Karl Halvor Teigen

Yes, but it is uncertain: Direction and communicative intention of verbal probabilistic terms

Abstract Previous studies comparing verbal and numerical probabilities have failed to take into account the directional aspect of verbal phrases. Some terms, like “probable” and “possible”, seem to be affirmative, whereas others, like “unlikely” and “doubtful”, function more like negations. This bi-directionality was explored in four studies in which American and Norwegian students were asked (1) to complete sentences containing various verbal and numerical phrases, and ending in “because ...”; (2) to evaluate the appropriateness of selected verbal phrases in otherwise complete sentences; (3) to evaluate the appropriateness of selected answering words ( yes, no, yes, but , and no, but ) in answers containing verbal and numerical probabilities; and (4) to select appropriate verbal phrases in situations characterized by specific p values of success and failure. It was found that most verbal probabilities are directionally unambiguous (more than numbers). Evidence was also found for a positivity bias, in that affirmative phrases apply to a wider variety of probabilities and outcomes (successes and failures) than do negative phrases. Even low numerical probabilities were more often treated as affirmations than as negations.

Surprises: low probabilities or high contrasts?

Outcome expectations can be expressed prospectively in terms of probability estimates, and retrospectively in terms of surprise. Surprise ratings and probability estimates differ, however, in some important ways. Surprises are generally created by low-probability outcomes, yet, as shown by several experiments, not all low-probability outcomes are equally surprising. To account for surprise, we propose a contrast hypothesis according to which the level of surprise associated with an outcome is mainly determined by the extent to which it contrasts with the default, expected alternative. Three ways by which contrasts can be established are explored: contrasts due to relative probabilities, where the obtained outcome is less likely than a default alternative; contrasts formed by novelty and change, where a contrast exists between the obtained outcome and the individuals previous experience; and contrasts due to the perceptual or conceptual distance between the expected and the obtained. In all these cases, greater contrast was accompanied by higher ratings of surprise.

The language of uncertainty

Abstract The article discusses subjective meaning components of the terms commonly used to express different varieties and degrees of probability and uncertainty. Some terms (like ‘risky’ and ‘promising’ prospects) have ambiguous referents, being in some cases interpreted to refer to possible gains and losses, in other cases to levels of uncertainty and certainty. Other terms (like ‘highly probable’, ‘doubtful’ ‘good chances’ etc.) are shown to have other communicative functions besides their purely probabilistic ones, some of the most important being to indicate the source of uncertainty (internal vs. external), non-commitment and vagueness, and emphasis on p or 1-p (probability vs. uncertainty). By asking subjects to compare the appropriateness of selected verbal expressions under different circumstances, e.g. with equipossible outcomes, or after the outcome is known, it is possible to identify important semantic components of such expressions, in addition to those elicited by probability scaling techniques.

When are low-probability events judged to be ‘probable’? Effects of outcome-set characteristics on verbal probability estimates

Abstract In four studies, students assigned verbal probabilistic phrases (like ‘improbable’, ‘probable’, ‘great chances’) to outcomes of uncertain events. High-probability terms were commonly used to characterize low-probability outcomes in situations having several alternatives, especially when these were approximately equiprobable. Thus in contents between 4 to 8 equally strong competitors, several of these may be described as having ‘great chances’ or as a ‘probable’ winner. Although both numerical and verbal probabilities tend to be overestimated in connection with multi-outcome events, situations with equally likely alternatives will favor distributive numerical probabilities (with a sum of 1.00) but non-distributive verbal probabilities (all outcomes reported to be ‘highly probable’). Such verbal expressions are interpreted to reflect a Leibnizian probability concept, in which ‘highly probable’ means that the alternative in question can ‘easily’ occur.

Ambiguous probabilities: when doesp=0.3 reflect a possibility, and when does it express a doubt?

