Maximizing Truth Learning in a Social Network is NP-hard

TL;DR

This paper proves that finding an optimal prediction order in a social network to maximize correct ground truth predictions is NP-hard, even under simple models, and that approximating this is also computationally hard.

Contribution

It establishes the NP-hardness of optimizing agent prediction order in social networks for both Bayesian and majority rule models.

Findings

Optimal ordering problem is NP-hard.

Approximation of the optimal ordering is also NP-hard.

Results hold for both Bayesian and simple majority models.

Abstract

Sequential learning models situations where agents predict a ground truth in sequence, by using their private, noisy measurements, and the predictions of agents who came earlier in the sequence. We study sequential learning in a social network, where agents only see the actions of the previous agents in their own neighborhood. The fraction of agents who predict the ground truth correctly depends heavily on both the network topology and the ordering in which the predictions are made. A natural question is to find an ordering, with a given network, to maximize the (expected) number of agents who predict the ground truth correctly. In this paper, we show that it is in fact NP-hard to answer this question for a general network, with both the Bayesian learning model and a simple majority rule model. Finally, we show that even approximating the answer is hard.