Reasoning about complex probabilistic concepts in childhood

The competencies of children, particularly their understanding of the more complex probabilistic concepts, have not been thoroughly investigated. In the present study participants were required to choose the more likely of two events, a single event, and a joint event (conjunctive or disjunctive). It was predicted that the operation of the representativeness heuristic would result in erroneous judgements when children compared an unlikely component event with a likely-unlikely conjunction (the conjunction fallacy) and when a likely component event was compared to a likely-unlikely disjunction. The results supported the first prediction with both older children aged between 9 and 10 years and younger children aged between 4 and 5 committing the conjunction fallacy. However, the second prediction was not confirmed. It is proposed that the basis of representativeness judgements may differ between the conjunctive and disjunctive cases with absolute frequency information possibly playing a differential role.     

Rules for Reasoning from Knowledge and Lack of Knowledge

In this paper, the traditional view that argumentum ad ignorantiam is a logical fallacy is challenged, and lessons are drawn on how to model inferences drawn from knowledge in combination with ones drawn from lack of knowledge. Five defeasible rules for evaluating knowledge-based arguments that apply to inferences drawn under conditions of lack of knowledge are formulated. They are the veridicality rule, the consistency of knowledge rule, the closure of knowledge rule, the rule of refutation and the rule for argument from ignorance. The basic thesis of the paper is that knowledge-based arguments, including the argument from ignorance, need to be evaluated by criteria for epistemic closure and other evidential rules that are pragmatic in nature, that need to be formulated and applied differently at different stages of an investigation or discussion. The paper helps us to understand practical criteria that should be used to evaluate all arguments based on knowledge and/or ignorance.

The sunk cost effect in pigeons and humans

The sunk cost effect is the increased tendency to persist in an endeavor once an investment of money, effort, or time has been made. To date, humans are the only animal in which this effect has been observed unambiguously. We developed a behavior-analytic model of the sunk cost effect to explore the potential for this behavior in pigeons as well as in humans. Each trial started out with a short expected ratio, but on some trials assumed a longer expected ratio part way through the trial. Subjects had the (usually preferable) option of "escaping" the trial if the longer expected ratio had come into effect in order to bring on a new trial that again had a short expected ratio. In Experiments 1 through 3, we manipulated two independent variables that we hypothesized would affect the pigeons' ability to discriminate the increase in the expected ratio within a trial: (a) the presence or absence of stimuli that signal an increase in the expected ratio, and (b) the severity of the increase in the expected ratio. We found that the pigeons were most likely to persist nonoptimally through the longer expected ratios when stimulus changes were absent and when the increase in the expected ratio was less severe. Experiment 4 employed a similar procedure with human subjects that manipulated only the severity of the increase in the expected ratio and found a result similar to that of the pigeon experiment. In Experiment 5, we tested the hypothesis that a particular history of reinforcement would induce pigeons to persist through the longer expected ratios; the results suggested instead that the history of reinforcement caused the pigeons to persist less compared to pigeons that did not have that history.     

Probability judgment in hierarchical learning: a conflict between predictiveness and coherence

Why are people's judgments incoherent under probability formats? Research in an associative learning paradigm suggests that after structured learning participants give judgments based on predictiveness rather than normative probability. This is because people's learning mechanisms attune to statistical contingencies in the environment, and they use these learned associations as a basis for subsequent probability judgments. We introduced a hierarchical structure into a simulated medical diagnosis task, setting up a conflict between predictiveness and coherence. Thus, a target symptom was more predictive of a subordinate disease than of its superordinate category, even though the latter included the former. Under a probability format participants tended to violate coherence and make ratings in line with predictiveness; under a frequency format they were more normative. These results are difficult to explain within a unitary model of inference, whether associative or frequency-based. In the light of this, and other findings in the judgment and learning literature, a dual-component model is proposed.     

How do supporters perceive positive and negative psychological momentum changes during a simulated cycling competition?

ObjectiveThe present study examined changes in sport supporters' psychological momentum (PM) during a simulated cycling competition through the lens of the dynamical systems approach.DesignParticipants were asked to support one of two competing cyclists involved in a race that was displayed on a screen in a lecture hall.MethodThe race scenario was manipulated so that the image of the supported cyclist underwent either positive or negative momentum. At regular intervals, participants indicated their PM perceptions during the race.ResultsPM perceptions rapidly changed at the onset of both the positive and negative momentum sequences and then remained stable, reflecting negative hysteresis. Supporters tended to anticipate the future performance of a given athlete on the basis of their current performance. Moreover, this anticipatory tendency was stronger during the positive momentum sequence than during the negative momentum sequence.ConclusionThese results provide initial insights into how PM perceptions of sport supporters change during a competition.     

Finishing on time: When do predictions influence completion times?

People typically predict they will finish projects earlier than they do. Whereas previous research has examined the determinants of this prediction bias, the present research explored potential consequences for behavior. In particular, we examined whether and when task completion predictions influence actual completion times. In four experiments we used anchoring manipulations to induce participants to make relatively early or late task completion predictions, and then examined when they started and/or finished the target tasks. As hypothesized, the prediction manipulation influenced completion times under certain conditions defined by the nature of the target task. Manipulated predictions affected completion times of closed tasks, defined as tasks carried out within a single, continuous session but not of open tasks, defined as tasks requiring multiple work sessions. This implies that task completion predictions help to initiate action, but their impact diminishes over the course of extensive, multi-stage projects.     

TRANSCENDING IRONY

A more complete understanding of the biocultural evolutionary origins of the concept of ought as developed by David Hume and G. E. Moore may lower the philosophical barrier between is and ought and provide new insights about the separations between the domains of religion and science. If this conjecture is correct, the resulting wisdom will help transcend a major source of irony that Philip Hefner has so aptly identified in his essay.