Benjamin Grant Purzycki and colleagues suggest that religion helps to explain cooperation in large societies (Nature 530, 327–330; 2016). In my view, knowledge of others' reputations forms a more stable basis for cooperation.
A network with redundant connections transmits these reputations (J. Bruggeman Social Networks; Routledge, 2008). It also avoids the strategic manipulation of information by religious entrepreneurs. Once such a cohesive network is established, religious solidarity can enhance cooperation, as can a shared enemy (J.-K. Choi and S. Bowles Science 318, 636–640; 2007) — but it is not essential.
Take the revolt against Communist regimes in 1989. These were overthrown by large-scale collective action, even though religion was negligible or subservient in those countries. Protesters united, despite each knowing only a few others (the regimes suppressed their critics). Religion is one road towards cooperation between strangers, as the experiments show, but not the only one.
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Bruggeman, J. Social cooperation among agnostics. Nature 532, 177 (2016). https://doi.org/10.1038/532177e
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DOI: https://doi.org/10.1038/532177e