On mechanisms eliciting ordinal preferences

Abstract

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 (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.

Random assignments and outside options

“…However, the preference for mechanisms eliciting cardinal preferences is not so clear-cut. A recent paper by Carroll (2018) is most related to ours. Carroll elaborates on the literature of robust mechanism design (see for instance the seminal paper by Bergemann and Morris, 2005) applied to Social Choice Correspondences.…”

“…We thank a referee and the associate editor for pointing this simpli…cation of the model 7. In what follows, 1 jSj+1 is a vector of ones with dimension jSj + 1 8. In an extreme case in which the …nal assignment could be enforced and no adaptation were allowed, our results (Lemma 1 and Theorem 1) would still follow.…”

A revelation principle for obviously strategy-proof implementation

“…In particular, we prove that if a stochastic rule has an OSP-implementation, then it is ordinal, and moreover has a round table implementation where agents make public announcements simply about their rankings of deterministic outcomes (Theorem 4). Whereas the justi-fication for ordinal mechanisms provided by Carroll (2017) relies on interdependence of agents' preferences over lotteries, ours does not due to our stronger solution concept.…”

“…In this section, we state a result inspired by a recent paper (Carroll, 2017), who seeks a justification for stochastic rules that elicit only ordinal information from the agents about their preferences over outcomes.…”

“…The proof is in Appendix F. In this sense, obvious strategy-proofness provides a foundation for ordinal mechanisms. This observation was inspired by Carroll (2017), who provides a foundation involving the interdependence of the agents' preferences over lotteries. The alternative foundation offered here does not rely on interdependence as it involves a stronger solution concept.…”