A note on superadditive probability judgment.

Macchi, Laura; Osherson, Daniel N.; Krantz, David H.

doi:10.1037/0033-295x.106.1.210

Cited by 110 publications

(51 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other researchers (e.g., Ayton, 1997) have reported that people's probability judgments tend to be subadditive (i.e., the sum of the individualestimates is greater than one). And evidence of superadditivityin the case of binary complementarity also has been found (see, e.g., Macchi, Osherson, & Krantz, 1999).…”

Section: The Additivity Principlementioning

confidence: 92%

The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle

2002

View full text Add to dashboard Cite

In judging posterior probabilities, people often answer with the inverse conditional probability-a tendency named the inverse fallacy. Participants (N = 45) were given a series of probability problems that entailed estimating both p(H | D) and p(,H | D). The findings revealed that deviations of participants' estimates from Bayesian calculations and from the additivity principle could be predicted by the corresponding deviations of the inverse probabilities from these relevant normative benchmarks. Methodological and theoretical implications of the distinction between inverse fallacy and base-rate neglect and the generalization of the study of additivity to conditional probabilities are discussed.

show abstract

Section: The Additivity Principlementioning

confidence: 92%

The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle

2002

View full text Add to dashboard Cite

show abstract

“…However, some descriptive models of judgment predict that judgments should be either additive or superadditive (e.g., Shafer, 1976), while others predict that they should be either additive or subadditive (e.g., Tversky & Koehler, 1994). Much of the literature in this area supports the latter prediction (e.g., Fischhoff et al, 1978;Fox, Rogers, & Tversky, 1996;Rottenstreich & Tversky, 1997;Tversky & Fox, 1995); other research, however, supports the former (e.g., Macchi, Osherson, & Krantz, 1999). Tversky and Koehler (1994) developed support theory (ST) to accommodate the finding that different descriptions of the same event lead to different subjective judgments for the event.…”

mentioning

confidence: 86%

MINERVA‐DM and subadditive frequency judgments

Bearden

Wallsten

2004

Behavioral Decision Making

View full text Add to dashboard Cite

There is considerable evidence that frequency (and probability) judgments are often subadditive. That is, the frequency judgment assigned to an event is often less than the sum of the frequency judgments assigned to the mutually exclusive component events that together form it. Explanations for subadditive judgments have typically relied on relatively high-level cognitive constructs such as the availability and representativeness heuristics. A lower-level explanation of subadditivity is presented in this paper through a model of memory and judgment processes, MINERVA-DM. Under MINERVA-DM, subadditivity is influenced by the similarity of the representations of the judged component events in memory to one another and by the placement of decision criteria. Results from two experiments support the model predictions. The first examines the effects of component event similarity on subadditivity. The second replicates the first and also provides support for the model's prediction of the effects of payoffs on similarity criteria.

show abstract

“…Moreover, partition elements sometimes attract a dearth of support rather than a surplus, leading to superadditivity. For example, in Macchi et al (1999), one group of undergraduates (in Italy) gave their probability that the Duomo in Milan is taller than Notre Dame in Paris, whereas another group gave the probability that Notre Dame is taller than the Duomo. All participants were informed that the heights are different.…”

Section: Introductionmentioning

confidence: 99%

On the provenance of judgments of conditional probability

Zhao¹,

Shah²,

Osherson³

2009

Cognition

Self Cite

View full text Add to dashboard Cite

In standard treatments of probability, Pr (A|B) is defined as the ratio of Pr (A∩B) to Pr (B), provided that Pr (B) > 0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr (A|B) arise in the mind via implicit calculation of Pr (A ∩ B)/Pr (B). We tested this hypothesis (Experiment 1) by presenting brief visual scenes composed of forms, and collecting estimates of relevant probabilities. Direct estimates of conditional probability were not well predicted by Pr (A ∩ B)/Pr (B). Direct estimates were also closer to the objective probabilities defined by the stimuli, compared to estimates computed from the foregoing ratio. The hypothesis that Pr (A|B) arises from the ratio Pr (A ∩ B)/[Pr (A ∩ B) + Pr (A ∩ B)] fared better (Experiment 2). In a third experiment, the same hypotheses were evaluated in the context of subjective estimates of the chance of future events.

show abstract

A note on superadditive probability judgment.

Cited by 110 publications

References 9 publications

The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle

The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle

MINERVA‐DM and subadditive frequency judgments

On the provenance of judgments of conditional probability

Contact Info

Product

Resources

About