Abstract
We introduce the notion of preference systems ⟨≿,{≿r} r∈X⟩ where ≿ is the classical (unreferenced) preference over X, and ≿r is a referenced preference that, adopting r ∈ X as a reference point, reevaluates the alternatives deemed better than r under ≿. Contrary to the recent literature with dictatorial rules of reference aggregation, we allow for their joint effect through plurality rule and focus on two behaviors: one where ≿r contracts ≿, and one where ≿r expands ≿. Interestingly, we show that the two are characterized as (only) one-step inductive generalizations of the weak axiom of revealed preference. Hence, akin to the classical theory where x ≿ y ⇔ x ∈ c{x,y}, referenced preference are revealed by x ≿ry ⇔ x ∈ c{x,y,r}. We assess the welfare implication of the two behaviors where we argue that the former does not suffer welfare loss, while the best reference point (w.r.t to ≿) is the upper bound to the latter’s loss.
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