A characterization for procedural choice based on dichotomous preferences over criteria

Abstract

Many lessons for procedural choice have been provided by axiomatic studies of decision procedures. However, there appears to be a gap between these axiomatic studies and the actual determination of appropriate procedures, as an axiomatic characterization does not directly answer which axiom should be appropriate—particularly when there is no agreement on the relative desirability of criteria. The present study proposes a formal model of procedural choice based on preferences over criteria (PCBPC). Specifically, we focus on the aggregation rule that maps a dichotomous preference profile over criteria for decision procedures to a nonempty set of decision procedures. We prove that the counting rule, which chooses the decision procedures with greatest supports, is the unique aggregation rule that satisfies anonymity (A), neutrality (N), strict monotonicity (SM), and partition consistency (PC), where PC is proposed based on the idea that representations of equivalent criteria in different ways should not affect the results. Two distinct standpoints for PCBPC are highlighted: one is to regard criteria as atomic, i.e., inseparable, objects and the other as composite, i.e., separable, objects. The difference between them is made explicit with two impossibility theorems showing the inconsistency between unanimity in the former standpoint and A (or PC) in the latter standpoint.