Document Type

Preprint

Publication Date

10-1-2023

Journal / Book Title

Annals of Pure and Applied Logic

Abstract

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.

DOI

10.1016/j.apal.2023.103302

Published Citation

Dubey, Ram Sewak and Laguzzi, Giorgio, Social welfare relations and irregular sets (April 26, 2024). Annals of Pure and Applied Logic, Volume 174, Issue 9, 2023 103302, ISSN 0168-0072, https://doi.org/10.1016/j.apal.2023.103302. (https://www.sciencedirect.com/science/article/pii/S0168007223000593) , Available at SSRN: https://ssrn.com/abstract=3476963 or http://dx.doi.org/10.2139/ssrn.3476963

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