The Converse Consistency Principle in Bargaining

We investigate the implications of converse consistency in the context of bargaining. A solution is conversely consistent if whenever for some problem, a feasible alternative has the property that for all proper subgroups of the agents it involves, the solution chooses the restriction of the alternative to the subgroup for the associated reduced problem this subgroup faces, then the alternative should be the solution outcome for the problem. We present two alternative characterizations of the egalitarian solution based on converse consistency as well as either weak consistency or population monotonicity, in addition to other standard axioms of weak Pareto optimality, symmetry, and continuity. However, if we strengthen weak Pareto optimality to Pareto opti-mality, then various impossibility results are obtained. On the other hand, by weakening converse consistency to weak converse consistency, which applies the hypotheses of converse consistency only to the problem whose solution outcome is smooth, we can recover both Pareto optimality and scale invari-ance. In fact, we obtain a characterization of the Nash solution based on restricted converse consistency, as well as other axioms of Pareto optimality, symmetry, scale invariance, continuity, and dummy.

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