Three mistakes in the moral mathematics of existential risk

Longtermists have recently argued that it is overwhelmingly important to do what we can to mitigate existential risks to humanity. I consider three mistakes that are often made in calculating the value of existential risk mitigation: focusing on cumulative risk rather than period risk; ignoring background risk; and neglecting population dynamics. I show how correcting these mistakes pushes the value of existential risk mitigation substantially below leading estimates, potentially low enough to threaten the normative case for existential risk mitigation. I use this discussion to draw four positive lessons for the study of existential risk: the importance of treating existential risk as an intergenerational coordination problem; a surprising dialectical flip in the relevance of background risk levels to the case for existential risk mitigation; renewed importance of population dynamics, including the dynamics of digital minds; and a novel form of the cluelessness challenge to longtermism.