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People's conditional probability judgments follow probability theory (plus noise).

Fintan Costello1, Paul Watts2

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People estimate conditional probabilities using a noisy, but fundamentally accurate, frequentist process. This model explains deviations from probability theory, offering a general account of probability estimation.

Keywords:
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Area of Science:

  • Cognitive Psychology
  • Probability Theory
  • Decision Making

Background:

  • Current psychological models suggest probability estimation relies on heuristics, deviating from normative probability theory.
  • Previous research highlights systematic biases in unconditional probability judgments.

Purpose of the Study:

  • To propose and validate a new model of conditional probability estimation.
  • To explain how human judgments align with or deviate from probability theory.
  • To provide a unified account of probability estimation mechanisms.

Main Methods:

  • Developed a computational model based on frequentist probability theory with added random noise.
  • Conducted two experiments to test predictions derived from the model regarding conditional probability judgments.
  • Analyzed participants' estimates against fundamental probability theory identities.

Main Results:

  • Human conditional probability judgments align with probability theory for noise-cancelling identities.
  • Judgments deviate from probability theory for non-noise-cancelling identities, precisely as predicted by the model.
  • The model successfully accounts for previously observed biases in direct probability judgment.

Conclusions:

  • Human probability estimation, particularly conditional probabilities, follows standard frequentist principles with superimposed noise.
  • The proposed model offers a more general and accurate framework for understanding probability judgment.
  • This work unifies accounts of both direct and conditional probability estimation.