Baumann on the Monty Hall problem and single-case probabilities

Peter Baumann uses the Monty Hall game to demonstrate that probabilities cannot be meaningfully applied to individual games. Baumann draws from this first conclusion a second: in a single game, it is not necessarily rational to switch from the door that I have initially chosen to the door that Monty Hall did not open. After challenging Baumann’s particular arguments for these conclusions, I argue that there is a deeper problem with his position: it rests on the false assumption that what justifies the switching strategy is its leading me to win a greater percentage of the time. In fact, what justifies the switching strategy is not any statistical result over the long run but rather the “causal structure” intrinsic to each individual game itself. Finally, I argue that an argument by Hilary Putnam will not help to save Baumann’s second conclusion above. See Moser and Mulder (1994, pp. 115–116, 118).     

Perceived threat: exploring its association with worry and its hypothesized antecedents

Two studies with college student participants (n's=262, 239) examined the relation between perceptions of threat (i.e., perceptions of the probabilities and costs of future undesirable outcomes) and: (a) worry; and (b) hypothesized antecedents of perceived threat. In both studies, higher levels of worrying were associated with higher perceived probability and cost. In Study 2, the association between perceived threat and worrying remained even when taking into account maladaptive worry beliefs and the desire for predictability; in fact, the relation between worrying and worry beliefs and desire for predictability were moderated by perceptions of threat. Higher levels of perceived probability were associated with perceiving oneself and others less favorably, whereas higher levels of perceived cost were associated with higher standards.     

Framing of imprecise quantities: When are lower interval bounds preferred to upper bounds?

Imprecisely known quantities (e.g., predictions) are often described in approximate terms as “more than X” or “less than Y” (e.g., “Ann will earn more than $50 000” or “less than $60 000”). Such phrases carry both quantitative and qualitative (pragmatic) information. Three studies are reported showing that lower limit estimates (more than, over, minimum) are generally more frequent, and considered more appropriate than upper limit estimates (less than, under, maximum) over a wide range of contexts. This is partly due to scalar properties of the number system, where lower numbers are attained before, and included in higher numbers, but not vice versa. As a result, upper limit statements are perceived as negations, and carry more specific information about the speaker's communicative concerns. Upper limit statements are preferred with amounts or quantities that can be perceived as small, whereas lower limit statements can be used both to indicate large quantities and as a default. Copyright © 2009 John Wiley & Sons, Ltd.     

Self- and other-estimates of multiple abilities in Britain and Turkey: a cross-cultural comparison of subjective ratings of intelligence

This study is part of a programmatic research effort into the determinants of self-assessed abilities. It examined cross-cultural differences in beliefs about intelligence and self- and other-estimated intelligence in two countries at extreme ends of the European continent. In all, 172 British and 272 Turkish students completed a three-part questionnaire where they estimated their parents', partners' and own multiple intelligences (Gardner (10) and Sternberg (3)). They also completed a measure of the 'big five' personality scales and rated six questions about intelligence. The British sample had more experience with IQ tests than the Turks. The majority of participants in both groups did not believe in sex differences in intelligence but did think there were race differences. They also believed that intelligence was primarily inherited. Participants rated their social and emotional intelligence highly (around one standard deviation above the norm). Results suggested that there were more cultural than sex differences in all the ratings, with various interactions mainly due to the British sample differentiating more between the sexes than the Turks. Males rated their overall, verbal, logical, spatial, creative and practical intelligence higher than females. Turks rated their musical, body-kinesthetic, interpersonal and intrapersonal intelligence as well as existential, naturalistic, emotional, creative, and practical intelligence higher than the British. There was evidence of participants rating their fathers' intelligence on most factors higher than their mothers'. Factor analysis of the ten Gardner intelligences yield two clear factors: cognitive and social intelligence. The first factor was impacted by sex but not culture; it was the other way round for the second factor. Regressions showed that five factors predicted overall estimates: sex (male), age (older), test experience (has done tests), extraversion (strong) and openness (strong). Results are discussed in terms of the growing literature in the field.     

Quantum mechanics and violations of the sure-thing principle: The use of probability interference and other concepts

The use of quantum mechanical concepts in social science is a fairly new phenomenon. This paper uses one of quantum mechanics’ most basic concepts, probability interference, to explain the violation of an important decision theory principle (the ‘sure-thing principle’). We also attempt to introduce other quantum mechanical concepts in relation to the sure-thing principle violation.     

