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Quantum probability updating from zero priors (by-passing Cromwell's rule)
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).ORCID-id: 0000-0003-2396-6193
City University London, UK.
Vanderbilt University, USA.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).ORCID-id: 0000-0002-9857-0938
Vise andre og tillknytning
2017 (engelsk)Inngår i: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 77, s. 58-69Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a straightforward implication of how Bayes' rule works). Relatedly, hypotheses with a very low prior cannot be updated to have a very high posterior without a tremendous amount of new evidence to support them (or to make other possibilities highly improbable). Cromwell's rule appears at odds with our intuition of how humans update probabilities. In this work, we report two simple decision making experiments, which seem to be inconsistent with Cromwell's rule. Quantum probability theory, the rules for how to assign probabilities from the mathematical formalism of quantum mechanics, provides an alternative framework for probabilistic inference. An advantage of quantum probability theory is that it is not subject to Cromwell's rule and it can accommodate changes from zero or very small priors to significant posteriors. We outline a model of decision making, based on quantum theory, which can accommodate the changes from priors to posteriors, observed in our experiments. (C) 2016 Elsevier Inc. All rights reserved.

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Elsevier, 2017. Vol. 77, s. 58-69
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Forskningsprogram
Naturvetenskap, Matematik
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URN: urn:nbn:se:lnu:diva-64306DOI: 10.1016/j.jmp.2016.08.005ISI: 000399066900006Scopus ID: 2-s2.0-85001889577OAI: oai:DiVA.org:lnu-64306DiVA, id: diva2:1098354
Tilgjengelig fra: 2017-05-24 Laget: 2017-05-24 Sist oppdatert: 2019-09-06bibliografisk kontrollert

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