“Randomized dictatorship,” one of the simplest ways to solve bargaining situations, works as follows: a fair coin toss determines the “dictator”—the player to be given his first-best payoff. The two major bargaining solutions, that of Nash (Econometrica 18:155–162, <CitationRef CitationID="CR8">1950</CitationRef>) and that of Kalai and Smorodinsky (Econometrica, 43:513–518, <CitationRef CitationID="CR5">1975</CitationRef>), Pareto-dominate this process (in the ex ante sense). However, whereas the existing literature offers axiomatizations of the Nash solution in which this ex ante domination plays a central role (Moulin, Le choix social utilitariste, Ecole Polytechnique Discussion Paper, <CitationRef CitationID="CR6">1983</CitationRef> ; de Clippel, Social Choice and Welfare, 29:201–210, <CitationRef CitationID="CR4">2007</CitationRef>), it does not provide an analogous result for Kalai–Smorodinsky. This paper fills in this gap: a characterization of the latter is obtained by combining the aforementioned domination with three additional axioms: Pareto optimality, individual monotonicity, and a weakened version of the Perles–Maschler (International Journal of Game Theory, 10:163–193, <CitationRef CitationID="CR9">1981</CitationRef>) super additivity axiom. Copyright Springer Science+Business Media New York 2014
