The study of the normative and positive theory of choice under uncertainty has made major advances through thought experiments often referred to as paradoxes: the St. Petersburg paradox, the Allais paradox, the Ellsberg paradox, and the Rabin paradox. Machina proposes a new thought experiment which posits a choice between two acts that have three outcomes. As in the Ellsberg paradox there are three events, but while the Ellsberg paradox has two (monetary) outcomes in Machina there are three. Machina shows that four prominent theories of ambiguity aversion predict indifference between the acts. Introspection, however, suggests that many people might very well strictly prefer one act over the other. This paper makes four contributions: first, to our knowledge, it is the first to experimentally implement the Machina thought experiment. Second, we employ a novel method to simultaneously elicit the certainty equivalent of an embedded lottery. Third, our results—across three experiments—indicate non-indifference, which rejects earlier theories of ambiguity aversion, but is consistent with a newer one, which we apply to explain our results. Fourth, we show that independence is a sufficient condition for indifference in the Machina paradox, and thereby explains why so many models predict indifference.
Ellsberg paradox; Machina paradox; uncertainty aversion; independence axiom;
- D81: Criteria for Decision-Making under Risk and Uncertainty
TSE Working Paper, n. 16-717, October 2016