Contingent approaches to making likelihood judgments about polychotomous cases: the influence of task factors

Two experiments tested the influence of three task factors on respondents' tendency to use normative, heuristic, and random approaches to making likelihood judgments about polychotomous cases (i.e., cases in which there is more than one alternative to a focal hypothesis). Participants estimated their likelihood of winning hypothetical raffles in which they and other players held various numbers of tickets. Responding on non‐numeric scales (vs. numeric ones) and responding under time pressure (vs. self‐paced) increased participants' use of a comparison‐heuristic approach, resulting in non‐normative judgment patterns. A manipulation of evidence representation (whether ticket quantities were represented by numbers or more graphically by bars) did not have reliably detectable effects on processing approaches to likelihood judgment. The authors discuss the implications of these findings for the further development of likelihood judgment theories, and they discuss parallels between contingent processing in choice and contingent processing in likelihood judgment. Copyright © 2005 John Wiley & Sons, Ltd.     

风险条件下的跨期选择

跨期选择是指对发生在未来不同时间点上的结果做出权衡的决策过程。由于大部分跨期选择的情景都处于某种风险之中, 把风险变量纳入跨期选择的研究中则至为关键。针对以往研究在研究范围、理论构建、现实意义等诸方面的不足, 本研究拟采用实验室实验与纸笔测验相结合的方法, 深入揭示高、中、低三种概率水平下风险对跨期选择的影响特征, 探索其发生的机制、各类经典效应的大小。在此基础上, 根据全国不同地区的大样本调查结果, 了解各地区风险条件下跨期选择的差异及其与本地宏观经济指标(如, 消费者物价指数)的关联, 进而探讨研究的现实意义。本研究期望对风险条件下的跨期选择做出系统、全面的科学探索, 并为国家相关部门制定政策提供有价值的参考。     

Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events

Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imprecision by rough sets over an approximation space presents an especially tractable case to help get one’s bearings. Two solutions present themselves: the first takes as upper and lower probabilities of the event X the (exact) probabilities assigned X’s upper and lower rough-set approximations; the second, motivated both by formal considerations and by a simple betting argument, is to treat X’s rough-set approximation as a conditional event and assign to it a point-valued (conditional) probability. With rough sets over an approximation space we get a lot of good behaviour. For example, in the first construction mentioned the lower probabilities are n-monotone, for every . When we examine other models of approximation/imprecision/vagueness, and in particular, proximity spaces, we lose a lot of that good behaviour. In the literature there is not (even) agreement on the definition of upper and lower approximations for events (subsets) in the underlying domain. Betting considerations suggest one choice and, again, ways to assign upper and lower and point-valued probabilities, but nothing works well. Special Issue on Vagueness Edited by Rosanna Keefe and Libor Bêhounek     

A new formulation of the Principle of Indifference

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for.     

Fallacies in probability judgments for conjunctions and disjunctions of everyday events

The conjunction fallacy occurs when people judge a conjunction B‐and‐A as more probable than a constituent B, contrary to probability theory's ‘conjunction rule’ that a conjunction cannot be more probable than either constituent. Many studies have demonstrated this fallacy in people's reasoning about various experimental materials. Gigerenzer objects that from a ‘frequentist’ standpoint probability theory is not valid for these materials, and so failure to follow the conjunction rule is not a fallacy. This paper describes three experiments showing that the conjunction fallacy occurs as consistently for conjunctions where frequentist probability theory is valid (conjunctions of everyday weather events) as for other conjunctions. These experiments also demonstrate a reliable correlation between the occurrence of the conjunction fallacy and the disjunction fallacy (which arises when a disjunction B‐or‐A is judged less probable than a constituent B). This supports a probability theory + random variation account of probabilistic reasoning. Copyright © 2008 John Wiley & Sons, Ltd.     

从贝叶斯主义的视角看迪昂问题

对于迪昂问题,贝叶斯主义有着独特的视角。本文主要通过介绍多林与斯特雷文斯各自运用贝叶斯方法解决迪昂问题的两个方案,试图说明迪昂问题在贝叶斯机制中的处理方式,并且对这两个方案作出比较,认为斯特雷文斯的方案更为客观与合理。     

On the existence of extremal cones and comparative probability orderings

We study the recently discovered phenomenon [Conder, M. D. E., & Slinko, A. M. (2004). A counterexample to Fishburn's conjecture. Journal of Mathematical Psychology, 48(6), 425-431] of existence of comparative probability orderings on finite sets that violate the Fishburn hypothesis [Fishburn, P. C. (1996). Finite linear qualitative probability. Journal of Mathematical Psychology, 40, 64-77; Fishburn, P. C. (1997). Failure of cancellation conditions for additive linear orders. Journal of Combinatorial Designs, 5, 353-365]—we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on a set of n=7 elements and showed that no extremal cones exist on a set of n?6 elements. In this paper we construct an extremal cone on a finite set of prime cardinality p if p satisfies a certain number theoretical condition. This condition has been computationally checked to hold for 1725 of the 1842 primes between 132 and 16,000, hence for all these primes extremal cones exist.     

An interaction between prosody and statistics in the segmentation of fluent speech

Sensitivity to prosodic cues might be used to constrain lexical search. Indeed, the prosodic organization of speech is such that words are invariably aligned with phrasal prosodic edges, providing a cue to segmentation. In this paper we devise an experimental paradigm that allows us to investigate the interaction between statistical and prosodic cues to extract words from a speech stream. We provide evidence that statistics over the syllables are computed independently of prosody. However, we also show that trisyllabic sequences with high transition probabilities that straddle two prosodic constituents appear not to be recognized. Taken together, our findings suggest that prosody acts as a filter, suppressing possible word-like sequences that span prosodic constituents.     

The reference class problem is your problem too

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains.