Richard Posner suggests several arguments for increasing health care spending on males and reducing it on females in his book, Aging and Old Age . I offer a new formalization of his verbal argument.

There is a secret paradox at the heart of social contract theories. Such theories assume that, because personal security and private property are at risk in a state of nature, subjects will agree to grant Leviathan a monopoly of violence. But what is to prevent Leviathan from turning on his...