Social welfare relations and irregular sets

Ram Sewak Dubey, Giorgio Laguzzi

Research output: Contribution to journalArticlepeer-review


Social welfare relations satisfying Pareto and equity principles on infinite utility streams have revealed a non-constructive nature, specifically by showing that in general they imply the existence of non-Ramsey sets and non-Lebesgue measurable sets. In [4, Problem 11.14], the authors ask whether such a connection holds with non-Baire sets as well. In this paper we answer such a question showing that several versions of Pareto principles acting on different utility domains imply the existence of non-Baire sets. Furthermore, we analyze in more details the needed fragments of AC and we start a systematic investigation of a social welfare diagram in a similar fashion done in the past decades concerning cardinal invariants and regularity properties of the reals. In doing that we use tools from forcing theory, such as specific tree-forcings (in particular variants of Silver and Mathias forcings) and Shelah's amalgamation.

Original languageEnglish
Article number103302
JournalAnnals of Pure and Applied Logic
Issue number9
StatePublished - 1 Oct 2023


  • Descriptive set theory
  • Forcing
  • Infinite utility streams
  • Social welfare relations


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