On the logical structure of de Finetti's notion of event

This paper sheds new light on the subtle relation between probability and logic by (i) providing a logical development of Bruno de Finetti's conception of events and (ii) suggesting that the subjective nature of de Finetti's interpretation of probability emerges in a clearer form against such a logical background. By making explicit the epistemic structure which underlies what we call Choice-based probability we show that whilst all rational degrees of belief must be probabilities, the converse doesn't hold: some probability values don't represent decision-relevant quantifications of uncertainty.     

Against Moral Character Evaluations: The Undetectability of Virtue and Vice

I defend the epistemic thesis that evaluations of people in terms of their moral character as good, bad, or intermediate are almost always epistemically unjustified. (1) Because most people are fragmented (they would behave deplorably in many and admirably in many other situations), one’s prior probability that any given person is fragmented should be high. (2) Because one’s information about specific people does not reliably distinguish those who are fragmented from those who are not, one’s posterior probability that any given person is fragmented should be close to one’s prior—and thus should also be high. (3) Because being fragmented entails being indeterminate (neither good nor bad nor intermediate), one’s posterior probability that any given person is indeterminate should also be high—and the epistemic thesis follows. (1) and (3) rely on previous work; here I support (2) by using a mathematical result together with empirical evidence from personality psychology.     

Knowledge,certainty and probability

In this essay, I discuss some of the important logical principles governing the concepts of knowledge, certainty and probability. In the first section, I suggest a series of definitions of epistemic terms, employing as primitive the locution ‘p is epistemi‐cally possible to S’ In the second section, I develop an epistemic concept of probability and compare it to the concepts of certainty and knowledge. In the third section, I relate the epistemic concepts of certainty and probability to the quantifiers of traditional logic and to a non‐episteznic concept of probability. I conclude by noting similarities and differences between the two concepts of probability.     

Rationality and indeterminate probabilities

We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required. Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our describing a world that plausibly has indeterminate chances. Rationality requires a certain alignment of your credences with corresponding hypotheses about the chances. Thus, if you hypothesize the chances to be indeterminate, your will inherit their indeterminacy in your corresponding credences. Our third argument is motivated by a dilemma. Epistemic rationality requires you to stay open-minded about contingent matters about which your evidence has not definitively legislated. Practical rationality requires you to be able to act decisively at least sometimes. These requirements can conflict with each other-for thanks to your open-mindedness, some of your options may have undefined expected utility, and if you are choosing among them, decision theory has no advice to give you. Such an option is playing Nover and Hájek??s Pasadena Game, and indeed any option for which there is a positive probability of playing the Pasadena Game. You can serve both masters, epistemic rationality and practical rationality, with an indeterminate credence to the prospect of playing the Pasadena game. You serve epistemic rationality by making your upper probability positive-it ensures that you are open-minded. You serve practical rationality by making your lower probability 0-it provides guidance to your decision-making. No sharp credence could do both.     

(Why) do I think what you think? Epistemic social tuning and implicit prejudice

This research examines whether people who experience epistemic motivation (i.e., a desire to acquire knowledge) came to have implicit attitudes consistent with the apparent beliefs of another person. People had lower implicit prejudice when they experienced epistemic motivation and interacted with a person who ostensibly held egalitarian beliefs (Experiments 1 and 2). Implicit prejudice was not affected when people did not experience epistemic motivation. Further evidence shows that this tuning of implicit attitudes occurs when beliefs are endorsed by another person, but not when they are brought to mind via means that do not imply that person's endorsement (Experiment 3). Results suggest that implicit attitudes of epistemically motivated people tune to the apparent beliefs of others to achieve shared reality.     

What shapes the probability weighting function? Influence of affect,numeric competencies,and information formats

Research suggests that people are less sensitive to variations in probability in affect‐rich compared with affect‐poor risky choices. This effect is modeled by a more curved probability weighting function (PWF). We investigated the role of different numeric competencies and the effectiveness of several intervention strategies to decrease this affect‐laden probability distortion. In two experiments, we manipulated the affect‐richness of a risky prospect. In Experiment 1 (N = 467), we measured numeracy and symbolic‐number mapping (i.e., the ability to accurately map numbers onto their underlying magnitudes). The affect‐based manipulations showed the expected effects only in participants with more accurate symbolic‐number mapping, who also reported more differentiated emotional reactions to the various probabilities and displayed more linear PWFs. Instructions to focus on the probability information decreased probability distortion and revealed differences in the use of probability information on the basis of symbolic‐number mapping ability. In Experiment 2 (N = 417), we manipulated the format in which the probability information was presented: using visual aids versus no visual aids and a positive frame (e.g., one person wins) versus combined frame (e.g., one person wins and 99 persons do not win). The affect‐based manipulations had no effect but both the visual aids and combined frame decreased probability distortion. Whereas affect‐richness manipulations require further research, results suggest that probability weighting is at least partially driven by the inability to translate numerical information into meaningful and well‐calibrated affective intuitions. Visual aids and simple framing manipulations designed to calibrate these intuitions can help decision makers extract the gist and increase sensitivity to probabilities.     

