Quantifying Inefficiency

TL;DR

This paper introduces an axiomatic social inefficiency measure based on vNM preferences, providing a unique quantification of inefficiency that does not rely on interpersonal comparisons, and applies it to analyze object allocation mechanisms.

Contribution

It defines a novel axiomatic social inefficiency function that assigns a unique inefficiency score to alternatives without external comparisons, and demonstrates its application to object allocation.

Findings

The inefficiency measure is uniquely defined by the axioms.

Applied to Random Serial Dictatorship, it yields an approximate efficiency result.

Provides a new tool for analyzing allocation mechanisms without interpersonal comparisons.

Abstract

We axiomatically define a cardinal social inefficiency function, which, given a set of alternatives and individuals' vNM preferences over the alternatives, assigns a unique number -- the social inefficiency -- to each alternative. These numbers -- and not only their order -- are uniquely defined by our axioms despite no exogenously given interpersonal comparison, outside option, or disagreement point. We interpret these numbers as per-capita losses in endogenously normalized utility. We apply our social inefficiency function to a setting in which interpersonal comparison is notoriously hard to justify -- object allocation without money -- leveraging techniques from computer science to prove an approximate-efficiency result for the Random Serial Dictatorship mechanism.