Theoretical Economics 13 (2018), 1275–1318

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.

Keywords: Cardinal extension, ex-post implementation, interdependence, ordinal mechanism, robust mechanism design

JEL classification: D81, D82