Whenever an authority has influence over a population — be it a social media platform moderating user comments, a government imposing laws on its citizens, or an employer placing restrictions on employees — some people will push back against the authority’s rules. In a study published in November in Proceedings of the National Academy of Sciences, SFI External Professor Stephanie Forrest and her colleagues devised a mathematical model for the give-and-take between dissenters, who break the rules, and authorities, who impose punishments.
“Pick any issue you like. You’ll express something in between what you really want, if there’s no penalty for doing so, and nothing at all, if the punishment is severe,” says Joshua Daymude, an Assistant Professor in the School of Computing and Augmented Intelligence at Arizona State University. Forrest and Daymude collaborated on the study with Robert Axelrod, the William D. Hamilton Distinguished University Professor Emeritus at the University of Michigan.
Key to the model is a quality the researchers call “boldness”: the willingness to risk punishment for the sake of genuine self-expression. As more and more individuals dissent, authorities tend to impose stricter and stricter punishments, and individuals must be increasingly bold if they want to continue to dissent. Without sufficient boldness, they begin to censor themselves for fear of the repercussions.
“That’s sort of obvious. But what surprised us was that small amounts of boldness are highly effective at delaying self-censorship,” says Forrest, who is also a Professor of Computer Science at Arizona State University and the Director of the Biodesign Center for Biocomputing, Security and Society.
That’s because punishments always come with a cost, such as the cost for a social media platform to hire moderators, explains Daymude. If individuals are very bold, then mild punishments impose a cost on the authority without doing anything to change behavior. When enough people dissent early and often, punishments can become too costly for the authority to maintain.
The study comes with caveats: The researchers omitted the impact of people who support the authority — the opposite of dissent. Furthermore, there’s no method for predicting what people would have done in the absence of authority, so the researchers lack empirical data with which to test their model. Instead, they offer examples of times their predictions have borne true. For example, during the 2022–23 protests in Hong Kong, people chose to self-censor on Twitter after new laws were passed that increased the severity of punishments.
The model shows that maintaining the right to self-expression “is about boldness,” Daymude says. “It’s about continuing to take risks to say what needs to be said, under threat of punishment.”
Read the paper “Strategic analysis of dissent and self-censorship” in PNAS (November 5, 2025). DOI: 10.1073/pnas.2508028122
MORE
- Arizona State University Press Release, November 4, 2025
- "When Do People Speak Out Against Tyranny?" Nautilus, November 4, 2025