Aspiration-Weighted Influence

We study directed social influence when an influencer chooses from a richer menu than a constrained follower (decision maker, the DM). The DM selects from a feasible set, while the influencer displays a distribution over a superset that includes infeasible alternatives. We propose the Aspiration-Weighted Luce Model (AWLM): the DM forms a convex combination of her idiosyncratic Luce preferences within the feasible set and the influencer’s distribution, then renormalizes this attempt target onto the feasible set. This renormalization generates an aspirational dampening effect: holding the influencer’s within-feasible composition fixed and shifting exposure toward infeasible alternatives attenuates influence on feasible choices. We provide an axiomatic characterization based on proportional responses to shifts in feasible exposure and a unit-slope leverage restriction across different levels of feasible share. The model allows for point identification of influence strength and idiosyncratic preferences from two exposure regimes, yielding testable overidentifying restrictions for empirical application.

💡 Research Summary

The paper investigates a setting in which an influencer can showcase a richer menu of alternatives than a constrained decision‑maker (DM). The DM can only choose from a feasible set S, whereas the influencer’s observed behavior is drawn from a superset I⊇S that contains infeasible (aspirational) alternatives. The authors introduce the Aspiration‑Weighted Luce Model (AWLM) to capture how exposure to such aspirational content reshapes the DM’s stochastic choice over the feasible set.

In the AWLM the DM possesses idiosyncratic Luce weights u(x)>0, generating the baseline choice probabilities p₀(x|S)=u(x)/∑_{y∈S}u(y). The influencer’s exposure distribution is q∈Δ(I). A scalar α∈