The influence of reasons on interpretations of probability forecasts

When providing a probability estimate for an event, experts often supply reasons that they expect will clarify and support that estimate. We investigated the possible unintended influence that these reasons might have on a listener's intuitive interpretation of the event's likelihood. Experiments 1 and 2 demonstrated that people who read positive reasons for a doctor's probability estimate regarding a hypothetical surgery were more optimistic than those who read negative reasons for the identical estimate. Experiment 3 tested whether a doctor's failure forecast for a surgery would result in differing levels of pessimism when the potential risk was attributed to one complication that had a probability of 0.30 versus three complications that had a disjunctive probability of 0.30. Overall, the findings are consistent with the argument that a probability estimate, albeit numerically precise, can be flexibly interpreted at an intuitive level depending on the reasons that the forecaster provides as the basis for the estimate. Copyright © 2003 John Wiley & Sons, Ltd.     

Effects of choice and relative frequency elicitation on overconfidence: further tests of an exemplar‐retrieval model

An experiment is reported in which participants rendered judgments regarding the disease states of hypothetical patients. Participants either reported likelihoods that patients had the target disease (no choice), or classified patients into disease categories and then reported likelihoods that their classifications were correct (choice included). Also, participants' likelihood judgments were made in response to either a probability probe question, or a relative frequency probe. Two distinct exemplar‐memory models were compared on their ability to predict overconfidence under these procedures. Both propose that people learn and judge by storing and retrieving examples. The exemplar retrieval model (ERM) proposes that amount of retrieval drives choice inclusion and likelihood probe effects. The alternative model assumes that response error mediates choice inclusion effects. Choice inclusion and the relative frequency probe reduced overconfidence, but the combined effects were subadditive. Only the ERM predicted this pattern, and it further provided good quantitative fits to these results. Copyright © 2003 John Wiley & Sons, Ltd.     

Three Models of Sequential Belief Updating on Uncertain Evidence

Jeffrey updating is a natural extension of Bayesian updating to cases where the evidence is uncertain. But, the resulting degrees of belief appear to be sensitive to the order in which the uncertain evidence is acquired, a rather un-Bayesian looking effect. This order dependence results from the way in which basic Jeffrey updating is usually extended to sequences of updates. The usual extension seems very natural, but there are other plausible ways to extend Bayesian updating that maintain order-independence. I will explore three models of sequential updating, the usual extension and two alternatives. I will show that the alternative updating schemes derive from extensions of the usual rigidity requirement, which is at the heart of Jeffrey updating. Finally, I will establish necessary and sufficient conditions for order-independent updating, and show that extended rigidity is closely related to these conditions.     

A counterexample to Fishburn's conjecture on finite linear qualitative probability

Kraft, Pratt and Seidenberg (Ann. Math. Statist. 30 (1959) 408) provided an infinite set of axioms which, when taken together with de Finetti's axiom, gives a necessary and sufficient set of “cancellation” conditions for representability of an ordering relation on subsets of a set by an order-preserving probability measure. Fishburn (1996) defined f(n) to be the smallest positive integer k such that every comparative probability ordering on an n-element set which satisfies the cancellation conditions C₄,…,C_k is representable. By the work of Kraft, Pratt, and Seidenberg (1959) and Fishburn (J. Math. Psychol. 40 (1996) 64; J. Combin. Design 5 (1997) 353), it is known that n-1?f(n)?n+1 for all n?5. Also Fishburn proved that f(5)=4, and conjectured that f(n)=n-1 for all n?5. In this paper we confirm that f(6)=5, but give counter-examples to Fishburn's conjecture for n=7, showing that f(7)?7. We summarise, correct and extend many of the known results on this topic, including the notion of “almost representability”, and offer an amended version of Fishburn's conjecture.     

A re‐examination of probability matching and rational choice

In a typical probability learning task participants are presented with a repeated choice between two response alternatives, one of which has a higher payoff probability than the other. Rational choice theory requires that participants should eventually allocate all their responses to the high‐payoff alternative, but previous research has found that people fail to maximize their payoffs. Instead, it is commonly observed that people match their response probabilities to the payoff probabilities. We report three experiments on this choice anomaly using a simple probability learning task in which participants were provided with (i) large financial incentives, (ii) meaningful and regular feedback, and (iii) extensive training. In each experiment large proportions of participants adopted the optimal response strategy and all three of the factors mentioned above contributed to this. The results are supportive of rational choice theory. Copyright © 2002 John Wiley & Sons, Ltd.     

The Future is Bright? Effects of Mood on Perception of the Future

Most people believe that the future will bring them more good things than bad, and therefore have high hopes for the future (MacLeod et al. Cogn Emot 10:69–85, 1996). However, many patients with mood disorders do not hold this positive belief about the future. At the extreme, low expectations of positive outcomes in the future can lead to feelings of hopelessness (O’Connor et al. Psychol Health Med 5:155–161, 2000). This paper aims to extend the literature on subjective probability of future events, using a mood induction paradigm to examine the effects of transient mood change on perceived likelihood of future events in a non-clinical community sample. Participants rated likelihood of future events from a standardized list and from their own lives. Ratings were made in both normal and experimentally-induced positive or negative mood. Results show that self-generated future events were perceived to be more likely than those from a standardized list, and that negative mood significantly biased perceived likelihood of other-generated future events. Participants rating standardized list events saw positive outcomes as less likely and negative outcomes as more likely in induced negative mood than they did in normal mood. Mood had no effect on ratings of self-generated events. Possible directions for future research are discussed.

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