Wiser than the Wisest of Crowds: The Asch Effect and Polarization Revisited

Abstract

In 1907, Sir Francis Galton independently requested 787 villagers to estimate the weight of an ox. Although none of them guessed the exact weight, the average estimate was remarkably accurate. This phenomenon is also known as wisdom of crowds. In a clever experiment, Asch employed actors to demonstrate the human tendency to conform to others’ opinions. The question we ask is the following: what would Sir Francis Galton have observed if Asch had interfered by employing actors? Would the wisdom of crowds become even wiser or not? The problem becomes intriguing when considering the inter-connectedness of the villagers. This is the central theme of this work. Specifically, we examine a scenario where n agents are interconnected and influence each other. The average of their innate opinions provides an estimator of a certain quality for an unknown quantity $\theta $ θ . How can one improve or reduce the quality of the original estimator in terms of the mean squared error (MSE) by utilizing Asch’s strategy of hiring a few stooges? We present a new formulation of this problem, assuming that the nodes adjust their opinions according to the Friedkin-Johnsen opinion dynamics with susceptibility parameters [ 2 ]. We demonstrate that selecting k stooges for both maximizing and minimizing the MSE is NP-hard. Additionally, we demonstrate that our formulation is closely related to either maximizing or minimizing polarization [ 39 ] and present an NP-hardness proof. We propose a greedy heuristic that we implement efficiently, enabling it to scale to large networks. We test our algorithm on various synthetic and real-world datasets collected from Twitter against various baselines. Although the MSE and polarization objectives differ, we find in practice that maximizing polarization often yields solutions that are nearly optimal for minimizing the wisdom of crowds in terms of MSE. Lastly, our analysis of real-world data reveals that even a small number of stooges can significantly influence the conversation surrounding the controversial topic of the war in Ukraine, resulting in a relative increase of the MSE of 207.80% (maximization) or a decrease of 50.62% (minimization).