Experimental Payment Protocols and the Bipolar Behaviorist
نویسندگان
چکیده
If someone claims that individuals behave as if they violate the independence axiom when making decisions over simple lotteries, it is invariably on the basis of experiments and theories that must assume the independence axiom through the use of the random lottery incentive mechanism. We refer to someone who holds this view as a Bipolar Behaviorist, exhibiting pessimism about the axiom when it comes to characterizing how individuals directly evaluate two lotteries in a binary choice task, but optimism about the axiom when it comes to characterizing how individuals evaluate multiple lotteries that make up the incentive structure for a multiple-task experiment. We reject the hypothesis about subject behavior underlying this stance: we find that preferences estimated with a model that assumes violations of the independence axiom are significantly affected when one elicits choices with procedures that require the independence assumption, as compared to choices elicited with procedures that do not require the assumption. The upshot is that one cannot consistently estimate popular models that relax the independence axiom using data from experiments that assume the validity of the random lottery incentive mechanism. Department of Risk Management & Insurance and Center for the Economic Analysis of Risk, † Robinson College of Business, Georgia State University, USA (Harrison); and Department of Economics, Andrew Young School of Policy Studies, Georgia State University, USA (Swarthout). E-mail contacts: [email protected] and [email protected]. We are grateful to Jim Cox, Jimmy Martínez, John Quiggin, Elisabet Rutström, Vjollca Sadiraj, Ulrich Schmidt, Uzi Segal and Nathaniel Wilcox for helpful discussions. The independence axiom plays a central role in most formal statements of expected utility theory (EUT), as well as popular alternative models of decision-making under objective or subjective risk. One such alternative is rank-dependent utility (RDU) theory, which assumes that the independence axiom is invalid in a certain way. The axiom also plays a central role in virtually every experiment used to characterize the way in which risk preferences deviate from EUT, through the use of the random lottery incentive mechanism (RLIM). For example, if someone claims that individuals behave as if they “probability weight” outcomes, and hence violate the independence axiom (IA), it is almost always on the basis of experiments and theories that assume the IA if the incentives are to be taken seriously. But there is an obvious inconsistency with saying that individuals behave as if they violate the IA on the basis of evidence collected under the maintained assumption that the axiom is magically valid. This inconsistency has long bothered theorists confronted with experimental data, and there have been responses from theorists and experimentalists. The primary theoretical response has been to argue that there is a way to write out a model of decision-making under risk that allows one to relax the IA but to still allow risk preferences to deviate from EUT predictions and for RLIM to be valid. In effect, to argue an existence proof: even though the inconsistency is real for the most popular alternatives to EUT, there exists a formal alternative to EUT where there is no inconsistency. We discuss this theoretical response later in section 5. The primary experimental response has been to develop some direct tests and some ingenious designs intended to trap the IA under some circumstances. But these direct and indirect experimental tests of the IA have been inconclusive. This is 1 frustrating: either the axiom applies or it does not. The uneasy state of the literature has evolved to assuming the axiom for the purposes of making the payment protocol of an experiment valid, but rejecting it when characterizing the risk preferences Cubitt, Starmer and Sugden [1991; p. 119] explain the logic of the indirect tests: “Our strategy is to take 1 as the maintained hypothesis that the random lottery design is unbiased. We test this hypothesis in situations in which we have a priori expectations that individuals’ preferences violate the independence axiom in ways which, if the contamination hypothesis were true, would induce observable biases.” All studies using indirect tests of this kind, which of course rest on premisses that might be false, also report direct tests.
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