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

Abstract

We conduct experiments measuring individual behavior under compound risk, simple risk, and ambiguity. We focus on (1) treatment of compound risks relative to simple risks and (2) the relationship between compound risk attitudes and ambiguity attitudes. We find that compound risks are valued differently than corresponding reduced simple risks. These differences measure compound risk attitudes. These attitudes display more aversion as the reduced probability of the winning event increases. Like Halevy [Halevy Y (2007) Ellsberg revisited: An experimental study. Econometrica 75:503-536], we find an association between compound risk reduction and ambiguity neutrality. However, in contrast to the almost perfect identification in Halevy's data, we find a substantially weaker relation in both directions. First, a majority of our ambiguity-neutral subjects fail to reduce compound risk. Second, almost a quarter of our subjects who reduce compound risk are nonneutral to ambiguity. All of the latter come from the more quantitatively sophisticated part of our subject pool.Data, as supplemental material, are available at http://dx

An Experimental Test of the Anscombe-Aumann Monotonicity Axiom

“…For recent reviews of the experimental literature see Hey (2014); Trautmann and van de Kuilen (2015) 2 Also see Abdellaoui, Klibanoff, and Placido (2015).…”

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

“…Qualitatively similar results were also obtained by Dean and Ortoleva (2015) and by Armantier and Treich (2015), who show that not only was attitude to compound risk tightly associated to attitude towards ambiguity, but so was attitude towards complex risk. 17 Abdellaoui et al (2015) also find, in a setup close to Halevy's, an association between compound risk reduction and ambiguity neutrality. The association they find is however weaker than in Halevy's data.…”

“…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.…”

The effect of delay on risk tolerance and probability weights

“…We suggest that this result is caused by lack of tolerance for conjunction of two types of uncertainty expressed by two different discounting processes: time discounting and uncertainty discounting. This can be considered analogous to compound risk aversion: prospects comprising more sources of uncertainty look less attractive than those comprising only one source of uncertainty (Dillenberger, 2001;Abdellaoui et al, 2015). There is also an alternative interpretation: lack of tolerance for conjunction of time discounting and uncertainty discounting could be caused by negative affect associated with the prolonged state of uncertainty -the delayed state of uncertainty could be extremely aversive.…”

“…Contrary to this axiom, research shows that when choosing between equivalent lotteries people prefer one-stage over multi-stage lotteries (Budescu & Fischer, 2001;Halevy, 2007). Dillenberger (2001) and Abdellaoui, Klibanoff, and Placido (2015) even introduced the concept of compound risk aversion, meaning that the decision maker's certainty equivalent for a compound lottery is below the certainty equivalent for a simple lottery. Spears (2013) showed that some people prefer simple over compound lotteries even when the simple lotteries offer lower expected value.…”