Are People Naïve Probability Theorists? A Further Examination of the Probability Theory + Variation Model

2016

Cognitive Psychology

A common view in current psychology is that people estimate probabilities using various 'heuristics' or rules of thumb that do not follow the normative rules of probability theory. We present a model where people estimate conditional probabilities such as P(A|B) (the probability of A given that B has occurred) by a process that follows standard frequentist probability theory but is subject to random noise. This model accounts for various results from previous studies of conditional probability judgment. This model predicts that people's conditional probability judgments will agree with a series of fundamental identities in probability theory whose form cancels the effect of noise, while deviating from probability theory in other expressions whose form does not allow such cancellation. Two experiments strongly confirm these predictions, with people's estimates on average agreeing with probability theory for the noise-cancelling identities, but deviating from probability theory (in just the way predicted by the model) for other identities. This new model subsumes an earlier model of unconditional or 'direct' probability judgment which explains a number of systematic biases seen in direct probability judgment (Costello & Watts, 2014). This model may thus provide a fully general account of the mechanisms by which people estimate probabilities.

Section: Previous Results On Conditional Probability Estimationsupporting

confidence: 79%

Section: Our Model Of Probability Estimationmentioning

confidence: 52%

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People’s conditional probability judgments follow probability theory (plus noise)

2016

Cognitive Psychology

“…Our model thus predicts that this expression will have a value of 0, on average, in people's probability judgments just as required by standard probability theory. Exactly this pattern of agreement is seen in experimental results (Costello & Mathison, ; Costello & Watts, , , ; Fisher & Wolfe, ).…”

Section: The Probability Theory Plus Noise Modelsupporting

confidence: 81%

Probability Theory Plus Noise: Descriptive Estimation and Inferential Judgment

Topics in Cognitive Science

2018

We describe a computational model of two central aspects of people's probabilistic reasoning: descriptive probability estimation and inferential probability judgment. This model assumes that people's reasoning follows standard frequentist probability theory, but it is subject to random noise. This random noise has a regressive effect in descriptive probability estimation, moving probability estimates away from normative probabilities and toward the center of the probability scale. This random noise has an anti-regressive effect in inferential judgement, however. These regressive and anti-regressive effects explain various reliable and systematic biases seen in people's descriptive probability estimation and inferential probability judgment. This model predicts that these contrary effects will tend to cancel out in tasks that involve both descriptive estimation and inferential judgement, leading to unbiased responses in those tasks. We test this model by applying it to one such task, described by Gallistel et al. ). Participants' median responses in this task were unbiased, agreeing with normative probability theory over the full range of responses. Our model captures the pattern of unbiased responses in this task, while simultaneously explaining systematic biases away from normatively correct probabilities seen in other tasks.

“…In an experiment asking participants to estimate the probability of a range of future events (such as a future increase in cigarette taxes and a future decline in smoking rates) and of various conjunctions and disjunctions of those events, we found that people's probability estimates gave values for the addition law that were, on average, very close to 0 as required by probability theory; similar results held for a number of other such ‘cancelling’ expressions (Costello & Watts, ). Finally, in an experiment where participants were given personality descriptions for a range of imaginary people and then asked to assess the probability of various direct, conjunctive, disjunctive and conditional statements being true for those people, Fisher and Wolfe () found that people's probability estimates gave a value for the addition law that was, again, very close to 0 as required by probability theory. Together, these results suggest that our model applies to probability estimation for events in general and is not limited solely to events that have previously been seen.…”

Section: Discussionmentioning

confidence: 99%

Explaining High Conjunction Fallacy Rates: The Probability Theory Plus Noise Account

Behavioral Decision Making

2016

The conjunction fallacy occurs when people judge the conjunctive probability P(A ∧ B) to be greater than a constituent probability P(A), contrary to the norms of probability theory. This fallacy is a reliable, consistent and systematic part of people's probability judgements, attested in many studies over at least 40 years. For some events, these fallacies occur very frequently in people's judgements (at rates of 80% or more), while for other events, the fallacies are very rare (occurring at rates of 10% or less). This wide range of fallacy rates presents a challenge for current theories of the conjunction fallacy. We show how this wide range of observed fallacy rates can be explained by a simple model where people reason according to probability theory but are subject to random noise in the reasoning process.