Could it be the Case that if I am Right My Opponents will be Pleased? A Rejoinder to Johnson-Laird,Byrne and Girotto

I take up the four issues considered by Johnson-Laird, Byrne and Girotto in their reply to Politzer (2007). Based on the conceptual clarification which they adduce, it seems that the disagreement can be settled about the first one (truth functionality) and can be attenuated about the second one (the paradoxes of material implication). However, I maintain and refine my criticisms on the last two (negation and the probability of conditionals), backed up by considerations borrowed from the perspective of the conditional probability semantics for conditionals.     

More than,less than,or minimum,maximum: how upper and lower bounds determine subjective interval estimates

Uncertain quantities can be described by single‐point estimates of lower interval bounds (X₁), upper interval bounds (X₂), two‐bound estimates (separate estimates of X₁ and X₂), and by ranges (X₁?X₂). A price estimation task showed that single‐bound estimates phrased as “T costs more than X₁” and “T costs less than X₂,” yielded much larger intervals than “minimum X₁” and “maximum X₂.” This difference can be attributed to exclusive interpretations of X₁ and X₂ in the first case (X₁ and X₂ are unlikely values), and inclusive interpretations in the second (X₁ and X₂ are likely values). This pattern of results was replicated in other domains where participants estimated single targets. When they estimated a distribution of targets, the pattern was reversed. “Minimum” and “maximum” values of variable quantities (e.g., flight prices) were found to delimit larger intervals than “more than” and “less than” estimates. Copyright © 2006 John Wiley & Sons, Ltd.     

Contrasting stochastic and support theory accounts of subadditivity

Numerous studies have found that likelihood judgment typically exhibits subadditivity in which judged probabilities of events are less than the sum of judged probabilities of constituent events. Whereas traditional accounts of subadditivity attribute this phenomenon to deterministic sources, this paper demonstrates both formally and empirically that subadditivity is systematically influenced by the stochastic variability of judged probabilities. First, making rather weak assumptions, we prove that regressive error (or variability) in mapping covert probability judgments to overt responses is sufficient to produce subadditive judgments. Experiments follow in which participants provided repeated probability estimates. The results support our model assumption that stochastic variability is regressive in probability estimation tasks and show the contribution of such variability to subadditivity. The theorems and the experiments focus on within-respondent variability, but most studies use between-respondent designs. Numerical simulations extend the work to contrast within- and between-respondent measures of subadditivity. Methodological implications of all the results are discussed, emphasizing the importance of taking stochastic variability into account when estimating the role of other factors (such as the availability bias) in producing subadditive judgments.     

How children make language out of gesture: morphological structure in gesture systems developed by American and Chinese deaf children

When children learn language, they apply their language-learning skills to the linguistic input they receive. But what happens if children are not exposed to input from a conventional language? Do they engage their language-learning skills nonetheless, applying them to whatever unconventional input they have? We address this question by examining gesture systems created by four American and four Chinese deaf children. The children's profound hearing losses prevented them from learning spoken language, and their hearing parents had not exposed them to sign language. Nevertheless, the children in both cultures invented gesture systems that were structured at the morphological/word level. Interestingly, the differences between the children's systems were no bigger across cultures than within cultures. The children's morphemes could not be traced to their hearing mothers' gestures; however, they were built out of forms and meanings shared with their mothers. The findings suggest that children construct morphological structure out of the input that is handed to them, even if that input is not linguistic in form.     

Probabilistic argumentation systems: A new way to combine logic with probability

Probability is usually closely related to Boolean structures, i.e., Boolean algebras or propositional logic. Here we show, how probability can be combined with non-Boolean structures, and in particular non-Boolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may or may not be valid. The uncertain information depends then on these uncertain assumptions, scenarios or interpretations. We propose to describe information in information systems, as introduced by Scott into domain theory. This captures a wide range of systems of practical importance such as many propositional logics, first order logic, systems of linear equations, inequalities, etc. It covers thus both symbolic as well as numerical systems. Assumption-based reasoning allows then to deduce supporting arguments for hypotheses. A probability structure imposed on the assumptions permits to quantify the reliability of these supporting arguments and thus to introduce degrees of support for hypotheses. Information systems and related information algebras are formally introduced and studied in this paper as the basic structures for assumption-based reasoning. The probability structure is then formally represented by random variables with values in information algebras. Since these are in general non-Boolean structures some care must be exercised in order to introduce these random variables. It is shown that this theory leads to an extension of Dempster–Shafer theory of evidence and that information algebras provide in fact a natural frame for this theory.