The geometry of consumer preference aggregation

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.