A Class of Practical and Acceptable Social Welfare Orderings That Satisfy the Principles of Aggregation and Non-Aggregation: Reexamination of the Tyrannies of Aggregation and Non-Aggregation

TL;DR

This paper reexamines the impossibility results related to aggregation principles in social choice, proposing new compatible principles and characterizing social welfare orderings that balance aggregation and non-aggregation.

Contribution

It introduces two new aggregation principles, analyzes their compatibility with non-aggregation, and characterizes a new class of social welfare orderings that satisfy both principles.

Findings

Quantitative aggregation and minimal non-aggregation are incompatible.

Ratio aggregation and minimal non-aggregation are compatible.

A new class of social welfare orderings offers practical advantages.

Abstract

This paper revisits impossibility results on the tyrannies of aggregation and non-aggregation. I propose two aggregation principles (quantitative aggregation and ratio aggregation) and investigate theoretical implications. As a result, I show that quantitative aggregation and minimal non-aggregation are incompatible while ratio aggregation and minimal non-aggregation are compatible under the assumption of standard axioms in social choice theory. Furthermore, this study provides a new characterization of the leximin rule by using replication invariance and the strong version of non-aggregation. Finally, I propose a class of practical and acceptable social welfare orderings that satisfy the principles of aggregation and non-aggregation, which has various advantages over the standard rank-discounted generalized utilitarianism.