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Minimax decision rules for planning under uncertainty: Drawbacks and remedies

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  • Anderson, Edward
  • Zachary, Stan

Abstract

It is common to use minimax rules to make planning decisions when there is great uncertainty about what may happen in the future. Using minimax rules avoids the need to determine probabilities for each future scenario, which is an attractive feature in many public sector settings. However there are potential problems in the application of a minimax approach. In this paper our aim is to give guidance for planners considering a minimax approach, including minimax regret which is one popular version of this. We give an analysis of the behaviour of minimax rules in the case with a finite set of possible future scenarios. Minimax rules will have sensitivity to the choice of a small number of scenarios. When regret-based rules are used there are also problems arising since the independence of irrelevant alternatives property fails, which can lead to opportunities to game the process. We analyse these phenomena considering cases where the decision variables are chosen from a convex set in Rn, as well as cases with a finite set of decision choices. We show that the drawbacks of minimax regret hold even when restrictions are placed on the problem setup, and we show how working with a structured set of scenarios can ameliorate the difficulty of having a final decision depend on the characteristics of just a handful of extreme scenarios.

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  • Anderson, Edward & Zachary, Stan, 2023. "Minimax decision rules for planning under uncertainty: Drawbacks and remedies," European Journal of Operational Research, Elsevier, vol. 311(2), pages 789-800.
    • Handle: RePEc:eee:ejores:v:311:y:2023:i:2:p:789-800
    DOI: 10.1016/j.ejor.2023.05.030
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    1. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. T. D. Pol & S. Gabbert & H.-P. Weikard & E. C. Ierland & E. M. T. Hendrix, 2017. "A Minimax Regret Analysis of Flood Risk Management Strategies Under Climate Change Uncertainty and Emerging Information," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 68(4), pages 1087-1109, December.
    3. Tamer Y. A. Fahmy & Yehia Fahmy & Fardous Mobarak & Mohamed El-Sakhawy & Ragab E. Abou-Zeid, 2020. "Biomass pyrolysis: past, present, and future," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 22(1), pages 17-32, January.
    4. Neal T. Graham & Mohamad I. Hejazi & Son H. Kim & Evan G. R. Davies & James A. Edmonds & Fernando Miralles-Wilhelm, 2020. "Future changes in the trading of virtual water," Nature Communications, Nature, vol. 11(1), pages 1-7, December.
    5. Shapiro, Alexander, 2012. "Minimax and risk averse multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 219(3), pages 719-726.
    6. Atanu Sengupta & Sanjoy De, 2020. "Summation and Future Roadmap," India Studies in Business and Economics, in: Assessing Performance of Banks in India Fifty Years After Nationalization, chapter 0, pages 133-143, Springer.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Howard Kunreuther & Geoffrey Heal & Myles Allen & Ottmar Edenhofer & Christopher B. Field & Gary Yohe, 2013. "Risk management and climate change," Nature Climate Change, Nature, vol. 3(5), pages 447-450, May.
    9. Gizelle D. Willows & Lawrence W.K. Ho & Darron West, 2020. "The effect of dividend payouts on future earnings," Afro-Asian Journal of Finance and Accounting, Inderscience Enterprises Ltd, vol. 10(4), pages 569-583.
    10. Mark Armstrong & John Vickers, 2010. "A Model of Delegated Project Choice," Econometrica, Econometric Society, vol. 78(1), pages 213-244, January.
    11. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    12. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    13. Ray, Paramesh, 1973. "Independence of Irrelevant Alternatives," Econometrica, Econometric Society, vol. 41(5), pages 987-991, September.
    14. Seeley, Brien A. MD. & Seeley, Damon & Rakas, Jasenka PhD, 2020. "A Report on the Future of Electric Aviation," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4t76186k, Institute of Transportation Studies, UC Berkeley.
    15. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
    16. Pedro Crespo del Granado & Christian Skar & Haris Doukas & Georgios P. Trachanas, 2019. "Investments in the EU Power System: A Stress Test Analysis on the Effectiveness of Decarbonisation Policies," Springer Books, in: Haris Doukas & Alexandros Flamos & Jenny Lieu (ed.), Understanding Risks and Uncertainties in Energy and Climate Policy, pages 97-122, Springer.
    17. Diecidue, Enrico & Somasundaram, Jeeva, 2017. "Regret theory: A new foundation," Journal of Economic Theory, Elsevier, vol. 172(C), pages 88-119.
    18. David L. McCollum & Ajay Gambhir & Joeri Rogelj & Charlie Wilson, 2020. "Energy modellers should explore extremes more systematically in scenarios," Nature Energy, Nature, vol. 5(2), pages 104-107, February.
    19. Han Bleichrodt & Peter P. Wakker, 2015. "Regret Theory: A Bold Alternative to the Alternatives," Economic Journal, Royal Economic Society, vol. 0(583), pages 493-532, March.
    20. Hughes, Nick & Strachan, Neil, 2010. "Methodological review of UK and international low carbon scenarios," Energy Policy, Elsevier, vol. 38(10), pages 6056-6065, October.
    21. Klamroth, Kathrin & Köbis, Elisabeth & Schöbel, Anita & Tammer, Christiane, 2017. "A unified approach to uncertain optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 403-420.
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    1. Lebeau, Alexis & Petitet, Marie & Quemin, Simon & Saguan, Marcelo, 2024. "Long-term issues with the Energy-Only Market design in the context of deep decarbonization," Energy Economics, Elsevier, vol. 132(C).

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