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, 2007a,b). 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, 1983a,b) applies to the arrival and departure of agents, while replacement-domination (Moulin,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, 2004), and with Pareto-efficiency if and only if the attribute space is a tree. Each of these combinations characterizes unanimity.