Framing experts' (dis)agreements about uncertain environmental events

Agreements and disagreements between expert statements influence lay people's beliefs. But few studies have examined what is perceived as a disagreement. We report six experiments where people rated agreement between pairs of probabilistic statements about environmental events, attributed to two different experts or to the same expert at two different points in time. The statements differed in frame, by focusing on complementary outcomes (45% probability that smog will have negative health effects vs. 55% probability that it will not have such effects), in probability level (45% vs. 55% probability of negative effects), or in both respects. Opposite frames strengthened disagreement when combined with different probability levels. Approximate probabilities can be “framed” in yet another way by indicating reference values they are “over” or “under”. Statements that use different directional verbal terms (over vs. under 50%) indicated greater disagreement than statements with the same directional term but different probability levels (over 50% vs. over 70%). Framing and directional terms similarly affected consistency judgments when both statements were issued by the same expert at different occasions. The effect of framing on perceived agreement was significant for medium (10 and 20 percentage points) differences between probabilities, whereas the effect of directional term was stable for numerical differences up to 40 percentage points. To emphasize agreement between different estimates, they should be framed in the same way. To accentuate disagreements or changes of opinion, opposite framings should be used.     

Synchronic Bayesian updating and the Sleeping Beauty problem: reply to Pust

I maintain, in defending “thirdism,” that Sleeping Beauty should do Bayesian updating after assigning the “preliminary probability” 1/4 to the statement S: “Today is Tuesday and the coin flip is heads.” (This preliminary probability obtains relative to a specific proper subset I of her available information.) Pust objects that her preliminary probability for S is really zero, because she could not be in an epistemic situation in which S is true. I reply that the impossibility of being in such an epistemic situation is irrelevant, because relative to I, statement S nonetheless has degree of evidential support 1/4.     

From the Terrible Loneliness to the Wonderful Agreement of Human Beings

What would be the “terrible loneliness” and what would be the “wonderful agreement” in the present paper? The “terrible loneliness” is the only reality that a person perceives and/or thinks during the now going on. For the person, an enormous quantity of occurrences is in the present moment absent. A very small quantity of occurrences is present. The person is the only being in having this. And, this is only during a little moment. The person never thinks about his loneliness in this moment. On the contrary, he thinks he is plenty of people and full of occurrences. But, if he were thinking about reality, he would live in a terrible loneliness. How does he escape himself from this loneliness? He thinks that the probable occurrences are real occurrences. He may be right in a plenty of times. Going through what I call opening hypotheses—basic hypotheses and non-basic but important hypotheses—and going through what I call simply hypotheses he is able to sanction a wonderful agreement of human beings about the known parts of the Universe. However, they are hypotheses, not absolute realities.     

Learning, risk attitude and hot stoves in restless bandit problems

This research examines decisions from experience in restless bandit problems. Two experiments revealed four main effects. (1) Risk neutrality: the typical participant did not learn to become risk averse, a contradiction of the hot stove effect. (2) Sensitivity to the transition probabilities that govern the Markov process. (3) Positive recency: the probability of a risky choice being repeated was higher after a win than after a loss. (4) Inertia: the probability of a risky choice being repeated following a loss was higher than the probability of a risky choice after a safe choice. These results can be described with a simple contingent sampler model, which assumes that choices are made based on small samples of experiences contingent on the current state.     

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.     

Probability matching in choice under uncertainty: Intuition versus deliberation

Gaissmaier and Schooler (2008) [Gaissmaier, W., & Schooler, L. J. (2008). The smart potential behind probability matching. Cognition, 109, 416-422] argue that probability matching, which has traditionally been viewed as a decision making error, may instead reflect an adaptive response to environments in which outcomes potentially follow predictable patterns. In choices involving monetary stakes, we find that probability matching persists even when it is not possible to identify or exploit outcome patterns and that many “probability matchers” rate an alternative strategy (maximizing) as superior when it is described to them. Probability matching appears to reflect a mistaken intuition that can be, but often is not, overridden by deliberate consideration of alternative choice strategies.     

Oughts and ends

This paper advances a reductive semantics for ‘ought’ and a naturalistic theory of normativity. It gives a unified analysis of predictive, instrumental, and categorical uses of ‘ought’: the predictive ‘ought’ is basic, and is interpreted in terms of probability. Instrumental ‘oughts’ are analyzed as predictive ‘oughts’ occurring under an ‘in order that’ modifer (the end-relational theory). The theory is then extended to categorical uses of ‘ought’: it is argued that they are special rhetorical uses of the instrumental ‘ought’. Plausible conversational principles explain how this end-relational ‘ought’ can perform the expressive functions of the moral ‘ought’. The notion of an ‘ought-simpliciter’ is also discussed.

The big bad bug bites anti-realists about chance

David Lewis’s ‘Humean Supervenience’ (henceforth ‘HS’) combines realism about laws, chances, and dispositions with a sparse ontology according to which everything supervenes on the overall spatiotemporal distribution of non-dispositional properties (Lewis 1986a, Philosophical papers: Volume II, pp. ix–xvii, New York: Oxford Univesity Press, 1994, Mind 103:473–490). HS faces a serious problem—a “big bad bug” (Lewis 1986a, p. xiv): it contradicts the Principal Principle, a seemingly obvious norm of rational credence. Two authors have tried to rescue Lewis’s ontology from the ‘big bad bug’ (henceforth ‘the Bug’) by rejecting realism about laws, chances, and dispositions (Halpin 1994, Aust J Phil 72:317–338, 1998, Phil Sci 65:349–360; Ward 2005, Phil Sci 71:241–261). I will argue that this strategy cannot possibly work: it is the ontology, not the realist thesis, that lies at the root of the problem.     

Extending probabilistic dynamic epistemic logic

This paper aims to extend in two directions the probabilistic dynamic epistemic logic provided in Kooi’s paper (J Logic Lang Inform 12(4):381–408, 2003) and to relate these extensions to ones made in van Benthem et al. (Proceedings of LOFT’06. Liverpool, 2006). Kooi’s probabilistic dynamic epistemic logic adds to probabilistic epistemic logic sentences that express consequences of public announcements. The paper (van Benthem et al., Proceedings of LOFT’06. Liverpool, 2006) extends (Kooi, J Logic Lang Inform 12(4):381–408, 2003) to using action models, but in both papers, the probabilities are discrete, and are defined on trivial σ-algebras over finite sample spaces. The first extension offered in this paper is to add a previous-time operator to a probabilistic dynamic epistemic logic similar to Kooi’s in (J Logic Lang Inform 12(4):381–408, 2003). The other is to involve non-trivial σ-algebras and continuous probabilities in probabilistic dynamic epistemic logic.     

Reliability and validity of mothers' developmental estimates for children between 4 and 41 months

The feasibility of mothers estimating their own children's development is explored in this paper. Construction, reliability and validity of a mothers' developmental inventory for children from 4 months to 41 months is described. The inventory consists of six subtests: Gross Motor, Fine Motor, Language Expression, Language Comprehension, Personal-Social Competence and Self Help. A preliminary version of the inventory was item analyzed on a sample of 105 mothers of 4 to 37 months old children. This reduced the inventory to 164 items with satisfactory reliability and age discrimination on half-year intervals. The list was cross-validated on a sample of 275 mothers, for which medians of alpha coefficients for the six subtests ranged from 0.69 to 0.96, with most (26 out of 36) coefficients being 0.77 or higher. Again, the age discrimination was satisfactory, although floor effects appeared on four subtests for children younger than 12 months and ceiling effects on two subtests for children older than 24 months.