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Possibility to agree on disagree from quantum information and decision making
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
Linnaeus University, Faculty of Technology, Department of Mathematics. Prokhorov Gen Phys Inst, Moscow, Russia.
2014 (English)In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 62-63, 1-15 p.Article in journal (Refereed) Published
Abstract [en]

The celebrated Aumann theorem states that if two agents have common priors, and their posteriors for a given event E are common knowledge, then their posteriors must be equal; agents with the same priors cannot agree to disagree. The aim of this note is to show that in some contexts agents using a quantum probability scheme for decision making can agree to disagree even if they have the common priors, and their posteriors for a given event E are common knowledge. We also point to sufficient conditions guaranteeing impossibility to agree on disagree even for agents using quantum(-like) rules in the process of decision making. A quantum(-like) analog of the knowledge operator is introduced; its basic properties can be formulated similarly to the properties of the classical knowledge operator defined in the set-theoretical approach to representation of the states of the world and events (Boolean logics). However, this analogy is just formal, since quantum and classical knowledge operators are endowed with very different assignments of truth values. A quantum(-like) model of common knowledge naturally generalizing the classical set-theoretic model is presented. We illustrate our approach by a few examples; in particular, on attempting to escape the agreement on disagree for two agents performing two different political opinion polls. We restrict our modeling to the case of information representation of an agent given by a single quantum question-observable (of the projection type). A scheme of extending of our model of knowledge/common knowledge to the case of information representation of an agent based on a few question-observables is also presented and possible pitfalls are discussed. (C) 2014 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
2014. Vol. 62-63, 1-15 p.
Keyword [en]
Quantum decision making, Agree on disagree, Aumann theorem, Common knowledge, Quantum probability, Quantum measurement theory, Projection postulate
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-39136DOI: 10.1016/j.jmp.2014.09.003ISI: 000346393900001OAI: oai:DiVA.org:lnu-39136DiVA: diva2:781080
Available from: 2015-01-15 Created: 2015-01-15 Last updated: 2016-05-03Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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