On Mechanisms Eliciting Ordinal Preferences

When is a mechanism designer justified in only asking for ordinal information about preferences? Simple examples show that, even if the planner’s goal (expressed by a social choice correspondence, or SCC) depends only on ordinal information, eliciting cardinal information may help with incentives. However, if agents may be uncertain about their own cardinal preferences, then a strong robustness requirement can justify the focus on ordinal mechanisms. Specifically, when agents’ preferences over pure outcomes are strict, if a planner is able to implement an SCC (in ex-post equilibrium) using a mechanism that is robust to interdependence of arbitrary form in cardinal preferences, then there must exist such a mechanism that elicits only ordinal preferences. The strictness assumption can be dropped if we further allow the possibility of non-expected-utility preferences. Thanks to (in random order) Juuso Toikka, Alex Wolitzky, Muhamet Yildiz, Yuichiro Kamada, Bengt Holmström, and Daron Acemoglu, and especially to Parag Pathak, for helpful discussions and advice. Suggestions from co-editor Thomas Mariotti and three referees also improved the paper. Dan Walton provided valuable research assistance.