War is a puzzle because, if states were rational, they should agree on their differences in power and reach a solution that avoids the costs of fighting. However, this thesis argues that states are only as rational as the men who lead them, who are well established to suffer from psychological "positive illusions" about their abilities, their control over events, and the future. I examine the effects of positive illusions on four turning points in twentieth-century history: two that erupted into war (World War I and Vietnam); and two that did not (the Munich Crisis and the Cuban Missile Crisis). In the two crises, I show that positive illusions were held in check, and thus avoided war. In the two wars, by contrast, I show that positive illusions substantially influenced politics, causing leaders to overestimate themselves, underestimate their adversaries, and resort to violence to settle a conflict against unreasonable odds.