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The Logic of Belief Persistence

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  • Battigalli, Pierpaolo
  • Bonanno, Giacomo

Abstract

The principle of belief persistence, or conservativity principle, states that ‘When changing beliefs in response to new evidence, you should continue to believe as many of the old beliefs as possible’ (Harman, 1986, p. 46). In particular, this means that if an individual gets new information, she has to accommodate it in her new belief set (the set of propositions she believes), and, if the new information is not inconsistent with the old belief set, then (1) the individual has to maintain all the beliefs she previously had and (2) the change should be minimal in the sense that every proposition in the new belief set must be deducible from the union of the old belief set and the new information (see, e.g., Gärdenfors, 1988; Stalnaker, 1984). We focus on this minimal notion of belief persistence and characterize it both semantically and syntactically.

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  • Battigalli, Pierpaolo & Bonanno, Giacomo, 1997. "The Logic of Belief Persistence," Economics and Philosophy, Cambridge University Press, vol. 13(1), pages 39-59, April.
    • Handle: RePEc:cup:ecnphi:v:13:y:1997:i:01:p:39-59_00
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    References listed on IDEAS

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    1. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
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    Cited by:

    1. Matthew Ryan, 2001. "Capacity Updating Rules and Rational Belief Change," Theory and Decision, Springer, vol. 51(1), pages 73-87, August.
    2. Giacomo Bonanno & Klaus Nehring, "undated". "Intersubjective Consistency Of Knowledge And Belief," Department of Economics 98-03, California Davis - Department of Economics.
    3. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 164, University of California, Davis, Department of Economics.
    4. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    5. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    6. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    7. Weijia Wang & Shaoan Huang, 2021. "Risk sharing and financial stability: a welfare analysis," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(1), pages 211-228, January.
    8. Samet, Dov, 1999. "Bayesianism without learning," Research in Economics, Elsevier, vol. 53(2), pages 227-242, June.
    9. Ryan, Matthew J., 2002. "Violations of Belief Persistence in Dempster-Shafer Equilibrium," Games and Economic Behavior, Elsevier, vol. 39(1), pages 167-174, April.
    10. Fukuda, Satoshi, 2020. "Formalizing common belief with no underlying assumption on individual beliefs," Games and Economic Behavior, Elsevier, vol. 121(C), pages 169-189.
    11. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 45, University of California, Davis, Department of Economics.
    12. Giacomo Bonanno & Klaus Nehring, "undated". "Intersubjective Consistency Of Knowledge And Belief," Department of Economics 98-03, California Davis - Department of Economics.
    13. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    14. Wang, Weijia, 2019. "A Pareto Criterion on Systemic Risk," MPRA Paper 93699, University Library of Munich, Germany.
    15. Giacomo Bonanno, "undated". "The Logic Of Prediction," Department of Economics 98-12, California Davis - Department of Economics.

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