Communicative functions of directional verbal probabilities: Speaker's choice, listener's inference, and reference points.

Verbal probabilities have directional communicative functions, and most can be categorized as positive (e.g., "it is likely") or negative (e.g., "it is doubtful"). We examined the communicative functions of verbal probabilities based on the reference point hypothesis According to this hypothesis, listeners are sensitive to and can infer a speaker's reference points based on the speaker's selected directionality. In four experiments (two of which examined speakers' choice of directionality and two of which examined listeners' inferences about a speaker's reference point), we found that listeners could make inferences about speakers' reference points based on the stated directionality of verbal probability. Thus, the directionality of verbal probabilities serves the communicative function of conveying information about a speaker's reference point.

The role of familiarity in binary choice inferences.

In research on the recognition heuristic (Goldstein & Gigerenzer, Psychological Review, 109, 75-90, 2002), knowledge of recognized objects has been categorized as "recognized" or "unrecognized" without regard to the degree of familiarity of the recognized object. In the present article, we propose a new inference model--familiarity-based inference. We hypothesize that when subjective knowledge levels (familiarity) of recognized objects differ, the degree of familiarity of recognized objects will influence inferences. Specifically, people are predicted to infer that the more familiar object in a pair of two objects has a higher criterion value on the to-be-judged dimension. In two experiments, using a binary choice task, we examined inferences about populations in a pair of two cities. Results support predictions of familiarity-based inference. Participants inferred that the more familiar city in a pair was more populous. Statistical modeling showed that individual differences in familiarity-based inference lie in the sensitivity to differences in familiarity. In addition, we found that familiarity-based inference can be generally regarded as an ecologically rational inference. Furthermore, when cue knowledge about the inference criterion was available, participants made inferences based on the cue knowledge about population instead of familiarity. Implications of the role of familiarity in psychological processes are discussed.

Directional verbal probabilities: inconsistencies between preferential judgments and numerical meanings.

Verbal probability expressions (e.g., it is possible or doubtful) convey not only vague numerical meanings (i.e., probability) but also semantic functions, called directionality. We performed two experiments to examine whether preferential judgments are consistent with numerical meanings of verbal probabilities regardless of directionality. The results showed that because of the effects of directionality, perceived degrees of certainty for verbal probabilities differed between a binary choice and a numerical translation (Experiment 1), and decisions based on a verbal probability do not correspond to those based on a numerical translation for verbal probabilities (Experiment 2). These findings suggest that directionality of verbal probabilities is an independent feature from numerical meanings; hence numerical meanings of verbal probability alone remain insufficient to explain the effects of directionality on preferential judgments.

[Vagueness and the directionality of verbal probability expressions: the properties of probability information and their effects on decision making].

We examined the relationship between two properties of verbal probability (VP) expressions, "vagueness" and "directionality", and investigated the effects of these properties on decision making. Vagueness is defined as its imprecise characteristic of uncertainty expressions in VP, whereas the directionality is communicative functions which cause one to focus on the occurrence or non-occurrence of the target event described by VP. Experiment 1 contrasted a disagreement in the literature as to whether one can predict the directionality from vagueness properties, and our analyses resolved the conflict by showing the ineffectiveness of the vagueness in predicting the directionality. Experiment 2 administered decision tasks involving VP and numerical translation tasks of VP. We discovered that the directionality affects only on decision tasks. The results of Experiments 1 and 2 indicated that the directionality is distinct characteristic from the vagueness of VP, and these properties affect decisions independently. Implications are discussed.

Effects of instructions and representation on mathematical problem-solving.

We investigated whether specific instructions have different representations for target problems, and hence whether task representations mostly affect the direction of typical errors in permutation problem-solving. We hypothesized that different instructions produce specific representations of a permutation problem in an identical description. The 39 participants were randomly assigned to the three groups: the equation instruction group, the subgoal instruction group, and the control group. Results confirmed our prediction that the treatment groups solved the problem more correctly than the control group. More importantly, a subgoal instruction (a set of steps in a meaningful task) decreased the typical mistakes. Educational implications are discussed.

Facilitating normative judgments of conditional probability: frequency or nested sets?

Recent probability judgment research contrasts two opposing views. Some theorists have emphasized the role of frequency representations in facilitating probabilistic correctness; opponents have noted that visualizing the probabilistic structure of the task sufficiently facilitates normative reasoning. In the current experiment, the following conditional probability task, an isomorph of the "Problem of Three Prisoners" was tested. "A factory manufactures artificial gemstones. Each gemstone has a 1/3 chance of being blurred, a 1/3 chance of being cracked, and a 1/3 chance of being clear. An inspection machine removes all cracked gemstones, and retains all clear gemstones. However, the machine removes 1/2 of the blurred gemstones. What is the chance that a gemstone is blurred after the inspection?" A 2 x 2 design was administered. The first variable was the use of frequency instruction. The second manipulation was the use of a roulette-wheel diagram that illustrated a "nested-sets" relationship between the prior and the posterior probabilities. Results from two experiments showed that frequency alone had modest effects, while the nested-sets instruction achieved a superior facilitation of normative reasoning. The third experiment compared the roulette-wheel diagram to tree diagrams that also showed the nested-sets relationship. The roulette-wheel diagram outperformed the tree diagrams in facilitation of probabilistic reasoning. Implications for understanding the nature of intuitive probability judgments are discussed.