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Interior Additivity and Subjective Probability Assessment of Continuous Variables

Author

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  • Robert T. Clemen

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Canan Ulu

    (McCombs School of Business, University of Texas at Austin, Austin, Texas 78712)

Abstract

One of the goals of psychological research on subjective probability judgment is to develop prescriptive procedures that can improve such judgments. In this paper, our aim is to reduce partition dependence, a judgmental bias that arises from the particular way in which a state space is partitioned for the purposes of making probability judgments. We explore a property of subjective probabilities called interior additivity (IA). Our story begins with a psychological model of subjective probability judgment that exhibits IA. The model is a linear combination of underlying support for the event in question and a term that reflects a prior belief that all elements in the state space partition are equally likely. The model is consistent with known properties of subjective probabilities, such as binary complementarity, subadditivity, and partition dependence, and has several additional properties related to IA. We present experimental evidence to support our model. The model further suggests a simple prescriptive method based on IA that decision and risk analysts can use to reduce partition dependence, and we present preliminary empirical evidence demonstrating the effectiveness of the method.

Suggested Citation

  • Robert T. Clemen & Canan Ulu, 2008. "Interior Additivity and Subjective Probability Assessment of Continuous Variables," Management Science, INFORMS, vol. 54(4), pages 835-851, April.
    • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:4:p:835-851
    DOI: 10.1287/mnsc.1070.0790
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    References listed on IDEAS

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    1. H. V. Ravinder & Don N. Kleinmuntz & James S. Dyer, 1988. "The Reliability of Subjective Probabilities Obtained Through Decomposition," Management Science, INFORMS, vol. 34(2), pages 186-199, February.
    2. Abramson, Bruce & Brown, John & Edwards, Ward & Murphy, Allan & Winkler, Robert L., 1996. "Hailfinder: A Bayesian system for forecasting severe weather," International Journal of Forecasting, Elsevier, vol. 12(1), pages 57-71, March.
    3. R. Winkler & Javier Muñoz & José Cervera & José Bernardo & Gail Blattenberger & Joseph Kadane & Dennis Lindley & Allan Murphy & Robert Oliver & David Ríos-Insua, 1996. "Scoring rules and the evaluation of probabilities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 5(1), pages 1-60, June.
    4. Craig R. Fox & Robert T. Clemen, 2005. "Subjective Probability Assessment in Decision Analysis: Partition Dependence and Bias Toward the Ignorance Prior," Management Science, INFORMS, vol. 51(9), pages 1417-1432, September.
    5. Fox, Craig R & Rogers, Brett A & Tversky, Amos, 1996. "Options Traders Exhibit Subadditive Decision Weights," Journal of Risk and Uncertainty, Springer, vol. 13(1), pages 5-17, July.
    6. George Wu & Richard Gonzalez, 1999. "Nonlinear Decision Weights in Choice Under Uncertainty," Management Science, INFORMS, vol. 45(1), pages 74-85, January.
    7. Craig R. Fox & Amos Tversky, 1998. "A Belief-Based Account of Decision Under Uncertainty," Management Science, INFORMS, vol. 44(7), pages 879-895, July.
    8. Osherson, Daniel & Shafir, Eldar & Krantz, David H. & Smith, Edward E., 1997. "Probability Bootstrapping: Improving Prediction by Fitting Extensional Models to Knowledgeable but Incoherent Probability Judgments," Organizational Behavior and Human Decision Processes, Elsevier, vol. 69(1), pages 1-8, January.
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