Summary: The objective of this paper is to describe various applications of a requirement of solidarity pertaining to situations in which the preferences of some of the agents may change. It says that the welfares of all agents whose preferences are fixed should be affected in the same direction: they should all weakly gain, or they should all weakly lose. We show how this condition, which we name “welfare-domination under preference-replacement”, can help in evaluating allocation rules. We discuss it in several contexts: private good allocation in classical economies, public good decision, binary choice with quasi-linear preferences, economies with indivisible goods, economies with single-peaked preferences, both in the private good case and in the public good case, and economies with time. For some of these models the implications of the property are well understood. For others, we state a number of open problems.