Solidarity with respect to small changes in preferences in public good economies with single-peaked preferences

• Agents have single-peaked preferences over an interval representing the location or level of a public good.
• A new family of axioms parameterize a familiar solidarity axiom, welfare dominance under preference replacement.
• For each ϵ>0ϵ>0, ϵϵ-welfare dominance and efficiency characterize a family of target rules.

We study the problem of choosing a point on an interval when agents have single-peaked preferences. Our primary concern is solidarity: When the environment changes, agents should gain or lose together. “Welfare dominance under preference replacement” requires this conclusion when the preferences of one agent change. Instead of requiring solidarity for all possible changes in preferences, we introduce a parameterized solidarity property, “ϵ-welfare dominance”, which requires the conclusion of welfare dominance only for arbitrarily small changes in preferences. In this model, welfare dominance and efficiency characterize a class of “target” rules, each of which selects the efficient point nearest to its target (Thomson, 1993). Although our property is weaker than and distinct from welfare dominance, it also characterizes the target rules when combined with efficiency.