Abstract

Agent-based models of 'flocking' and 'schooling' have shown that a weighted average of neighbor velocities, with weights that decay gradually with distance, yields emergent collective motion. Weighted averaging thus offers a potential mechanism of self-organization that recruits an increasing, but self-limiting, number of individuals into collective motion. Previously, we identified and modeled such a 'soft metric' neighborhood of interaction in human crowds that decays exponentially to zero at a distance of 4-5m. Here we investigate the limits of weighted averaging in humans and find that it is surprisingly robust: pedestrians align with the mean heading direction in their neighborhood, despite high levels of noise and diverging motions in the crowd, as predicted by the model. In three Virtual Reality experiments, participants were immersed in a crowd of virtual humans in a mobile head-mounted display and were instructed to walk with the crowd. By perturbing the heading (walking direction) of virtual neighbors and measuring the participant's trajectory, we probed the limits of weighted averaging. (1) In the 'Noisy Neighbors' experiment, the neighbor headings were randomized (range 0-90°) about the crowd's mean direction (±10° or ±20°, left or right); (2) in the 'Splitting Crowd' experiment, the crowd split into two groups (heading difference = 10-40°) and the proportion of the crowd in one group was varied (50-84%); (3) in the 'Coherent Subgroup' experiment, a perturbed subgroup varied in its coherence (heading SD = 0-2°) about a mean direction (±10° or ±20°) within a noisy crowd (heading range = 180°), and the proportion of the crowd in the subgroup was varied. In each scenario, the results were predicted by the weighted averaging model, and attraction strength (turning rate) increased with the participant's deviation from the mean heading direction, not with group coherence. However, the results indicate that humans ignore highly discrepant headings (45-90°). These findings reveal that weighted averaging in humans is highly robust and generates a common heading direction that acts as a positive feedback to recruit more individuals into collective motion, in a self-reinforcing cascade. Therefore, this 'soft' metric neighborhood serves as a mechanism of self-organization in human crowds.

Highlights

  • Much like schools of herring and murmurations of starlings, groups of humans exhibit collective motion, whether a group of friends walking together down a sidewalk or large crowds in a shopping plaza or a mass protest

  • The results show that individuals are not attracted to more coherent neighbors, but to the mean heading in their neighborhood

  • It is clear that the mean response in the 10° turn condition and the 20° turn condition (M 20.30°, dark blue curve) are close to their respective crowd turn angles, and constant across noise conditions

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Summary

Introduction

Much like schools of herring and murmurations of starlings, groups of humans exhibit collective motion, whether a group of friends walking together down a sidewalk or large crowds in a shopping plaza or a mass protest. It is generally believed that such patterns of collective motion emerge via similar processes of selforganization, where local interactions between individuals give rise to patterns of global behavior [1, 2]. An understanding of these local interactions has two aspects: first, identifying the rules of engagement that govern how an individual responds to a neighbor, and second, characterizing the neighborhood of interaction over which these rules operate and how neighbor influences are combined. We focus instead on the alignment of velocity direction or heading, which is sufficient to generate collective motion [12, 13]

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