The geometry of consumer preference aggregation

TL;DR

This paper introduces a new method for aggregating individual consumer preferences with homothetic preferences, simplifying the process to a weighted average in a transformed space, with applications in welfare analysis and market design.

Contribution

It develops a novel aggregation technique for homothetic preferences, characterizes preference domains, and explores indecomposable preferences, advancing understanding of aggregate consumer behavior.

Findings

Identifies aggregation-invariant preference domains

Characterizes aggregate preferences for common domains like linear and Leontief

Describes indecomposable preferences not arising from any non-trivial population

Abstract

We revisit a classical question of how individual consumer preferences and incomes shape aggregate behavior. We develop a method that applies to populations with homothetic preferences and reduces the hard problem of aggregation to simply computing a weighted average in the space of logarithmic expenditure functions. We apply the method to identify aggregation-invariant preference domains, characterize aggregate preferences from common domains like linear or Leontief, and describe indecomposable preferences that do not correspond to the aggregate behavior of any non-trivial population. Applications include robust welfare analysis, information design, discrete choice models, pseudo-market mechanisms, and preference identification.