Measuring Social Influence with Networked Synthetic Control

TL;DR

Measuring social influence is challenging due to counterfactuals; this paper introduces Social Value (SV), a networked synthetic-control metric that attributes influence by predicting an outcome with and without social inputs and distributing the resulting delta across neighbors. The approach unifies predictive modeling (linear, interaction, and ensemble) with a network-distribution step, formalized as $\Delta y(j)=F(X,S)-F(X,0)$ and $SV(i)=\sum_{j\in neigh(i)} w_{i,j} \frac{\Delta y(j)}{deg(j)}$, with $SV$ expressed as $\Vec{SV}=\mathbf{A}\times\Vec{\Delta y}\odot\Vec{S^{-1}}$. Theoretical results show SV reduces to simple forms under linear models, incorporates neighbor covariates under interactions, and decomposes cleanly for ensembles; simulations on lattice, scale-free, and random graphs illustrate how network structure and the generalized friendship paradox govern SV distributions and the relation between a node and its neighbors. The work offers a practical, interpretable method for quantifying individual influence in networks, with implications for policy, online behavior, and political communication, by linking counterfactual modeling with local network dynamics.

Abstract

Measuring social influence is difficult due to the lack of counter-factuals and comparisons. By combining machine learning-based modeling and network science, we present general properties of social value, a recent measure for social influence using synthetic control applicable to political behavior. Social value diverges from centrality measures on in that it relies on an external regressor to predict an output variable of interest, generates a synthetic measure of influence, then distributes individual contribution based on a social network. Through theoretical derivations, we show the properties of SV under linear regression with and without interaction, across lattice networks, power-law networks, and random graphs. A reduction in computation can be achieved for any ensemble model. Through simulation, we find that the generalized friendship paradox holds -- that in certain situations, your friends have on average more influence than you do.

Figures (2)

• Figure 1: Social Value distributions under a) linear models and b) linear models with interaction.
• Figure 2: Heat map for social value by varying the coefficient strength $\beta_S$ and correlation $c$ between asocial co-variates and degree. Results are shown for the scale-free graph on the top row, with the mean SV (a), standard deviation of SV (b), and the friendship paradox generalized to SV in (c); for the random graph, the mean SV (d), standard deviation of SV (e), and GFP of SV in (f).