Verbal phrases denoting uncertainty are usually held to be more vague than numerical probability statements. They are, however, directionally more precise, in the sense that they are either positive, suggesting the occurrence of a target outcome, or negative, drawing attention to its non-occurrence. A numerical probability will, in contrast, sometimes be perceived as positive and sometimes as negative. When asked to complete sentences such as ‘The operation has a 30% chance of success, because’ some people will give reasons for success (‘the doctors are expert surgeons’), whereas others will give reasons for failure (‘it is a difficult operation’). It is shown in two experiments that positive reasons are given more often than negative ones, even for p values below 0.5, especially when the probability is higher than expected, and the target outcome is non-normal, undesirable, and phrased as a negation. We conclude that the directionality of numerical probabilities (as opposed to verbal phrases) is context-dependent, but biased towards a positive interpretation. Copyright

Why isp = .90 better thanp = .70? Preference for definitive predictions by lay consumers of probability judgments

What do people regard as an informative and valuable probability statement? This article reports four experiments that show participants to have a clear preference for more extreme and higher probabilities over less extreme and lower ones. This pattern emerged in Experiment 1, in which no context was provided, and was further explored in Experiment 2 within a positive and a negative context. The findings were further confirmed in Experiment 3, which employed a Bayesian framework with revisions of opinions. Finally, Experiment 4 showed how preference for high probabilities can lead people to prefer an overconfident to a more well-calibrated (accurate) forecaster. The results are interpreted as manifestations of asearch for definitive predictions principle, which asserts that high probabilities are preferred to medium ones and often favored over the corresponding complementary low probabilities on the basis of their capacity to predict the occurrence of single outcomes.

Giver-receiver asymmetries in gift preferences.

When people are asked to choose between gift items, givers and receivers sometimes show different patterns of preferences. The article reports four experimental studies exploring these giver-receiver asymmetries. Whereas givers tend to prefer exclusive, but smaller gift items, receivers appear to prefer less luxurious, and more useful gifts (Experiment 1). Givers prefer gift vouchers to cash, and are concerned about timing, whereas more receivers accept cash gifts, and claim that it does not matter if the gift arrives late (Experiment 2). One interpretation of the results could be that givers conform more strongly to gift conventions (cultural norms for gift exchange). It is further argued that these differences are not due to a perceived difference between self and others (Experiment 3), but rather because of situational differences. When receivers perform separate evaluations of gifts rather than joint evaluations (pairwise comparisons), they tend to change their preference pattern towards a higher rating of exclusive gift items (Experiment 4).

Linda versus World Cup: Conjunctive Probabilities in Three‐event Fictional and Real‐life Predictions

Conjunction errors in probability judgments have been explained in terms of representatives, non-normative combination procedures, and linguistic, conversational, or conceptual misunderstandings. In two studies, a three-event variant of the classical Linda scenario (Tversky and Kahneman, 1983) was contrasted with estimates of Norway’s chances in three coming World Cup soccer matches. Conjunction errors occurred even in the latter, real-life prediction task, but much less frequently than in the fictional Linda case. Magnitude of the conjunction effect was found to be dependent upon type of constituent (fictional versus dispositional), unequal versus equal probabilities of constituent events, prediction of positive versus negative outcomes, and, for real-life predictions only, umber of constitutent events. Fictional probability ratings were close to but lower than representativenss ratings, giving evidence for a representativeness and adjustment-for-uncertainty strategy, whereas probabilities of real-life events were given a causal model interpretation.

When the unreal is more likely than the real : Post hoc probability judgements and counterfactual closeness

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 ones expectations before the event. But if asked about the probability of an alternative, counterfactual outcome, a simpler strategy is available, based on this outcomes 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 l...

Good luck and bad luck: how to tell the difference

Good luck implies comparison with a worse counterfactual outcome, whereas bad luck implies upward comparisons. People will accordingly describe themselves as particularly lucky after recollecting situations where they avoided something negative, and as particularly unlucky after recollecting episodes in which they missed something positive (Study 1). Upward and downward comparisons can be created by the way a situation develops, and are accentuated by the way a story is told. Good luck stories typically change for the better only in the last stage, whereas bad luck stories show a more steady downward progression (Study 2). This is also reflected in phrases believed to be characteristic of good luck versus bad luck stories, with good luck stories involving surprise and reference to close counterfactuals, whereas bad luck stories focus on initial normal events (Study 3). Good and bad luck imply different orders of events (negative–positive versus positive–negative), so by rearranging the narrative sequence, the same set of outcomes can form the basis for a good luck story as well as a bad luck story (Study 4). The final experiment (Study 5) shows that negative outcome expectations are typical for chance-determined and uncontrolled situations. Under such circumstances, factual outcomes do not have to be exceptionally good to be considered as lucky. Copyright