Susan Butler

ABSTRACTTreating conditionals as probabilistic statements has been referred to as a defining feature of the “new paradigm” in cognitive psychology. Doing so is attractive for several reasons, but it complicates the problem of assessing the merits of conditional arguments. We consider several variables that relate to judging the persuasiveness of conditional arguments with uncertain premises. We also explore ways of judging the consistency of people's beliefs as represented by components of conditional arguments. Experimental results provide evidence that inconsistencies in beliefs are more prevalent if the arguments’ components are spatially and temporally dispersed than if they are contiguous in space and time. This supports the idea that assuring the consistency among even a small number of beliefs is difficult to do, especially if the beliefs in question are not brought into consciousness at the same time; but consistency can be enhanced when beliefs are considered simultaneously or nea...

The "two-envelopes" problem has stimulated much discussion on probabilistic reasoning, but relatively little experimentation. The problem specifies two identical envelopes, one of which contains twice as much money as the other. You are given one of the envelopes and the option of keeping it or trading for the other envelope. Variables of interest include the possible amounts of money involved, what is known about the process by which the amounts of money were assigned to the envelopes, and whether you are allowed to know how much money is in the envelope in hand before deciding whether to keep or trade. In an earlier study, Butler and Nickerson found that when participants were allowed to know how much was in the envelope in hand, they generally elected to trade if that amount was small relative to the range of possibilities and to keep otherwise. The present experiments showed that this propensity was independent of the amount of money in the envelopes. Participants made decisions with a strong bias for avoiding the risk of losing by trading, particularly when the amount in hand was known and large relative to the range of possible amounts, regardless of the absolute value of the gamble. The results illustrate the dependence of thinking on the context in which it occurs, and demonstrate a tendency to treat quantities that are large or small relative to a particular context in which they are encountered as though they were large or small in a more general sense

The “exchange paradox”—also referred to in the literature by a variety of other names, notably the “two-envelopes problem”—is notoriously difficult, and experts are not all agreed as to its resolution. Some of the various expressions of the problem are open to more than one interpretation; some are stated in such a way that assumptions are required in order to fill in missing information that is essential to any resolution. In three experiments several versions of the problem were used, in each of which the information given was sufficient to determine an optimal choice strategy when it exists or to justify indifference regarding keeping or trading when such a strategy does not exist. College students who were presented with the various versions of the problem tended to base their choices on simple heuristics and to give little evidence of understanding the probabilistic implications of the differences in the problem statements

Two experiments were conducted with variants of Wason's (1966) selection task. The common focus was the effect of differences in the sizes of the sets represented by P and not-Q in assertions of the form _If P then Q_ (conditional) or _All P are Q_ (categorical). Results support the conclusion that such set size differences affect the strategies people adopt when asked to determine, efficiently, the truth or falsity of such assertions, but they do not entirely negate the tendency to select the term represented by P (the antecedent of the conditional or the subject of the categorical) in preference to the term represented by not-Q (the complement of the consequent of the conditional or the complement of the predicate of the categorical). Several possible explanations of this perseverance are considered. Results also support the conclusion that people find it easier to assess categorical assertions than logically equivalent conditional assertions

Participants attempted to solve a modified version of Wason's selection task. Variables were: sizes of the sets referenced by a specified assertion, form of the assertion, thematic content of the assertion, and the need for sampling or not. In Experiment 1, participants were given enough information to determine the truth or falsity of the specified assertion with certainty; in Experiment 2, they had to rely on sampling and could not determine the assertion's truth or falsity with certainty. Performance was better in Experiment 1 than in Experiment 2, but in both cases much better than what is typically obtained with the conventional selection task. The results support the hypothesis that performance of the selection task is sensitive to the sizes of the sets involved, add credence to the conclusion that framing the task in a thematically meaningful way can facilitate performance, and demonstrate that facilitation does not require deontic reasoning or a well-known convention being involved. The relationship between expressed confidence and level of performance is consistent with other studies showing the former to be a good predictor of the latter.