A foundation for support theory based on a non-Boolean event space

A new foundation is presented for the theory of subjective judgments of probability known in the psychological literature as “Support Theory”. It is based on new complementation operations that, unlike those of classical probability theory (set-theoretic complementation) and classical logic (negation), need not satisfy the principles of the Law of The Excluded Middle and the Law of Double Complementation. Interrelationships between the new complementation operations and the Kahneman and Tversky judgmental heuristic of availability are described.     

Regular Minimality and Thurstonian-type modeling

A Thurstonian-type model for pairwise comparisons is any model in which the response (e.g., “they are the same” or “they are different”) to two stimuli being compared depends, deterministically or probabilistically, on the realizations of two randomly varying representations (perceptual images) of these stimuli. The two perceptual images in such a model may be stochastically interdependent but each has to be selectively dependent on its stimulus. It has been previously shown that all possible discrimination probability functions for same–different comparisons can be generated by Thurstonian-type models of the simplest variety, with independent percepts and deterministic decision rules. It has also been shown, however, that a broad class of Thurstonian-type models, called “well-behaved” (and including, e.g., models with multivariate normal perceptual representations whose parameters are smooth functions of stimuli) cannot simultaneously account for two empirically plausible properties of same–different comparisons, Regular Minimality (which essentially says that “being least discriminable from” is a symmetric relation) and nonconstancy of the minima of discrimination probabilities (the fact that different pairs of least discriminable stimuli are discriminated with different probabilities). These results have been obtained for stimulus spaces represented by regions of Euclidean spaces. In this paper, the impossibility for well-behaved Thurstonian-type models to simultaneously account for Regular Minimality and nonconstancy of minima is established for a much broader notion of well-behavedness applied to a much broader class of stimulus spaces (any Hausdorff arc-connected ones). The universality of Thurstonian-type models with independent perceptual images and deterministic decision rules is shown (by a simpler proof than before) to hold for arbitrary stimulus spaces.     

封面故事、选项框架和损益概率对风险偏好的影响

以股市投资为背景设计决策问题,考查了问题的封面故事类型、备择选项框架和风险项的概率水平对327名股民被试和465名大学生被试的风险偏好的影响。结果表明,股民被试的风险偏好不同于大学生被试,前者在所有实验处理上呈现出稳定的风险回避倾向。大学生被试在不同类型的封面故事下呈现出不同的风险偏好。在传统的坏封面故事下,风险偏好只受到备择选项框架的影响,不受损益概率的影响,即出现经典的框架效应现象。在好封面故事下,风险偏好受到备择选项框架、损益概率及两者交互作用的影响,即在高概率水平上出现框架效应现象,在低概率水平上出现框架效应反转现象     

Comments on “Getting scarred and winning lotteries: Effects of exemplar cuing and statistical format on imagining low‐probability events,” By Newell,Mitchell, and Hayes (2008)

Newell, Mitchell, and Hayes (NMH) conduct three experiments designed to test whether exemplar cuing (EC) theory or a statistical format theory provides a more accurate account for how people make judgments about low‐probability events. They report finding support for the statistical format theory and little or no support for EC. However, NMH misstate the requirements for the production of exemplars in EC theory. As a result, they confuse non‐exemplar conditions with exemplar conditions in their experiments, and find results that are virtually irrelevant to EC theory. Copyright © 2009 John Wiley & Sons, Ltd.     

Evidence and inference in educational assessment

Educational assessment concerns inference about students' knowledge, skills, and accomplishments. Because data are never so comprehensive and unequivocal as to ensure certitude, test theory evolved in part to address questions of weight, coverage, and import of data. The resulting concepts and techniques can be viewed as applications of more general principles for inference in the presence of uncertainty. Issues of evidence and inference in educational assessment are discussed from this perspective.Probability isn't really about numbers; it's about the structure of reasoning.Presidential address to the Psychometric Society, presented June 25, 1994, in Champaign, Illinois.Supported by (1) Contract No. N00014-91-J-4101, R&T 4421573-01, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research, (2) the National Center for Research on Evaluation, Standards, Student Testing (CRESST), Educational Research and Development Program, cooperative agreement number R117G10027 and CFDA catalog number 84.117G, as administered by the Office of Educational Research and Improvement, U.S. Department of Education, and (3) the Statistical and Psychometric Research Division of Educational Testing Service. I am grateful for comments and suggestions from Henry Braun, Drew Gitomer, Richard Patz, Jonathan Troper, and Howard Wainer.     

Hypothetical and real consequences in experimental auctions for insurance against low-probability risks

Laboratory experiments have provided useful information about how people behave in risky situations. In particular, such experiments have allowed for the observation of many deviations from the predictions of expected utility theory. There is some dispute, however, over the effect of the use of real versus hypothetical money in these experiments and over the impact of experience. In this paper we describe auction experiments in which subjects faced a low-probability risk with either hypothetical or real-money consequences and varying amounts of experience. Using hypothetical payoffs resulted in behavior that provides a reasonable qualitative prediction of behavior with real consequences, but that seems to indicate a less diligent altitude toward spending the money as well as less concern about the risk.     

More Triviality

This paper uses the framework of Popper and Miller's work on axiom systems for conditional probabilities to explore Adams' thesis concerning the probabilities of conditionals. It is shown that even very weak axiom systems have only a very restricted set of models satisfying a natural generalisation of Adams' thesis, thereby casting severe doubt on the possibility of developing a non-Boolean semantics for conditionals consistent with it.     

Partitions and Conditionals

The literature on conditionals is rife with alternate formulations of the abstract semantics of conditional logic. Each formulation has its own advantages in terms of applications and generalizations; nevertheless, they are for the most part equivalent, in the sense that they underwrite the same range of logical systems. The purpose of the present note is to bring under this umbrella the partition semantics introduced by Brian Skyrms in (Skyrms, 1984).     

Negotiating the Boundaries of Science and Religion: The Case of Henry Margenau

The life of Henry Margenau (1901–1997) offers a case study in the complexity of the science-religion relation. As a physicist-philosopher at Yale University, he pursued a public program of "amalgamating religion with science." He drew upon his authority as a physicist and a tradition of philosophical idealism to advocate a "reciprocity" between the two spheres. He argued that a "new modesty" and "metaphysical attitude" among scientists created new opportunities for collaboration. At the same time, his view of faith and his sense of the religiousness of science created troubling ambiguities. In the end, Margenau embodied the ambivalent relation between science and religion while revealing the limits of renegotiating the boundaries.