Solidarity and Unanimity in Attribute-Based Domains

We study the implications of population-monotonicity (Thomson, 1983) and replacement-domination (Moulin, 1987) in the class of attributebased preference domains (Nehring and Puppe 2002 a,b). Both conditions require that when some parameters of the economy change, the agents whose parameters are kept …xed, should either all weakly lose or all weakly win. Population-monotonicity applies to the arrival and departure of agents, while replacement-domination applies to changes in preferences. Using results by Nehring and Puppe (2002b) on strategyproof and onto choice functions, we characterize on attribute-based preference domains the unanimity rules as the class of choice functions that satisfy either condition of solidarity and are in addition strategyproof and onto. We also characterize the attribute-based domains on which these properties are compatible. Next, we characterize the class of tree-structured domains as the ones where population-monotonicity and Pareto-e¢ ciency are compatible. Unanimity rules are the rules that satisfy these conditions on these domains. Department of Managerial Economics and Decision Sciences and Department of Management and Strategy, Kellogg School of Management, Northwestern University, 2001 Sheridan road, Evanston IL 60208. I bene…ted from very helpful conversations with James Schummer and William Thomson and from interesting correspondance with Klaus Nehring and Clemens Puppe.