用文字概率衡量不确定性：特征和问题

文字概率是衡量不确定性的方式之一, 即人们使用诸如“也许”、“未必”的词汇来描述特定事件发生的可能性。文字概率不同于数字概率, 主要体现在文字概率的模糊性、非概率运算性和语义特性上。这使得相对于数字概率, 用文字概率衡量不确定性既有优势也有问题, 进而对人们的不确定信息沟通和风险决策造成影响。虽然文字概率与数字概率存在特征上的差异并且人们在日常交流中偏爱文字概率, 但是大部分风险领域的研究却仅局限于数字概率, 今后有必要研究使用文字概率测量的风险决策。在已有文字概率特征研究的基础上, 还可以进一步探究其不同于数字概率的其它特征(文字/数字概率与双系统模型的联系、文字概率的跨文化差异等)及其对风险决策的影响。     

Maximum Entropy Inference with Quantified Knowledge

We investigate uncertain reasoning with quantified sentencesof the predicate calculus treated as the limiting case of maximumentropy inference applied to finite domains.     

Verbal probabilities: a question of frame?

Verbal expressions of probability and uncertainty are of two kinds: positive (‘probable’, ‘possible’) and negative (‘not certain’, ‘doubtful’). Choice of term has implications for predictions and decisions. The present studies show that positive phrases are rated to be more optimistic (when the target outcome is positive), and more correct, when the target outcome actually occurs, even in cases where positive and negative phrases are perceived to convey the same probabilities (Experiments 1 and 2). Selection of phrase can be determined by linguistic frame. Positive quantifiers (‘some’, ‘several’) support positive probability phrases, whereas negative quantifiers (‘not all’) suggest negative phrases (Experiment 3). Positive frames induced by numeric frequencies (e.g. the number of students to be admitted) imply positive probability phrases, whereas negative frames (e.g. the number of students to be rejected) call for negative probability phrases (Experiment 4). It is concluded that choice of verbal phrase is based not only on level of probability, but also on situational and linguistic cues. Copyright © 2002 John Wiley & Sons, Ltd.     

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.