Egalitarianism, utilitarianism, and the Nash bargaining solution
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A bargaining solution satisfies egalitarian–utilitarian monotonicity (EUM) if the following holds under feasible-set-expansion: a decrease in the value of the Rawlsian (resp. utilitarian) objective is accompanied by an increase in the value of the utilitarian (resp. Rawlsian) objective. A bargaining solution is welfarist if it maximizes a symmetric and strictly concave social welfare function. Every 2-person welfarist solution satisfies EUM, but for \(n\ge 3\) every n-person welfarist solution violates it. In the presence of other standard axioms, EUM characterizes the Nash solution in the 2-person case, but leads to impossibility in the n-person case.
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