, multilinear, multiplicative and additive decompositions have been widely discussed. These utility functions can be more easily assessed in practical situations. In this paper we present a theory of decomposition in the context of nonadditive expected utility such as anticipated utility or Choquet expected utility. We show that many of the results used in conventional expected utility carry over to these more general frameworks. If preferences over lotteries depend only on the marginal probability distributions, then in expected utility the utility function is additively decomposable. We show that in anticipated utility the marginality condition implies not only that the utility function is additively decomposable but also that the distortion function is the identity function. We further demonstrate that a decision maker who is bivariate risk neutral has a utility function that is additively decomposable and a distortion function q for which q(½) = ½.     

Statistics as psychometrics

In this paper, modern statistics is considered as a branch of psychometrics and the question of how the central problems of statistics can be resolved using psychometric methods is investigated. Theories and methods developed in the fields of test theory, scaling, and factor analysis are related to the principle problems of modern statistical theory and method. Topics surveyed include assessment of probabilities, assessment of utilities, assessment of exchangeability, preposterior analysis, adversary analysis, multiple comparisons, the selection of predictor variables, and full-rank ANOVA. Reference is made to some literature from the field of cognitive psychology to indicate some of the difficulties encountered in probability and utility assessment. Some methods for resolving these difficulties using the Computer-Assisted Data Analysis (CADA) Monitor are described, as is some recent experimental work on utility assessment.1980 Psychometric Society presidential address.I am indebted to Paul Slovic and David Libby for valuable consultation on the issues discussed in this paper and to Nancy Turner and Laura Novick for assistance in preparation.Research reported herein was supported under contract number N00014-77-C-0428 from the Office of Naval Research to The University of Iowa, Melvin R. Novick, principal investigator. Opinions expressed herein reflect those of the author and not those of sponsoring agencies.     

风险决策心理因素的理论综述

风险决策理论对于人们是否作出冒险行为的选择提出了两种比较典型的解释:一种解释把风险决策归因于人们共有的基本过程,即“较冷”的心理和认知过程。这些理论认为风险选择是由人类基本的心理和感觉机制引起的。而另一种解释则把风险决策归因于“较热”的情感和动机过程。这些理论认为,情境和人格因素会增强风险决策的动机并导致风险决策个体差异的存在。本文对这两种解释的不同理论作了较为系统的论述。     

Decomposition,Interdependence and Precision in Multiattribute Utility Measurements

Traditionally, parameters of multiattribute utility models, representing a decision maker's preference judgements, are treated deterministically. This may be unrealistic, because assessment of such parameters is potentially fraught with imprecisions and errors. We thus treat such parameters as stochastic and investigate how their associated imprecision/errors are propagated in an additive multiattribute utility function in terms of the aggregate variance. Both a no information and a rank order case regarding the attribute weights are considered, assuming a uniform distribution over the feasible region of attribute weights constrained by the respective information assumption. In general, as the number of attributes increases, the variance of the aggregate utility in both cases decreases and approaches the same limit, which depends only on the variances as well as the correlations among the single-attribute utilities. However, the marginal change in aggregate utility variance decreases rather rapidly and hence decomposition as a variance reduction mechanism is generally useful but becomes relatively ineffective if the number of attributes exceed about 10. Moreover, it was found that utilities which are positively correlated increase the aggregate utility variance, hence every effort should be made to avoid positive correlations between the single-attribute utilities. We also provide guidelines for determining under what condition and to what extent a decision maker should decompose to obtain an aggregate utility variance that is smaller than that of holistic assessments. Extensions of the current model and empirical research to support some of our behavioural assumptions are discussed. © 1997 John Wiley & Sons, Ltd.     

LOT 2: The Language of Thought Revisited

A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. Realists argue that it does; anti-realists argue that it doesn't. Part of this debate depends on how mathematics might be able to do explanatory work in an explanation. Everyone agrees that it's not enough that there merely be some mathematics in the explanation. Anti-realists claim there is nothing mathematics can do to make an explanation mathematical; realists think something can be done, but they are not clear about what that something is.

