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.

在许多具有内生物理风险的环境中——例如，家庭、邻里交通平静、生产质量控制——降低风险是当地的公共产品。降低风险的激励措施则取决于受保护人口的规模。专注于建模为具有内生“成功”概率的 iid Bernoulli 试验序列的家庭物理风险，我给出了安全的充分条件，通过单调比较静态方法和“一阶”方法保护的数量增加。我利用涉及二项式变量和一级随机优势 (FSD) 的单调函数的协方差的递归分解。因为“保护”问题一般是非凹的，所以我再次通过 FSD 对二阶条件进行详细处理。