Protection in numbers? Self-protection as a local public good

In many contexts with endogenous physical risks – e.g., households, neighbourhood traffic calming, production quality control – risk reduction is a local public good. Risk-reduction incentives then depend on the protected population’s size. Focusing on a household’s physical risks modelled as an i.i.d. Bernoulli trials sequence with endogenous “success” probability, I give sufficient conditions for safety to increase with the number protected via both monotone comparative statics methodology and a “first-order” approach. I utilise a recursive decomposition of a covariance involving a monotonic function of a binomial variable and first-degree stochastic dominance (FSD). Because “protection” problems are generally non-concave, I give a detailed treatment of the second-order condition, again via FSD.