Arrow's theorem, many agents, and invisible dictators☆
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Cited by (170)
The structure of two-valued coalitional strategy-proof social choice functions
2021, Journal of Mathematical EconomicsPreference aggregation and atoms in measures
2021, Journal of Mathematical EconomicsCitation Excerpt :A pioneering work by Kirman and Sondermann (1972) provides basic results for Arrovian social choice theory with a measure space of agents. Kirman and Sondermann (1972) consider another version of non-dictatorship, coalitional non-dictatorship, which requires a lower bound on the size of a decisive coalition, and show that in any atomless society, there exists no social welfare function that satisfies weak Pareto, independence of irrelevant alternatives, and coalitional non-dictatorship. In this paper, we examine a finitely additive measure (or mass), and allow it to be atomic.2
Superset-robust collective choice rules
2021, Mathematical Social SciencesAcyclicity, anonymity, and prefilters
2020, Journal of Mathematical EconomicsCitation Excerpt :We conclude this section with two results that apply to an infinite population. There is a quite substantial literature on infinite-population social welfare functions and transitive collective choice rules; see, for instance, Kirman and Sondermann (1972), Hansson (1976), Mihara (1997a, b), and Takayama and Yokotani (2017). As mentioned in the introduction, a fundamental observation is that, as soon as the finiteness requirement is no longer imposed, social welfare functions that satisfy Arrow’s axioms do exist.
ARROW'S THEOREM, ULTRAFILTERS, AND REVERSE MATHEMATICS
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Don Brown drew the attention of one of us to Fishburn's theorem [4]. He observed the fact that Fishburn's probability measures define free ultrafilters. In a later conversation Fishburn made the same observation. We are indebted to Werner Hildenbrand, Jerry Green and a referee for helpful comments on an earlier version of this paper.