Eliciting Choice Correspondences A General Method and an Experimental Implementation

I introduce a general method for identifying choice correspondences experimentally, i.e., the sets of best alternatives of decision makers in each choice sets. Most of the revealed preference literature assumes that decision makers can choose sets. In contrast, most experiments force the choice of a single alternative in each choice set. In this paper, I allow decision makers to choose several alternatives, provide a small incentive for each alternative chosen, and then randomly select one for payment. I derive the conditions under which the method at least partially identifies the choice correspondence, by obtaining supersets and subsets for each choice set. I illustrate the method with an experiment, in which subjects chose between four paid tasks. I can retrieve the full choice correspondence for 26% of subjects and bind it for another 46%. Subjects chose sets of size 2 or larger 60% of the time, whereas only 3% of them always chose singletons. I then show that 46% of all observed choices can be rationalized by complete, reflexive and transitive preferences in my experiment, i.e., satisfy the Weak Axiom of Revealed Preferences – WARP hereafter. Weakening the classical model, incomplete preferences or just-noticeable difference preferences do not rationalize more choice correspondences. Going beyond WARP, however, I show that complete, reflexive and transitive preferences with menu-dependent choices rationalize 93% of observed choices. Having elicited choice correspondences allows me to conclude that indifference is widespread in the experiment. These results pave the way for exploring various behavioral models with a unified method.