<Para ID="Par1">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, <CitationRef CitationID="CR27">2007a</CitationRef>; Nehring and Puppe, J Econ Theory 135:269–305, <CitationRef CitationID="CR28">2007b</CitationRef>). 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, <CitationRef CitationID="CR31">1983a</CitationRef>; Thomson, J Econ Theory 31:211–226, <CitationRef CitationID="CR32">1983b</CitationRef>) applies to the arrival and departure of agents, while replacement-domination (Moulin, Q J Econ 102:769–783, <CitationRef CitationID="CR23">1987</CitationRef>) 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, <CitationRef CitationID="CR25">2004</CitationRef>), and with Pareto-efficiency if and only if the attribute space is a tree. Each of these combinations characterizes unanimity. Copyright Springer-Verlag Berlin Heidelberg 2015
