Theories of choice in economics typically assume that interacting agents act individualistically and maximize their own utility. Specifically, game theory proposes that rational players should defect in one-shot prisoners' dilemmas (PD). Defection also appears to be the inevitable outcome for agents who learn by reinforcement of past choices, because whatever the other player does, defection leads to greater reinforcement on each trial. In a computer simulation and 4 experiments, the authors show that, apparently paradoxically, when players' choices are correlated by an exogenous factor (here, the cooperativeness of the specific PD chosen), people obtain greater average reinforcement for cooperating, which can sustain cooperation. This effect arises from a well-known statistical paradox, Simpson's paradox. The authors speculate that this effect may be relevant to aspects of real-world human cooperative behavior. (Contains 11 tables, 1 figure and 4 footnotes.)