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Normal form backward induction for decision trees with coherent lower previsions

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  • Nathan Huntley
  • Matthias Troffaes

Abstract

We examine normal form solutions of decision trees under typical choice functions induced by lower previsions. For large trees, finding such solutions is hard as very many strategies must be considered. In an earlier paper, we extended backward induction to arbitrary choice functions, yielding far more efficient solutions, and we identified simple necessary and sufficient conditions for this to work. In this paper, we show that backward induction works for maximality and E-admissibility, but not for interval dominance and Γ-maximin. We also show that, in some situations, a computationally cheap approximation of a choice function can be used, even if the approximation violates the conditions for backward induction; for instance, interval dominance with backward induction will yield at least all maximal normal form solutions. Copyright Springer Science+Business Media, LLC 2012

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  • Nathan Huntley & Matthias Troffaes, 2012. "Normal form backward induction for decision trees with coherent lower previsions," Annals of Operations Research, Springer, vol. 195(1), pages 111-134, May.
    • Handle: RePEc:spr:annopr:v:195:y:2012:i:1:p:111-134:10.1007/s10479-011-0968-2
    DOI: 10.1007/s10479-011-0968-2
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    1. McClennen,Edward F., 1990. "Rationality and Dynamic Choice," Cambridge Books, Cambridge University Press, number 9780521360470.
    2. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    3. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    4. Ray, Paramesh, 1973. "Independence of Irrelevant Alternatives," Econometrica, Econometric Society, vol. 41(5), pages 987-991, September.
    5. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    6. Irving H. LaValle & Kenneth R. Wapman, 1986. "Note---Rolling Back Decision Trees Requires the Independence Axiom!," Management Science, INFORMS, vol. 32(3), pages 382-385, March.
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    Cited by:

    1. Bogumił Kamiński & Michał Jakubczyk & Przemysław Szufel, 2018. "A framework for sensitivity analysis of decision trees," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 135-159, March.
    2. Yongzhi Cao, 2014. "Reducing Interval-Valued Decision Trees to Conventional Ones: Comments on Decision Trees with Single and Multiple Interval-Valued Objectives," Decision Analysis, INFORMS, vol. 11(3), pages 204-212, September.
    3. Enrique Miranda & Ignacio Montes, 2023. "Centroids of the core of exact capacities: a comparative study," Annals of Operations Research, Springer, vol. 321(1), pages 409-449, February.

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