Aspiration-Weighted Influence

TL;DR

This paper introduces the Aspiration-Weighted Luce Model (AWLM) to analyze directed social influence, accounting for influencers displaying richer choice menus than followers, with implications for understanding influence attenuation and empirical measurement.

Contribution

The paper develops the AWLM, a novel model that captures how aspirational influences affect decision-making and provides a method for empirical identification of influence strength.

Findings

Model characterizes influence attenuation due to aspirational exposure.

Provides axiomatic foundations for the influence model.

Offers testable restrictions for empirical application.

Abstract

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.