Reduction of compound lotteries with objective probabilities: Theory and evidence

Abstract

The reduction of compound lotteries (ROCL) has assumed a central role in the evaluation of behavior towards risk and uncertainty. We present experimental evidence on its validity in the domain of objective probabilities. Our experiment explicitly recognizes the impact that the random lottery incentive mechanism payment procedure may have on preferences, and so we collect data using both "1-in-1" and "1-in-K" payment procedures, where K>1. We do not find violations of ROCL when subjects are presented with only one choice that is played for money. However, when individuals are presented with many choices and random lottery incentive mechanism is used to select one choice for payoff, we do find violations of ROCL. These results are supported by both non-parametric analysis of choice patterns, as well as structural estimation of latent preferences. We find evidence that the model that best describes behavior when subjects make only one choice is the Rank-Dependent Utility model. When subjects face many choices, their behavior is better characterized by our source-dependent version of the Rank-Dependent Utility model which can account for violations of ROCL. We conclude that payment protocols can create distortions in experimental tests of basic axioms of decision theory.

Temporal Stability, Cross-Validity, and External Validity of Risk Preferences Measures: Experimental Evidence from a UK Representative Sample

“…These choices were thus increasing in the variance of the outcomes and in the risk they represented, with 7 See for instance Conlisk (1989);Starmer and Sugden (1991);Wilcox (1993);Bernasconi (1994); Beattie and Loomes (1997); Cubitt et al (1998); Harrison et al (2002); Drehmann et al (2005); Harrison et al (2007b); Harrison and Rutström (2008). See Baltussen et al (2012), Harrison and Swarthout (2014), Cox et al (2015), Harrison et al (2015b), andMarch et al (2016) for some recent studies looking more closely at the random lottery incentive mechanism.…”

Experiments on Compound Risk in Relation to Simple Risk and to Ambiguity

“…Experimental evidence on these points is mixed but is generally supportive of RIS in practice. See Starmer and Sugden (1991) and Cubitt et al (1998) for supportive evidence and Harrison et al (2013) for a finding of some distortion. Wakker (2007) provides an informative discussion of the issue.…”

Ellsberg Re-Revisited: An Experiment Disentangling Model Uncertainty and Risk Aversion

“…engineers), compound risk reduction is compatible with ambiguity non-neutrality, suggesting that failure to reduce compound risk and ambiguity non-neutrality do not necessarily share the same behavioral grounds. In a recent study, Harrison et al (2015) specifically test the reduction of compound lotteries with objective probabilities both in a setup with multiple choices and a random incentive system, and in a setup with a unique choice. They find evidence of violation of reduction of compound lotteries (towards compound risk loving behaviors) in the first case, but not in the second.…”

“…Although we do not explicitly test any specific theory that might explain why compound risk may be associated with ambiguity, we try to shed light on this issue through an experimental setup where the compound lottery is extremely simple. If cognitive inability is at the basis of failures to reduce compound probabilities (Abdellaoui et al, 2015;Harrison et al, 2015), and aversion to compound lottery reflects a deficiency of the 'human intuitive statistician' (Budescu and Fischer, 2001), then by designing a compound risk situation that is very easily reducible, we partly rule out instances based on limited cognitive ability, and we expect subjects to effectively reduce compound risk if the probabilities of the two layers of uncertainty are objectively given.…”