Arrow proved that a social welfare function with transitive values cannot simultaneously satisfy independence of irrelevant alternatives, the Pareto criterion, and non-dictatorship. We use asymptotic density to determine bounds on the trade-off between violations of the Pareto criterion and violations of non-dictatorship when the set X of outcomes is countably infinite.
- Asymptotic density
ASJC Scopus subject areas
- Sociology and Political Science
- Social Sciences(all)
- Statistics, Probability and Uncertainty