Probabilistic Subset Conjunction

The authors introduce subset conjunction as a classification rule by which an acceptable alternative must satisfy some minimum number of criteria. The rule subsumes conjunctive and disjunctive decision strategies as special cases. Subset conjunction can be represented in a binary-response model, for example, in a logistic regression, using only main effects or only interaction effects. This results in a confounding of the main and interaction effects when there is little or no response error. With greater response error, a logistic regression, even if it gives a good fit to data, can produce parameter estimates that do not reflect the underlying decision process. The authors propose a model in which the binary classification of alternatives into acceptable/unacceptable categories is based on a probabilistic implementation of a subset-conjunctive process. The satisfaction of decision criteria biases the odds toward one outcome or the other. The authors then describe a two-stage choice model in which a (possibly large) set of alternatives is first reduced using a subset-conjunctive rule, after which an alternative is selected from this reduced set of items. They describe methods for estimating the unobserved consideration probabilities from classification and choice data, and illustrate the use of the models for cancer diagnosis and consumer choice. They report the results of simulations investigating estimation accuracy, incidence of local optima, and model fit. The authors thank the Editor, the Associate Editor, and three anonymous reviewers for their constructive suggestions, and also thank Asim Ansari and Raghuram Iyengar for their helpful comments. They also thank Sawtooth Software, McKinsey and Company, and Intelliquest for providing the PC choice data, and the University of Wisconsin for making the breast-cancer data available at the machine learning archives.     

Linear relations amongk sets of variables

A family of solutions for linear relations amongk sets of variables is proposed. It is shown how these solutions apply fork=2, and how they can be generalized from there tok3.The family of solutions depends on three independent choices: (i) to what extent a solution may be influenced by differences in variances of components within each set; (ii) to what extent the sets may be differentially weighted with respect to their contribution to the solution—including orthogonality constraints; (iii) whether or not individual sets of variables may be replaced by an orthogonal and unit normalized basis.Solutions are compared with respect to their optimality properties. For each solution the appropriate stationary equations are given. For one example it is shown how the determinantal equation of the stationary equations can be interpreted.     

On the Determination of Minimal Facets and Edges of a Polyhedral Set

In this paper we investigate the image of a polyhedral set under a linear map. Moreover, we present an algorithm for the determination of so-called minimal facets and certain minimal irredundant proper edges of a convex polyhedral set in ℝ³. © 1997 John Wiley & Sons, Ltd.     

When “decoy effect” meets gender bias: The role of choice set composition in hiring decisions

A large body of research has found evidence that hiring decisions are frequently subject to strong gender bias and has explored factors that help to predict and prevent such a bias from occurring. In this paper, we explore a novel factor that has received only little attention: the composition of the choice set. Drawing on prior research on the attraction effect of decoys in consumer choice and personnel decisions, we posit that when decision makers need to decide whether to hire a male or a female applicant for a stereotypically male position, the presence of a third applicant whose profile is asymmetrically dominated by one of the two applicants can in many circumstances strongly increase the odds that the male applicant will be selected, but will not be beneficial for the female applicant. We test our hypotheses in five experimental studies with different designs, experimental settings, and participant pools—including managers with professional experience in hiring decisions. Our results provide robust evidence demonstrating the strong effects of choice set composition on the emergence of gender bias. In addition, we found that the presence of asymmetrically dominated applicants makes decision makers more confident in their biased decisions and more likely to implement them immediately without searching for further information. Finally, our results also provide some initial evidence that our results for stereotypically male positions will be reversed when hiring decisions are made for stereotypically female positions where the presence of decoys instead gives an advantage to female over male applicants.     

An examination of indexes for determining the number of clusters in binary data sets

The problem of choosing the correct number of clusters is as old as cluster analysis itself. A number of authors have suggested various indexes to facilitate this crucial decision. One of the most extensive comparative studies of indexes was conducted by Milligan and Cooper (1985). The present piece of work pursues the same goal under different conditions. In contrast to Milligan and Cooper's work, the emphasis here is on high-dimensional empirical binary data. Binary artificial data sets are constructed to reflect features typically encountered in real-world data situations in the field of marketing research. The simulation includes 162 binary data sets that are clustered by two different algorithms and lead to recommendations on the number of clusters for each index under consideration. Index results are evaluated and their performance is compared and analyzed.Author names are listed in alphabetical order.This piece of research was supported by the Austrian Science Foundation (FWF) under grant SFB#010 (Adaptive Information Systems and Modeling in Economics and Management Science).The authors would like to thank the anonymous reviewers and especially the associate editor for their helpful comments and suggestions.     

Set-Theoretic Absoluteness and the Revision Theory of Truth

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.     

On Consistent Subsets of Large Sets of Satisfiable Sentences

We extend some results of Adam Kolany to show that large sets of satisfiable sentences generally contain equally large subsets of mutually consistent sentences. In particular, this is always true for sets of uncountable cofinality, and remains true for sets of denumerable cofinality if we put appropriate bounding conditions on the sentences. The results apply to both the propositional and the predicate calculus. To obtain these results, we use delta sets for regular cardinals, and, for singular cardinals, a generalization of delta sets. All of our results are theorems in ZFC.     

Delta图分析方法及其在冲突控制研究中的应用

近年来,反应时分布分析方法被应用于冲突控制研究领域,以弥补只计算平均反应时和错误率的不足。所谓delta指的是不一致条件与一致条件反应时之差,即冲突效应量。冲突效应量随反应时间的变化图称为delta图。与该分析方法相应的理论模型包括双通路模型和激活－抑制模型。本文介绍了delta图分析的具体方法及其与冲突控制理论模型的关系,然后列举了有关的研究例证,并强调了其优缺点与适用范围