A Truth Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes

Offerman, Theo; Sonnemans, Joep; Kuilen, Gijs van de; Wakker, Peter P.

doi:10.1111/j.1467-937x.2009.00557.x

Cited by 187 publications

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“…In effect, the score or payment penalizes the subject by the squared deviation of the report from the true binary-valued outcome, 1, which is 1 3 There exist mechanisms that will elicit subjective probabilities without requiring that one correct for risk attitudes, such as the procedures proposed by Köszegi and Rabin [2008;p.199], Karni [2009], Grether [1992, Holt andSmith [2009], andOfferman, Sonnemans, van de Kuilen andWakker [2009], discussed further below. The latter three employ these mechanisms in an experimental evaluation.…”

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confidence: 99%

“…However, all use the valuation methods due to Becker DeGroot and Marshak [1964] instead of the QSR. Qiu and Steiger [2010] extend the approach of Offerman et al [2009] to identify the role of probability weighting on the correction of raw responses to the QSR.…”

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“…Only one study attempts to explicitly calibrate the beliefs for non-linear utility functions and/or probability weighting : Offerman, Sonnemans, van de Kuilen and Wakker [2009;§6]. 6 Their elegant approach has a reduced form simplicity, and is agnostic about which structural model of decision making under risk one uses.…”

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Estimating subjective probabilities

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ABSTRACT. Subjective probabilities play a role in many economic decisions. There is a large theoretical literature on the elicitation of subjective probabilities, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover subjective probabilities, but stresses the need to make strong auxiliary assumptions or "calibrating adjustments" to elicited reports in order to recover the latent probability. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We illustrate how the joint estimation of risk attitudes and subjective probabilities using structural maximum likelihood methods can provide the calibration adjustments that theory calls for. This allows the observer to make inferences about the latent subjective probability, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective beliefs assuming that choices are made consistently with expected utility theory or rank-dependent utility theory. Inferred subjective probabilities are significantly different when calibrated according to either theory, thus showing the importance of undertaking such exercises. Our findings also have implications for the interpretation of probabilities inferred from prediction markets. † Department of Economics, Copenhagen Business School, Copenhagen, Denmark (Andersen); Department of Economics, University of Canterbury, Christchurch, New Zealand (Fountain); Department of Risk Management & Insurance and CEAR, Robinson College of Business, Georgia State University, USA (Harrison); and Robinson College of Business, Georgia State University, USA (Rutström). E-mail contacts: sa.eco@cbs.dk, john.fountain@canterbury.ac.nz, gharrison@gsu.edu and erutstrom@gmail.com. We thank the U.S. National Science Foundation for research support under grants NSF/HSD 0527675 and NSF/SES 0616746. We are grateful to John Duffy, Peter Wakker, Randall Walsh and Nathaniel Wilcox for discussions.-1-Subjective probabilities about some event are operationally defined as those probabilities that lead an agent to make certain choices over outcomes that depend on that event. These choices could be as natural as placing a bet on a horse race, or as structured as responding to the payoffs provided by some scoring rule. In order to infer subjective probabilities from observed choices of this kind, however, one either has to make some strong assumptions about risk attitudes or jointly estimate risk attitudes and subjective probabilities. We show how the latter can be implemented by pairing several tasks together, some of which identify risk attitudes and some of which identify the interplay between risk attitudes and subjective probabilities. Joint estimation of a structural model of choice across these two types of ta...

