Threshold Models of Collective Behavior

TLDR

Models of collective behavior with binary choices depend on thresholds of others’ decisions, where the net benefit of an action exceeds the cost once enough peers adopt it. The authors propose applying these threshold models to phenomena such as riots, innovation diffusion, rumors, strikes, voting, and migration, while addressing measurement, falsification, and verification issues. Beginning with a frequency distribution of thresholds, the models calculate the equilibrium number choosing each decision. Equilibrium stability depends sensitively on the exact threshold distribution, and groups with similar average preferences can produce markedly different outcomes, making it hazardous to infer individual dispositions from aggregate results or to assume norm‑driven behavior.

Abstract

Models of collective behavior are developed for situations where actors have two alternatives and the costs and/or benefits of each depend on how many other actors choose which alternative. The key concept is that of "threshold": the number or proportion of others who must make one decision before a given actor does so; this is the point where net benefits begin to exceed net costs for that particular actor. Beginning with a frequency distribution of thresholds, the models allow calculation of the ultimate or "equilibrium" number making each decision. The stability of equilibrium results against various possible changes in threshold distributions is considered. Stress is placed on the importance of exact distributions distributions for outcomes. Groups with similar average preferences may generate very different results; hence it is hazardous to infer individual dispositions from aggregate outcomes or to assume that behavior was directed by ultimately agreed-upon norms. Suggested applications are to riot behavior, innovation and rumor diffusion, strikes, voting, and migration. Issues of measurement, falsification, and verification are discussed.