I argue that many of the examples of mathematical explanations of empirical facts in the literature can be accounted for in terms of Jackson and Pettit's [1990] notion of program explanation, and that mathematical realists can use the notion of program explanation to support their realism. This is exactly what has happened in a recent thread of the debate over moral realism (in this journal). I explain how the two debates are analogous and how moves that have been made in the moral realism debate can be made in the mathematical realism debate. However, I conclude that one can be a mathematical realist without having to be a moral realist.     

Multi‐Criteria Evaluation for Collaborative Circulating Farming with Collective Operations Between Arable and Cattle Farmers

Tokachi sub‐prefecture in Hokkaido is one of the most famous dairy and crop farming regions in Japan. It is known that Tokachi is faced with various difficult problems such as soil degradation, water contamination and unpleasant odours because of the excessive use of chemical fertilizers and inappropriate treatment of livestock excretion. In this paper, we focus on Shihoro town where agricultural outputs are relatively large in Tokachi, and propose collaborative circulating farming with collective operations between arable and cattle farmers. Under the assumption that the decision‐maker in this problem is a representative of a farming organization who hopes for sustainable agricultural development and values the intentions of local residents including arable and cattle farmers in this region, we employ multi‐attribute utility theory in order to evaluate multiple alternatives of the farming management problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Early Positive Information Impacts Final Evaluations: No Deliberation‐Without‐Attention Effect and a Test of a Dynamic Judgment Model

Evaluation judgments were affected by information order and not by subsequent unconscious versus conscious deliberation. In three experiments, we examined the influence of early positive information on final evaluations of four objects. Based on a task analysis, we predicted primacy effects in judgments in a sequential data acquisition task. Thinking periods following presentation were used to manipulate conscious or unconscious processing. In all three studies, we found no effects of thinking manipulations but instead found reliable order effects. We developed and tested an online judgment model on the basis of the belief updating model of Hogarth and Einhorn. The model accounted for large proportion of the individual level variability, and model comparison tests supported the presence of a primacy effect. Copyright © 2013 John Wiley & Sons, Ltd.     

Order effects and memory for evidence in individual versus group decision making in auditing

Sequential processing of evidence may lead to recency effect, a potential bias in judgment. The present research seeks to extend the literature on recency effects by assessing the potential moderating influence of team work: whether group decision making moderates the severity of recency effects predicted by Hogarth and Einhorn (1992), and whether group processing influences the accuracy of, and confidence in memory for evidence. Experienced auditors from a Big‐6 accounting firm made audit judgments, either individually or as groups. They were randomly assigned to one of two levels of evidence presentation order. After performing the judgment task, participants completed two evidence recognition tests. Consistent with prior findings, recency effects on judgments were observed, but only for individuals. Group judgments or audit reports were not affected by recency. Order effects, however, did not translate into different choices of audit reports, and did not persist in memories of either individuals or groups. As expected, group memory was more accurate than individual memory and groups were more confident than individuals. Overall, confidence in accurate memories was greater than in inaccurate ones. Copyright © 1999 John Wiley & Sons, Ltd.     

A methodology to assess the utility of future space systems

The Air Force SPACECAST 2020 study identified and prioritized some future space systems and technologies required in the next century. This paper presents the results of research on the SPACECAST 2020 value model. The model determines and prioritizes future space systems’ utility towards controlling and exploiting space. This research identifies the assumptions and simplifications in the additive utility function and assesses modifications. The research shows that mutual utility independence of the mission areas is a reasonable assumption. Mutual utility independence allows the use of the multiplicative and multilinear utility functions. Also, the SPACECAST 2020 scoring functions used the same scoring scale and only measured the utility of future capabilities. This study makes modifications to the SPACECAST 2020 measure-of-merit scoring functions. It replaces most of these functions with either a concave, convex, linear or ‘S’ scoring function, which have expanded capability ranges to include both current and future capabilities. The modified scoring functions and alternative utility functions do not alter the SPACECAST 2020 results but do improve the credibility and future usefulness of the model. This study shows that the initial assumption of using an additive utility function is also valid. © 1997 John Wiley & Sons, Ltd.