IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

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

Listed author(s):
  • 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Article provided by INFORMS in its journal Management Science.

Volume (Year): 31 (1985)
Issue (Month): 10 (October)
Pages: 1213-1231

in new window

Handle: RePEc:inm:ormnsc:v:31:y:1985:i:10:p:1213-1231
Contact details of provider: Postal:
7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA

Phone: +1-443-757-3500
Fax: 443-757-3515
Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:31:y:1985:i:10:p:1213-1231. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.