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Arrow's Theorem, Weglorz' Models and the Axiom of Choice
Author(s) -
Brunner Norbert,
Reiju Mihara H.
Publication year - 2000
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200008)46:3<335::aid-malq335>3.0.co;2-x
Subject(s) - ultrafilter , axiom of choice , arrow , social choice theory , mathematics , arrow's impossibility theorem , axiom , zermelo–fraenkel set theory , choice function , mathematical economics , constructive set theory , social welfare function , set (abstract data type) , function (biology) , set theory , discrete mathematics , welfare , computer science , economics , geometry , evolutionary biology , biology , market economy , programming language
Applying Weglorz' mode s of set theory without the axiom of choice, we investigate Arrow‐type social we fare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying “finite discrimination”, if and only if in Weglorz' mode there is a free ultrafilter on a set representing the individuals.