Five mistakes in moral mathematics

Abstract

Moral decision-making in large-scale populations is frequently distorted by five common errors in moral mathematics. Evaluation of an individual’s contribution to a collective outcome must reject the “share-of-the-total” view, which erroneously assigns a fixed fraction of a total benefit or harm to each participant. Instead, actions should be assessed by the specific difference they make relative to alternative choices. Furthermore, the moral significance of an act is not confined to its isolated consequences; an action may be wrong if it belongs to a set of acts that collectively produce harm, even when the individual contribution is overdetermined or seemingly negligible. In scenarios involving high stakes or large populations, extremely small probabilities of significant outcomes cannot be rationally ignored, as the expected value remains significant when multiplied by the number of people affected. Crucially, the belief that imperceptible or trivial effects lack moral weight is logically untenable. Aggregate harms—such as those found in resource depletion or environmental degradation—often consist of individual contributions that are individually unnoticeable but collectively disastrous. Common-sense morality, developed for small communities where effects are immediate and visible, fails to address modern coordination problems. Solving these collective action dilemmas requires a revised framework that recognizes how dispersed, minute individual actions aggregate into substantial ethical outcomes. – AI-generated abstract.