A foundation for support theory based on a non-Boolean event space

Abstract A new foundation is presented for the theory of subjective judgments of probability known in the psychological literature as “Support Theory”. It is based on new complementation operations that, unlike those of classical probability theory (set-theoretic complementation) and classical logic (negation), need not satisfy the principles of the Law of The Excluded Middle and the Law of Double Complementation. Interrelationships between the new complementation operations and the Kahneman and Tversky judgmental heuristic of availability are described.

[1]  The Relation Between Probability and Evidence Judgment: An Extension of Support Theory , 2001 .

[2]  C. Fox,et al.  Forecasting Trial Outcomes: Lawyers Assign Higher Probability to Possibilities That Are Described in Greater Detail , 2002, Law and human behavior.

[3]  D A Redelmeier,et al.  Probability judgement in medicine: discounting unspecified possibilities. , 1995, Medical decision making : an international journal of the Society for Medical Decision Making.

[4]  R. Sikorski,et al.  The mathematics of metamathematics , 1963 .

[5]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[6]  Yuval Rottenstreich,et al.  Typical versus atypical unpacking and superadditive probability judgment. , 2004, Journal of experimental psychology. Learning, memory, and cognition.

[7]  Paolo Mancosu,et al.  From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s , 1997 .

[8]  A. Tversky,et al.  Heuristics and Biases: Unpacking, Repacking, and Anchoring: Advances in Support Theory , 2002 .

[9]  A. Tversky,et al.  Unpacking, repacking, and anchoring: advances in support theory. , 1997 .

[10]  Louis Narens,et al.  Theories of Probability: An Examination of Logical and Qualitative Foundations , 2007 .

[11]  A. Tversky,et al.  Options traders exhibit subadditive decision weights , 1996 .

[12]  A. Kolmogoroff.  Zur Deutung der intuitionistischen Logik , 1932 .

[13]  A. Tversky,et al.  Judgments of and by Representativeness , 1981 .

[14]  Lyle Brenner,et al.  Focus, repacking, and the judgment of grouped hypotheses , 1999 .

[15]  Louis Narens,et al.  A Theory of Belief for Scientific Refutations , 2005, Synthese.

[16]  D. Krantz,et al.  A Note on Superadditive Probability Judgment , 1999 .

[17]  Rami Zwick,et al.  Comparing the calibration and coherence of numerical and verbal probability judgments , 1993 .

[18]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[19]  A. Heyting.  Die formalen Regeln der intuitionistischen Logik , 1930 .

[20]  A. Tversky,et al.  Support theory: A nonextensional representation of subjective probability. , 1994 .