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On Strongly-equitable Social Welfare Orders Without the Axiom of Choice
- Publication Year :
- 2024
-
Abstract
- Social welfare orders seek to combine the disparate preferences of an infinite sequence of generations into a single, societal preference order in some reasonably-equitable way. In [2] Dubey and Laguzzi study a type of social welfare order which they call SEA, for strongly equitable and (finitely) anonymous. They prove that the existence of a SEA order implies the existence of a set of reals which does not have the Baire property, and observe that a nonprincipal ultrafilter on $\mathbb{N}$ can be used to construct a SEA order. Questions arising in their work include whether the existence of a SEA order implies the existence of either a set of real numbers which is not Lebesgue-measurable or of a nonprincipal ultrafilter on $\mathbb{N}$. We answer both these questions, the solution to the second using the techniques of geometric set theory as set out by Larson and Zapletal in [11]. The outcome is that the existence of a SEA order does imply the existence of a set of reals which is not Lebesgue-measurable, and does not imply the existence of a nonprincipal ultrafilter on $\mathbb{N}$.<br />Comment: 15 pages; comments welcome
- Subjects :
- Mathematics - Logic
03E05, 03E75, 91B15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.08684
- Document Type :
- Working Paper