Moral Sunk Costs in War and Self-Defence

The problem of moral sunk costs pervades decision-making with respect to war. In the terms of just war theory, it may seem that incurring a large moral cost results in permissiveness: if a just goal may be reached at a small cost beyond that which was deemed proportionate at the outset of war, how can it be reasonable to require cessation? On this view, moral costs already expended could have major implications for the ethics of conflict termination. Discussion of sunk costs in moral theorizing about war has settled into four camps: Quota, Prospect, Addition, and Discount. In this paper, I offer a mathematical model that articulates each of these views. The purpose of the mathematisation is threefold. First, to unify the sunk costs problem. Second, to show that these views differ in the nature of their justifications: some are justified qualitatively and others quantitatively. Third, to clarify the differential force of qualitative and quantitative critiques of these four views.