Experiments that elicit preferences usually presume completeness, one of the most contested axioms of choice theory. I study incentive compatibility in experiments that let subjects report incomplete preferences. To tell incomparability apart from indifference, I attach a sure monetary payment to each option and require incomparability to survive small changes in that payment. The frontier of incentive compatibility under incomplete preferences is comparable-side strict incentive compatibility: subjects have a strict incentive to report truthfully when they can compare two options, and only a weak incentive when they cannot. Reported incomparability is therefore a conservative measure that never overstates incompleteness. I construct a class of mechanisms that attain this frontier and apply to any domain. In a laboratory experiment, these mechanisms also prove behaviourally incentive compatible.

Status quo bias is one of the leading robust behaviors that challenge standard economic modeling, but its source has been debated in theoretical and experimental studies. We provide experimental evidence that accounting for incomplete preferences is crucial in diagnosing SQB. We develop an identification strategy that bounds the behavior of a very general class of complete preferences and uses violations of these bounds as indication of incomparability. Implementing this strategy in a laboratory experiment, we find that incomplete preferences are widespread, with roughly one third of subjects exhibiting incomparability. These subjects are significantly more likely to retain the status quo when facing incomparable alternatives, and display substantially higher status quo bias than subjects whose choices are consistent with complete preferences. Furthermore, we demonstrate that ignoring preference incompleteness is empirically consequential: once subjects with incomplete preferences are excluded, the evidence against the Coase Theorem is no longer robust, and the case for the Endowment Effect largely disappears.