Additive representations on a simplex

Wei zhi Qin, Hendrik Rommeswinkel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We characterize additive representations on subsets of product spaces with an empty interior such as simplexes and certain homeomorphisms thereof. Previously, all additive representation theorems only applied to spaces in which any coordinate can be changed without changing any of the other coordinates. We identify a novel preference condition that is necessary and sufficient for the existence of additive representations. Our results provide, for instance, a characterization of utilitarianism on the Pareto frontier of a cake division problem.

Original languageEnglish
Article number102769
JournalJournal of Mathematical Economics
Publication statusPublished - 2022 Dec
Externally publishedYes


  • Additive Separability
  • Preferences
  • Simplex
  • Utilitarianism
  • Utility representation

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics


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