Abstract
A family of solutions to the bargaining problem with a variable population, generalizing the Egalitarian solution, is introduced under the name of Truncated Egalitarian solutions. A Truncated Egalitarian solution solves small problems at thier Egalitarian outcome and larger problems at some fixed and therefore non-optimal point, violations of optimality being more severe for large than for small groups. Any solution satisfying Symmetry, Independence of Irrelevant Alternatives, Continuity and Monotonicity (when the claims of more agents have to be accomodated, all agents should sacrifice) coincides with a Truncated Egalitarian solution except perhaps when only two agents are involved, in which case utility substitutions are possible in some limited range.
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