Epistemology and probability

Probability is sometimes regarded as a universal panacea for epistemology. It has been supposed that the rationality of belief is almost entirely a matter of probabilities. Unfortunately, those philosophers who have thought about this most extensively have tended to be probability theorists first, and epistemologists only secondarily. In my estimation, this has tended to make them insensitive to the complexities exhibited by epistemic justification. In this paper I propose to turn the tables. I begin by laying out some rather simple and uncontroversial features of the structure of epistemic justification, and then go on to ask what we can conclude about the connection between epistemology and probability in the light of those features. My conclusion is that probability plays no central role in epistemology. This is not to say that probability plays no role at all. In the course of the investigation, I defend a pair of probabilistic acceptance rules which enable us, under some circumstances, to arrive at justified belief on the basis of high probability. But these rules are of quite limited scope. The effect of there being such rules is merely that probability provides one source for justified belief, on a par with perception, memory, etc. There is no way probability can provide a universal cure for all our epistemological ills.     

A latent trait model for dichotomous choice data

The PARELLA model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences. The data analyzed are the dichotomous responses of persons to stimuli, with a one (zero) indicating agreement (disagreement) with the content of the stimulus. The model provides a unidimensional representation of persons and items. The response probabilities are a function of the distance between person and stimulus: the smaller the distance, the larger the probability that a person will agree with the content of the stimulus. An estimation procedure based on expectation maximization and marginal maximum likelihood is developed and the quality of the resulting parameter estimates evaluated.I gratefully acknowledge Ivo Molenaar and Wijbrandt van Schuur for their advice and encouragement during the course of the investigation, Derk-Jan Kiewiet who constructed the program for the ML estimator for the person parameter and Anne Boomsma, Wendy Post, Tom Snijders, and David Thissen for their comments on smaller aspects of the investigation.     

Should the probabilities count?

When facing a choice between saving one person and saving many, some people have argued that fairness requires us to decide without aggregating numbers; rather we should decide by coin toss or some form of lottery, or alternatively we should straightforwardly save the greater number but justify this in a non-aggregating contractualist way. This paper expands the debate beyond well-known number cases to previously under-considered probability cases, in which not (only) the numbers of people, but (also) the probabilities of success for saving people vary. It is shown that, in these latter cases, both the coin toss and the lottery lead to what is called an awkward conclusion, which makes probabilities count in a problematic way. Attempts to avoid this conclusion are shown to lead into difficulties as well. Finally, it is shown that while the greater number method cannot be justified on contractualist grounds for probability cases, it may be replaced by another decision method which is so justified. This decision method is extensionally equivalent to maximising expected value and seems to be the least problematic way of dealing with probability cases in a non-aggregating manner.     

Saying and doing: A contingency-space analysis

Correspondences between verbal responding (saying) and nonverbal responding (doing) may be organized in terms of the classes of verbal/nonverbal relations into which particular instances of verbal/nonverbal response sequences can enter. Contingency spaces, which display relations among events in terms of the probability of one event given or not given another, have been useful in analyses of nonverbal behavior. We derive a taxonomy of verbal/nonverbal behavior relations from a contingency space that takes into account two conditional probabilities: the probability of a nonverbal response given a verbal response and that probability given the absence of the verbal response. For example, positive correspondence may be said to exist as a response class when the probability of doing is high given saying but is otherwise low. Criteria for other generalized classes, including negative correspondence, follow from this analysis.     

The role of epistemic and social characteristics in children’s selective trust: Three meta‐analyses

Over the last 15 years, researchers have been increasingly interested in understanding the nature and development of children’s selective trust. Three meta‐analyses were conducted on a total of 51 unique studies (88 experiments) to provide a quantitative overview of 3‐ to 6‐year‐old children’s selective trust in an informant based on the informant’s epistemic or social characteristics, and to examine the relation between age and children’s selective trust decisions. The first and second meta‐analyses found that children displayed medium‐to‐large pooled effects in favor of trusting the informant who was knowledgeable or the informant with positive social characteristics. Moderator analyses revealed that 4‐year‐olds were more likely to endorse knowledgeable informants than 3‐year‐olds. The third meta‐analysis examined cases where two informants simultaneously differed in their epistemic and social characteristics. The results revealed that 3‐year‐old children did not selectively endorse informants who were more knowledgeable but had negative social characteristics over informants who were less knowledgeable but had positive social characteristics. However, 4‐ to 6‐year‐olds consistently prioritized epistemic cues over social characteristics when deciding who to trust. Together, these meta‐analyses suggest that epistemic and social characteristics are both valuable to children when they evaluate the reliability of informants. Moreover, with age, children place greater value on epistemic characteristics when deciding whether to endorse an informant’s testimony. Implications for the development of epistemic trust and the design of studies of children’s selective trust are discussed.     

