People participate in protests even though it is costly, their participation has a negligible impact on the outcome, and the benefits are not exclusive to participants. I propose a framework where people choose optimally to participate, even if the number of potential protesters is arbitrarily large. Opportunities to participate arrive stochastically over time, and the protest succeeds if participation surpasses a threshold. A player with an opportunity becomes pivotal if, after choosing not to join, it is likely that the protest will end before another opportunity arrives.
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