The solidarity axiom for quasi-linear social choice problems

Recently, Moulin gave various axiomatic characterizations of solutions to quasi-linear social choice problems. He used a consistency axiom, which relates solutions for societies of different sizes, in addition to some basic axioms. In this paper, we introduce another axiom relating solutions for societies of different sizes, called the Solidarity Axiom. This axiom demands that when additional agents enter the scene, all of the original agents be affected in the same direction, i.e., all of them gain or all of them lose. Our main result is a complete characterization of solutions satisfying the solidarity axiom, in addition to Pareto optimality, anonymity and two normalization axioms. All solutions satisfying these five axioms are in the egalitarian spirit; each solution assigns to every agent an equal share of the surplus over some reference level, but uses a different method to compute the reference level. Then, using additional milder axioms, we give further characterization results concerning various subfamilies.I am extremely grateful to Professor William Thomson for his numerous comments which have considerably improved the exposition of the paper. I would like to thank Professor Hervé Moulin for helpful discussions and insightful comments. The comments from an editor and a referee of this journal are also gratefully acknowledged. I retain, however, full responsibility for any shortcommings