 The game labeled a many-person PD in Schelling, in Molander 1992, and elsewhere requires that the payoff to each co-operator and defector increases strictly with the number of cooperators and that the sum of the payoffs to all parties increases with the number of cooperators (so that one party's switching from defection to cooperation always raises the sum). Neither of these conditions is met by the formulation above, and one may question whether they are appropriate for the examples given. The margin of victory would not seem to raise the value of winning an election. Natural filtering systems may allow a body of water to absorb a certain amount of waste with zero harmful effects. It is often plausible, however, to maintain that they hold “locally,” i.e., for \(j\) close to the threshold \(t\) for minimally effective cooperation, it may be reasonable to assume that: