Responsibility for believing

Many assume that we can be responsible only what is voluntary. This leads to puzzlement about our responsibility for our beliefs, since beliefs seem not to be voluntary. I argue against the initial assumption, presenting an account of responsibility and of voluntariness according to which, not only is voluntariness not required for responsibility, but the feature which renders an attitude a fundamental object of responsibility (that the attitude embodies one’s take on the world and one’s place in it) also guarantees that it could not be voluntary. It turns out, then, that, for failing to be voluntary, beliefs are a central example of the sort of thing for which we are most fundamentally responsible.     

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。     

Evidence for the role of self-priming in epistemic action: expertise and the effective use of memory

Epistemic actions are physical actions people take to simplify internal problem solving rather than to move closer to an external goal. When playing the video game Tetris, for instance, experts routinely rotate falling shapes more than is strictly needed to place the shapes. Maglio and Kirsh [Kirsh, D., & Maglio, P. (1994). On distinguishing epistemic from pragmatic action. Cognitive Science, 18, 513-549; Maglio, P. P. (1995). The computational basis of interactive skill. PhD thesis, University of California, San Diego] proposed that such actions might serve the purpose of priming memory by external means, reducing the need for internal computation (e.g., mental rotation), and resulting in performance improvements that exceed the cost of taking additional actions. The present study tests this priming hypothesis in a set of four experiments. The first three explored precisely the conditions under which priming produces benefits. Results showed that presentation of multiple orientations of a shape led to faster responses than did presentation of a single orientation, and that this effect depended on the interval between preview and test. The fourth explored whether the benefit of seeing shapes in multiple orientations outweighs the cost of taking the extra actions to rotate shapes physically. Benefits were measured using a novel statistical method for mapping reaction-time data onto an estimate of the increase in processing capacity afforded by seeing multiple orientations. Cost was measured using an empirical estimate of time needed to take action in Tetris. Results showed that indeed the increase in internal processing capacity obtained from seeing shapes in multiple orientations outweighed the time to take extra actions.     

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.