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Estimating subjective probabilities

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“…Camerer (1989) and Bossaerts and Plott (2004) report findings suggesting that individuals tend not to accept the notion of independence. How to train subjects away from these tendencies is not obvious, but the literature suggests ideas including the use of formal training models (Offerman et al 2009) and training methods that work through subject involvement in the lottery procedures (Fong and McCabe, 1999).…”

Section: Revealed Theory Methodology and Controlling For Lottery mentioning

confidence: 99%

Endowment Effect Theory, Subject Misconceptions and Enhancement Effect Theory: A Reply to Isoni, Loomes and Sugden

Plott

Zeiler

2010

SSRN Journal

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The purpose of Plott and Zeiler (PZ) (2005) was to investigate whether previously published experiments using consumption goods such as mugs and candy bars to measure gaps between willingness to pay (WTP) and willingness to accept (WTA) support endowment effect theory (EET). Our results demonstrate that the gap for commodities can be turned on and off by implementing procedures designed to control for subject misconceptions about the value elicitation procedures. Although our purpose was limited to that narrow focus, ILS claim that our purpose was much broader. Here we make clear that our focus was clearly stated and that the conclusions of our paper are supported by all of ILS's and our data.Following experiments traditionally used to demonstrate the endowment effect, we used mug valuations to test EET. We used lottery rounds only to provide our subjects with paid practice using the value elicitation device prior to employing that device to elicit subjects' mug valuations. In our paper, we provided no detailed analysis of the lottery data, and the absence of any detailed analysis of those data forms the foundation of the ILS paper and the discussion in this Reply. In a footnote, we reported evidence of contamination in the lottery data that rendered it inappropriate for our purposes. (PZ, 2005, fn. 15) Our footnote summarized the details of misconceptions reported in a data supplement provided to all who request our lottery data. The supplement was not referenced in our paper; we include it here as Appendix 2.ILS claim that our 2005 paper is misleading and has misled researchers. They are concerned that our paper produces, and has been interpreted as producing, a set of procedures sufficient to remove all gaps, including gaps in lotteries. To justify their concern, they focus on the wording of our abstract and overlook the context of paragraphs from which they quote sentences to support their thesis. The result is what we consider to be a misleading picture of the content of our paper and the facts that we report, namely that mug gaps disappear after we implement controls for misconceptions and that none of our data provides support for EET. We want to 2 emphasize that our focus was on EET and not on more general theories of preference formation, reference effects and decision processes that have emerged in the literature more recently and might explain our results. 1In Section 1, we demonstrate that we did not make broad claims about our procedures.ILS make three additional claims. First, they claim that endowment effect theory "appears to be a loosely-related family of theories…" (ILS, p. 8) From their immediately subsequent discussion, one might infer that testing EET is a futile endeavor. In Section 2, we demonstrate that endowment effect theory is well-specified and makes clear predictions given our experimental environment. We also emphasize that ILS's and our mug data do not support EET. When controls for misconceptions about the elicitation device are implemented in mug experiments, the valuation gap ...

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“…Either the decision or the belief (subjective assessment of the probability of guilt) was rewarded (both with probability 50%): the decision according to table 1 with, in points, a=d=100, b=-1500 and c=-300, and the belief according to a quadratic scoring rule. This scoring rule is incentive compatible for risk neutral individuals (see Offerman et al, 2008). This procedure prevents hedging behavior by participants 5 .…”

Section: Part 1: Verdictmentioning

confidence: 99%

Errors in Judicial Decisions: Experimental Results

Sonnemans

Dijk²

2011

Journal of Law, Economics, and Organization

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In criminal cases the task of the judge is to transform the uncertainty about the facts into the certainty of the verdict. In this experiment we examine the relationship between evidence of which the strength is known, subjective probability of guilt and verdict for abstract cases. We look at two situations: (1) all evidence is given and (2) evidence can be acquired. Roughly half of the participants do not base their decision on a subjective belief of the probability of guilt. The others underestimate in general the probability of guilt, but this is more than compensated by a tendency to convict at too low probability of guilt. In the situation where evidence can be acquired, participants do not acquire enough evidence.

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A Truth Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes

Cited by 187 publications

References 81 publications

Estimating subjective probabilities

Estimating subjective probabilities

Endowment Effect Theory, Subject Misconceptions and Enhancement Effect Theory: A Reply to Isoni, Loomes and Sugden

Errors in Judicial Decisions: Experimental Results

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