Occasionally, people are called upon to estimate probabilities after an event has occurred. In hindsight, was this an outcome we could have expected? Could things easily have turned out differently? One strategy for performing post hoc probability judgements would be to mentally turn the clock back and reconstruct one's expectations before the event. But if asked about the probability of an alternative, counterfactual outcome, a simpler strategy is available, based on this outcome's perceived closeness to what actually happened. The article (...) presents five studies exploring the relationship between counterfactual closeness and counterfactual probability. The first study indicates that post hoc probabilities typically refer to the counterfactual rather than the factual outcome. Studies 2-5 show that physical, temporal, or conceptual proximity play a decisive role for post hoc probability assessments of counterfactual events. When margins are narrow, the probabilities of, for instance, winning a match (when losing), and of losing (when actually winning) may even be rated higher than the corresponding probabilities of what really happened. Closeness is also more often referred to, and rated to be a better reason for believing there is a ''good chance" of the counterfactual rather than of the factual result occurring. Finally, the closeness of the alternative outcome in success and failure stories is shown to be significantly correlated to its rated probability. (shrink)

When people are asked to estimate the probabilities of uncertain events, they often neglect the additivity principle, which requires that the probabilities assigned to an exhaustive set of outcomes should add up to 100%. Previous studies indicate that additivity neglect is dependent on response format, self-generated probability estimates being more coherent than estimates on rating scales. The present study made use of eye-tracking methodology, recording the movement, frequency and duration of fixations during the solution of ten additivity problems and two (...) control tasks. Participants produced more non-additive estimates in the Scale format than in the Self-generated format. Self-generated estimates also led to longer decision time and a higher number of repeated inspections, suggesting a deliberate comparison process. In contrast, the Scale format seemed to encourage a case-based approach where each outcome is evaluated in isolation. (shrink)

The distinction between abstract (rule-based) and contextual (intuitive) thinking is illustrated by studies of numeric versus linguistic expressions of probability. Verbal probabilities are believed to reflect intuitions that can be adaptive and occasionally normative (e.g., counteracting conjunction errors). Stanovich & West's interpretation of analytic thinking in terms of ability suggests a complementary ability perspective on intuitive thinking.

People commonly use terms like ‘random’, ‘by chance’, or ‘accidentally’ when they describe occurrences that sidestep the normal course of events, with no apparent causal link to ongoing activities. Such intrusive events are typically perceived as happening all of a sudden. This was demonstrated in seven experiments (N = 1299) by asking people to identify statements they believed belonged to stories about chance events, and by comparing chance vs. non-chance events from their own life and from the lives of others. (...) Suddenness also appeared to be more strongly associated with beginnings than with endings of an episode. Thus, statements about sudden beginnings of a career or a relationship were more readily believed to happen ‘by chance’ than ‘not by chance’. But life-changing events did not become more accidental simply by being placed in the beginning of a ‘life chapter’. These studies highlight a central but neglected feature of perceived randomness. (shrink)

ABSTRACTCurrent theories of probability recognise a distinction between external certainty and internal certainty. The present studies investigated this distinction in lay people's judgements of probability statements formulated to suggest either an internal or an external interpretation. These subtle differences in wording influenced participants' perceptions and endorsements of such statements, and their impressions of the speaker. External expressions were seen to signal more reliable task duration estimates, and a lower degree of external than internal certainty was deemed necessary to advise a (...) course of action. In conversations about football, internal expressions were perceived as signalling more personal interest, and were expected to be on the average 10% higher than corresponding external probabilities. Finally, people who reported their outcome expectations for two m... (shrink)