Partial Ambiguity

Abstract

We extend Ellsberg's two‐urn paradox and propose three symmetric forms of partial ambiguity by limiting the possible compositions in a deck of 100 red and black cards in three ways. Interval ambiguity involves a symmetric range of 50 − n to 50 + n red cards. Complementarily, disjoint ambiguity arises from two nonintersecting intervals of 0 to n and 100 − n to 100 red cards. Two‐point ambiguity involves n or 100 − n red cards. We investigate experimentally attitudes towards partial ambiguity and the corresponding compound lotteries in which the possible compositions are drawn with equal objective probabilities. This yields three key findings: distinct attitudes towards the three forms of partial ambiguity, significant association across attitudes towards partial ambiguity and compound risk, and source preference between two‐point ambiguity and two‐point compound risk. Our findings help discriminate among models of ambiguity in the literature.

Ambiguity preferences for health

“…Cubitt et al (2017) find that the smooth ambiguity model explains their subjects' ambiguity preferences better than α-maxmin, an SDW model. Chew et al (2017) interpret their data as supporting the model of Ergin and Gul (2009), an SDU model. On the other hand, the data in Baillon and Bleichrodt (2015) are most consistent with two SDW models, prospect theory and, to a lesser extent, α-maxmin.…”

“…A popular SDW model is prospect theory (Kahneman & Tversky, 1979;Tversky & Kahneman, 1992). The empirical literature is divided as to which of these models best describes people's ambiguity preferences (Baillon & Bleichrodt, 2015;Cubitt et al, 2017;Chew, Miao, & Zhong, 2017). Cubitt et al (2017) find that the smooth ambiguity model explains their subjects' ambiguity preferences better than α-maxmin, an SDW model.…”

The value of a statistical life under changes in ambiguity

“…The empirical literature gives no clear answer which ambiguity model best describes people's preferences. While the results in Cubitt et al (forthcoming) are consistent with the smooth model, Baillon and Bleichrodt (2015) and Chew et al (2017) observed that models like Choquet expected utility (Schmeidler 1989) and α-maxmin (Ghirardato et al 2004) could better explain their data. In this section we explore the robustness of our results under the neo-additive model of Chateauneuf et al (2007).…”

Ambiguity and excuse-driven behavior in charitable giving

“…Under "partial ambiguity", the probability is defined in the interval [0.25, 0.75], reducing the interval size by half. Two levels of ambiguity are implemented because ambiguity aversion has been shown to increase with the size of the probability interval (Chew et al, 2017). This variation allows us to test whether this behavioral difference also exists for excuse-driven behavior.…”