From the casino to the jungle

Clear-cut cases of decision-making under risk (known probabilities) are unusual in real life. The gambler’s decisions at the roulette table are as close as we can get to this type of decision-making. In contrast, decision-making under uncertainty (unknown probabilities) can be exemplified by a decision whether to enter a jungle that may contain unknown dangers. Life is usually more like an expedition into an unknown jungle than a visit to the casino. Nevertheless, it is common in decision-supporting disciplines to proceed as if reasonably reliable probability estimates were available for all possible outcomes, i.e. as if the prevailing epistemic conditions were analogous to those of gambling at the roulette table. This mistake can be called the tuxedo fallacy. It is argued that traditional engineering practices such as safety factors and multiple safety barriers avoid this fallacy and that they therefore manage uncertainty better than probabilistic risk analysis (PRA). PRA is a useful tool, but it must be supplemented with other methods in order not to limit the analysis to dangers that can be assigned meaningful probability estimates.     

Counterfactuals and Epistemic Probability

Philosophers have often attempted to use counterfactual conditionals to analyze probability. This article focuses on counterfactual analyzes of epistemic probability by Alvin Plantinga and Peter van Inwagen. I argue that a certain type of counterfactual situation creates problems for these analyses. I then argue that Plantinga’s intuition about the role of warrant in epistemic probability is mistaken. Both van Inwagen’s and Plantinga’s intuitions about epistemic probability are flawed.     

An account of subjective probability judgment for joint events: Conjunctive and disjunctive

Probability judgment is a vital part of many aspects of everyday life. In the present paper, we present a new theory of the way in which individuals produce probability estimates for joint events: conjunctive and disjunctive. We propose that a majority of individuals produce conjunctive (disjunctive) estimates by making a quasi‐random adjustment, positive or negative, from the less (more) likely component probability with the other component playing no obvious role. In two studies, we produce evidence supporting propositions that follow from our theory. First, the component probabilities do appear to play the distinct roles we propose in determining the joint event probabilities. Second, contrary to probability theory and other accounts of probability judgment, we show that the conjunctive‐less likely probability difference is unrelated to the more likely disjunctive probability difference (in normative theory these quantities are identical). In conclusion, while violating the norms of probability judgment, we argue that estimates produced in the manner we propose will be close enough to the normative values especially given the changing nature of the external environment and the incomplete nature of available information.     

The Social Virtue Of Blind Deference

Recently, it has become popular to account for knowledge and other epistemic states in terms of epistemic virtues. The present paper focuses on an epistemic virtue relevant when deferring to others in testimonial contexts. It is argued that, while many virtue epistemologists will accept that epistemic virtue can be exhibited in cases involving epistemically motivated hearers, carefully vetting their testimonial sources for signs of untrustworthiness prior to deferring, anyone who accepts that also has to accept that an agent may exhibit epistemic virtue in certain cases of blind deference, involving someone soaking up everything he or she is told without any hesitation. Moreover, in order to account for the kind of virtue involved in the relevant cases of blind deference, virtue epistemologists need to abandon a widespread commitment to personalism, i.e., the idea that virtue is possessed primarily on account of features internal to the psychology of the person, and accept that some virtues are social virtues, possessed in whole or in large part on account of the person being embedded in a reliable social environment.     

Prejudice as Viciousness: Marie de Gournay and Anton Wilhelm Amo

Marie de Gournay and Anton Wilhelm Amo, though thinking and writing in different social contexts, each offer an account of prejudice which bears a deep philosophical resonance to that of the other. This resonance is striking and mutually illuminating: Gournay and Amo develop a view of prejudice as a kind of epistemic and moral viciousness that damages both the prejudicial person and their socio-epistemic neighbors. Their accounts highlight how agents are rightly held responsible for prejudice, as it is the agents' epistemic negligence and moral failure that allows prejudice to take hold. As such, their view offers a balance between a critical examination of individuals and an acknowledgement of the deep sociality that pervades the epistemic domain.     

Does probability weighting matter in probability elicitation?

One of the most widely used methods for probability encoding in decision analysis uses binary comparisons (choices) between two lotteries: one that depends on the values of the random variable of interest and another that is contingent on an external reference chance device (typically a probability wheel). This note investigates the degree to which differences in probability weighting functions between the two types of events could affect the practice of subjective probability encoding. We develop a general methodology to investigate this question and illustrate it with two popular probability weighting functions over the range of parameters reported in the literature. We use this methodology to (a) alert decision analysts and researchers to the possibility of reversals, (b) identify the circumstances under which overt preferences for one lottery over the other are not affected by the weighting function, (c) document the magnitude of the differences between choices based on probabilities and their corresponding weighting functions, and (d) offer practical recommendations for probability elicitation.     

Naive probability: a mental model theory of extensional reasoning

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning.