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Probability Versus Certainty Equivalence Methods in Utility Measurement: Are they Equivalent?


  • John C. Hershey

    (The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Paul J. H. Schoemaker

    (Graduate School of Business, University of Chicago, Chicago, Illinois 60637)


Certainty equivalence (CE) and probability equivalence (PE) methods are the two most frequently used procedures for constructing von Neumann-Morgenstern utility functions. In this paper, we compare these methods experimentally, using a two-stage within-subject design. By asking subjects first for a CE judgment and later for a related PE judgment (or vice versa), a consistency test is devised which any deterministic expectation model, including those allowing probability transformations, should meet. Using four related experiments, this consistency test is applied separately to gain and loss questions, and to the two sequences of linked equivalence judgments, namely CE-PE and PE-CE. The empirical results reveal serious inconsistencies between the CE and PE responses for each of the four experiments. The extent of discrepancy depends strongly on the subject's initial risk attitude and whether the gain or loss domain is examined. To explain the complex pattern of results, the second part of the paper explores several plausible hypotheses. The first of these concerns the role of random error, in either the responses or the utility function itself. It is shown that both can lead to bias, although not of a type that could explain our results. Thereafter shifts in reference points are examined. A particular reframing of the PE response mode is postulated in which a pure gamble is psychologically translated into a mixed one, leading to increased risk aversion. This hypothesis, which is also supported by other evidence, offers a complete and simple explanation of the results. Finally, several other behavioral hypotheses are examined, after developing a weighted average model to simulate them. They concern anchoring effects, differences in salience between the probability and outcome dimensions, strategic misrepresentation, regret or rejoice influences, and endowment effects. Although each hypothesis predicts some type of bias, none of these five could singly explain the particular pattern of bias observed. In general, the study demonstrates (1) that serious discrepancies exist between the CE and PE methods of utility measurement, (2) that the particular results are incompatible with traditional deterministic choice models, (3) how random response errors, through propagation, can induce systematic biases in the utility function, (4) that reframing of the PE mode offers a simple reference shift explanation of the complex findings, and (5) how various heuristics and biases can be operationalized and simulated to assess their effects on utility measurement. As such, this study represents a further step toward a systematic investigation of response mode biases in utility measurement.

Suggested Citation

  • John C. Hershey & Paul J. H. Schoemaker, 1985. "Probability Versus Certainty Equivalence Methods in Utility Measurement: Are they Equivalent?," Management Science, INFORMS, vol. 31(10), pages 1213-1231, October.
  • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:10:p:1213-1231
    DOI: 10.1287/mnsc.31.10.1213

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