An Arrovian impossibility in combining ranking and evaluation

Abstract

In a world where voters not only rank the alternatives but also qualify them as "approved" or "disapproved", we observe that majoritarianism in preferences and majoritarianism in approvals are logically incompatible. We show that this observation generalises to the following result: every aggregation rule that respects unanimity and decomposes the aggregation of preferences and approvals is dictatorial. Our result implies an incompatibility between ordinal and evaluative approaches to social choice theory under two weak assumptions: respect for unanimity and independence of evaluation of each alternative. We describe possibilities when the latter assumption is relaxed. On the other hand, our impossibility generalises to the case where there are more than the two evaluative levels of "approved" and "disapproved". JEL Classifications: D71.

A family of distances for preference–approvals

“…They investigated a preferences aggregation model in the context of group decision-making based on the proposed axiomatic distance function. Kruger and Sanver (2021) investigated the compatibility between ordinal and evaluative approaches to social choice theory under two weak assumptions: respect for unanimity and independence of evaluation of each alternative. They claimed that there is an incompatibility between the two, and described some options whenever the second assumption is relaxed.…”