Foundations Of Statistics

The purpose of Plott and Zeiler (2005)—henceforth, PZ—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 willingnessto-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. 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 a footnote, we report 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, so we make it available as an online Appendix to our Reply. 1 Andrea Isoni, Graham Loomes, and Robert Sugden (2011)—henceforth, ILS—use experimental procedures similar to ours and observe, just as we did, no gap in mug valuations. 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 emphasize that our focus was on EET and not on more general theories of prefer ence formation, reference effects and decision processes that have emerged in the literature more recently and might explain our results. 2 In Section I, we demonstrate

The Willingness to Pay-Willingness to Accept Gap, the "Endowment Effect," Subject Misconceptions, and Experimental Procedures for Eliciting Valuations

We study a contest with multiple (not necessarily equal) prizes. Contestants have private information about an ability parameter that affects their costs of bidding. The contestant with the highest bid wins the first prize, the contestant with the second-highest bid wins the second prize, and so on until all the prizes are allocated. All contestants incur their respective costs of bidding. The contest's designer maximizes the expected sum of bids. Our main results are: 1) We display bidding equlibria for any number of contestants having linear, convex or concave cost functions, and for any distribution of abilities. 2) If the cost functions are linear or concave, then, no matter what the distribution of abilities is, it is optimal for the designer to allocate the entire prize sum to a single ''first'' prize. 3) We give a necessary and sufficient conditions ensuring that several prizes are optimal if contestants have a convex cost function.

The Optimal Allocation of Prizes in Contests

Agrowing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect theory, can explain a variety of field and experimental data. Quantifications of loss aversion are, however, hindered by the absence of a general preference-based method to elicit the utility for gains and losses simultaneously. This paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions. Thus, it is the first to obtain a parameter-free elicitation of prospect theory's utility function on the whole domain. Our method also provides an efficient way to elicit utility midpoints, which are important in axiomatizations of utility. Several definitions of loss aversion have been put forward in the literature. According to most definitions we find strong evidence of loss aversion, at both the aggregate and the individual level. The degree of loss aversion varies with the definition used, which underlines the need for a commonly accepted definition of loss aversion.

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Loss Aversion Under Prospect Theory: A Parameter-Free Measurement

textA growing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect theory, can explain a variety of field and experimental data. Quantifications of loss aversion are, however, hindered by the absence of a general preference-based method to elicit the utility for gains and losses simultaneously. This paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions. Thus, it is the first to obtain a parameter-free elicitation of prospect theory's utility function on the whole domain. Our method also provides an efficient way to elicit utility midpoints, which are important in axiomatizations of utility. Several definitions of loss aversion have been put forward in the literature. According to most definitions we find strong evidence of loss aversion, at both the aggregate and the individual level. The degree of loss aversion varies with the definition used, which underlines the need for a commonly accepted definition of loss aversion.

Loss aversion under prospect theory: A parameter-free measurement

This paper proposes a new model that explains the violations of expected utility theory through the role of random errors The paper analyzes decision making under risk when individuals make random errors when they compute expected utilities Errors are drawn from the normal distribution, which is truncated so that the stochastic utility of a lottery cannot be greater (lower) than the utility of the highest (lowest) possible outcome The standard deviation of random errors is higher for lotteries with a wider range of possible outcomes It converges to zero for lotteries converging to a degenerate lottery The model explains all major stylized empirical facts such as the Allais paradox and the fourfold pattern of risk attitudes The model fits the data from ten well-known experimental studies at least as good as cumulative prospect theory

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A Stochastic Expected Utility Theory

We select a menu of seven popular decision theories and embed each theory in five models of stochastic choice including tremble, Fechner and random utility model. We find that the estimated parameters of decision theories differ significantly when theories are combined with different models. Depending on the selected model of stochastic choice we obtain different rankings of decision theories with regard to their goodness of fit to the data. The fit of all analyzed decision theories improves significantly when they are embedded in a Fechner model of heteroscedastic truncated errors or a random utility model.

Models of Stochastic Choice and Decision Theories: Why Both are Important for Analyzing Decisions

This paper proposes a new decision theory of how individuals make random errors when they compute the expected utility of risky lotteries. When dis- torted by errors, the expected utility of a lottery never exceeds (falls below) the utility of the highest (lowest) outcome. This assumption implies that errors are likely to overvalue (undervalue) lotteries with expected utility close to the utility of the lowest (highest) outcome. Proposed theory explains many stylized empirical facts such as the fourfold pattern of risk attitudes, common consequence effect (Allais paradox), common ratio effect and violations of betweenness. Theory fits the data from ten well- known experimental studies at least as well as cumulative prospect theory.

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Stochastic expected utility theory

The conventional parameterizations of cumulative prospect theory do not explain the St. Petersburg paradox. To do so, the power coefficient of an individual's utility function must be lower than the power coefficient of an individual's probability weighting function.

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Back to the St. Petersburg Paradox

In imperfectly discriminating contests, the contestants contribute effort to win a prize but the highest contributed effort does not necessarily secure a win. The contest success function (CSF) is the technology that translates an individual's effort into his or her probability of winning. This paper provides an axiomatization of CSF when there is the possibility of a draw (the sum of winning probabilities across all contestants is non-additive).

Pavlo R. Blavatskyy

Papers

A Stochastic Expected Utility Theory

Models of Stochastic Choice and Decision Theories: Why Both are Important for Analyzing Decisions

Stochastic expected utility theory

Back to the St. Petersburg Paradox

Contest Success Function with the Possibility of a Draw: Axiomation