Partition-edit-count: naive extensional reasoning in judgment of conditional probability.

@article{Fox2004PartitioneditcountNE,
  title={Partition-edit-count: naive extensional reasoning in judgment of conditional probability.},
  author={Craig R. Fox and Jonathan Levav},
  journal={Journal of experimental psychology. General},
  year={2004},
  volume={133 4},
  pages={
          626-42
        }
}
  • C. Fox, Jonathan Levav
  • Published 1 December 2004
  • Psychology
  • Journal of experimental psychology. General
The authors provide evidence that people typically evaluate conditional probabilities by subjectively partitioning the sample space into n interchangeable events, editing out events that can be eliminated on the basis of conditioning information, counting remaining events, then reporting probabilities as a ratio of the number of focal to total events. Participants' responses to conditional probability problems were influenced by irrelevant information (Study 1), small variations in problem… 

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References

SHOWING 1-10 OF 56 REFERENCES
Naive probability: a mental model theory of extensional reasoning.
TLDR
The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases, and explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem.
Partition Priming in Judgment Under Uncertainty
TLDR
It is shown that likelihood judgments are biased toward an ignorance-prior probability that assigns equal credence to each mutually exclusive event considered by the judge, and systematic partition dependence is observed.
Support theory: A nonextensional representation of subjective probability.
This article presents a new theory of subjective probability according to which different descriptions of the same event can give rise to different judgments. The experimental evidence confirms the
Judgment under Uncertainty: Heuristics and Biases.
TLDR
Three heuristics that are employed in making judgements under uncertainty are described: representativeness, availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development.
The use of statistical heuristics in everyday inductive reasoning
In reasoning about everyday problems, people use statistical heuristics, that is, judgmental tools that are rough intuitive equivalents of statistical principles. Statistical heuristics have improved
AMBIGUITIES AND UNSTATED ASSUMPTIONS IN PROBABILISTIC REASONING
Ostensibly simple probabilistic reasoning problems are sometimes surprisingly difficult. One source of difficulty is the omission from a problem description of information essential to an unambiguous
Some teasers concerning conditional probabilities
Unpacking, repacking, and anchoring: advances in support theory.
TLDR
A significant extension of the theory in which the judged probability of an explicit disjunction is less than or equal to the sum of the judged probabilities of its disjoint components (explicit subadditivity) is presented.
...
...