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Interior Additivity and Subjective Probability Assessment of Continuous Variables

Fuqua School of Business, Duke University, Durham, North Carolina 27708
McCombs School of Business, University of Texas at Austin, Austin, Texas 78712
clemen{at}duke.edu
canan.ulu{at}mccombs.utexas.edu

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.

Key Words: decision analysis; subjective probability assessment; support theory; partition dependence; ignorance prior; debiasing
History: Received: March 27, 2006;