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In many contexts with endogenous risks - e.g., the household, a neighbourhood's traffic calming measures, quality control on production runs - risk reduction is a local public good. The decision-maker's incentive to reduce risk then naturally depends on the protected population's size. Modelling risk as a sequence of i.i.d. Bernoulli trials with endogenous “success” probability, we give sufficient conditions for safety to increase with the number protected. We utilise an elementary recursive decomposition of a covariance involving a monotonic function of a binomially distributed variable and first degree stochastic dominance (FSD). Because “protection” problems are generally non-concave, we give a detailed treatment of the second-order condition, again via FSD.
