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.     

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.     

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.     

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.     

Conscious thoughts from reflex-like processes: A new experimental paradigm for consciousness research

The contents of our conscious mind can seem unpredictable, whimsical, and free from external control. When instructed to attend to a stimulus in a work setting, for example, one might find oneself thinking about household chores. Conscious content thus appears different in nature from reflex action. Under the appropriate conditions, reflexes occur predictably, reliably, and via external control. Despite these intuitions, theorists have proposed that, under certain conditions, conscious content resembles reflexes and arises reliably via external control. We introduce the Reflexive Imagery Task, a paradigm in which, as a function of external control, conscious content is triggered reliably and unintentionally: When instructed to not subvocalize the name of a stimulus object, participants reliably failed to suppress the set-related imagery. This stimulus-elicited content is considered ‘high-level’ content and, in terms of stages of processing, occurs late in the processing stream. We discuss the implications of this paradigm for consciousness research.