Unanimity in attribute-based preference domains

We provide several characterizations of unanimity decision rules, in a public choice model where preferences are constrained by attributes possessed by the alternatives (Nehring and Puppe, Games Econ Behavior 59:132-153, 2007a; Nehring and Puppe, J Econ Theory 135:269-305, 2007b). Solidarity conditions require that when some parameters of the economy change, the agents whose parameters are kept fixed either all weakly lose or they all weakly win. Population-monotonicity (Thomson, Math Oper Res 8:319-326, 1983a; Thomson, J Econ Theory 31:211-226, 1983b) applies to the arrival and departure of agents, while replacement-domination (Moulin, Q J Econ 102:769-783, 1987) applies to changes in preferences. We show that either solidarity property is compatible with voter-sovereignty and strategy-proofness if and only if the attribute space is quasi-median (Nehring, Social aggregation without veto, Mimeo, 2004), and with Pareto-efficiency if and only if the attribute space is a tree. Each of these combinations characterizes unanimity.