Are preferences incomplete?An experimental study using flexible choices

Completeness, the most commonly assumed axiom in preference theory,has not received much attention from the experimental literature. Indeed,incomplete preferences model a cognitive phenomenon (an agent's inabilityto compare alternatives), and therefore cannot be directly revealed throughchoice behavior. Implementing a solution to this methodological issue re-cently proposed by Danan (2003), we build an experimental protocol in-volving choices among menus of lotteries, and reveal cognitive preferences'incompleteness by means of the concept of preference for flexibility. Ourexperimental protocol is designed to assess the descriptive validity of thecompleteness axiom, as well as to relate its possible violations to lotteries'riskiness. Two-thirds of the subjects whose choices reveal preferences inaccordance with the underlying theory exhibit a strictly positive measureof incompleteness. The observed average measure of incompleteness equalsapproximately 17 percent and it is significantly greater than 10 percent. Wedo not find a significant relationship between a lottery's riskiness and itscognitive comparability with certain payoffs.