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This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold beliefs of both types simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List. The nature, relevance, and implications of the tension are explained and assessed. more...

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold beliefs of both types simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List. The nature, relevance, and implications of the tension are explained and assessed. [ABSTRACT FROM AUTHOR] more...

It is important to reveal how humans evaluate an explanation of the recent development of explainable artificial intelligence. So, what makes people feel that one explanation is more likely than another? In the present study, we examine how explanatory virtues affect the process of estimating subjective posterior probability. Through systematically manipulating two virtues, Simplicity—the number of causes used to explain effects—and Scope—the number of effects predicted by causes—in three different conditions, we clarified two points in Experiment 1: (i) that Scope's effect is greater than Simplicity's; and (ii) that these virtues affect the outcome independently. In Experiment 2, we found that instruction about the explanatory structure increased the impact of both virtues' effects but especially that of Simplicity. These results suggest that Scope predominantly affects the estimation of subjective posterior probability, but that, if perspective on the explanatory structure is provided, Simplicity can also affect probability estimation. more...

It is important to reveal how humans evaluate an explanation of the recent development of explainable artificial intelligence. So, what makes people feel that one explanation is more likely than another? In the present study, we examine how explanatory virtues affect the process of estimating subjective posterior probability. Through systematically manipulating two virtues, Simplicity—the number of causes used to explain effects—and Scope—the number of effects predicted by causes—in three different conditions, we clarified two points in Experiment 1: (i) that Scope's effect is greater than Simplicity's; and (ii) that these virtues affect the outcome independently. In Experiment 2, we found that instruction about the explanatory structure increased the impact of both virtues' effects but especially that of Simplicity. These results suggest that Scope predominantly affects the estimation of subjective posterior probability, but that, if perspective on the explanatory structure is provided, Simplicity can also affect probability estimation. [ABSTRACT FROM AUTHOR] more...

Elicitation methods aim to build participants' distributions about a parameter of interest. In most elicitation studies this parameter is rarely known in advance and hinders an objective comparison between elicitation methods. In two experiments, participants were first presented with a fixed random sequence of images and numbers and subsequently their subjective distributions of percentages of one of those numbers was elicited. Importantly, the true percentage was set in advance. The first experiment tested whether receiving instructions as to the elicitation method would assist in estimating a true value more accurately than receiving no instructions and whether accuracy was determined by the numerical skills of the participants. The second experiment sought to compare the elicitation method used in the first experiment with a variation of a graphical elicitation method. The results indicate that (i) receiving instructions as to the elicitation method does assist in producing estimates closer to a true percentage value, (ii) the level of numerical skills does not play a part in the accuracy of the estimation (Experiment 1), and (iii) although the average estimates of the betting and graphical method are not significantly different, the betting method leads to more precise estimations than the graphical method (Experiment 2). Both studies featured statistical procedures (functional data analysis and a novel clustering technique) not considered in past research on the elicitation of subjective distributions. The implications of these results are discussed in relation to a recent key study. more...

Elicitation methods aim to build participants' distributions about a parameter of interest. In most elicitation studies this parameter is rarely known in advance and hinders an objective comparison between elicitation methods. In two experiments, participants were first presented with a fixed random sequence of images and numbers and subsequently their subjective distributions of percentages of one of those numbers was elicited. Importantly, the true percentage was set in advance. The first experiment tested whether receiving instructions as to the elicitation method would assist in estimating a true value more accurately than receiving no instructions and whether accuracy was determined by the numerical skills of the participants. The second experiment sought to compare the elicitation method used in the first experiment with a variation of a graphical elicitation method. The results indicate that (i) receiving instructions as to the elicitation method does assist in producing estimates closer to a true percentage value, (ii) the level of numerical skills does not play a part in the accuracy of the estimation (Experiment 1), and (iii) although the average estimates of the betting and graphical method are not significantly different, the betting method leads to more precise estimations than the graphical method (Experiment 2). Both studies featured statistical procedures (functional data analysis and a novel clustering technique) not considered in past research on the elicitation of subjective distributions. The implications of these results are discussed in relation to a recent key study. [ABSTRACT FROM AUTHOR] more...

Psychological research on people's understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants' truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people's interpretations of natural language connectives. We find that de Finetti's (1936/1995) three-valued system is the best approximation to participants' truth tables. more...

Humans' judgment of relative-frequency, similar to their use of probability in decision-making, is often distorted as an inverted-S-shape curve—small relative-frequency overestimated and large relative-frequency underestimated. Here we investigated how the judgment of relative-frequency, despite its natural reference points (0 and 1) and stereotyped distortion, may adapt to the environmental statistics. The task was to report the relative-frequency of black (or white) dots in a visual array of black and white dots. We found that participants' judgment was distorted in the typical inverted-S-shape, but the distortion curve was influenced by both the central tendency and spread of the distribution of objective relative-frequencies: the lower the central tendency, the higher the overall judgment (contrast effect); the higher the spread, the more curved the inverted-S-shape (curvature effect). These context effects are in the spirit of efficient coding but opposite to what would be predicted by Bayesian inference. We further modeled the context effects on the level of individual trials, through which we found not only a trial-by-trial adaptation, but also the non-linear sequential effects that were recently reported mainly in circularly distributed visual stimuli. more...

An introduction to the book "Improving Bayesian Reasoning: What Works and Why" is presented.