 We can view the situation here as a multi-player PD in which each “player” is the temporal stage of a single person. So viewed, it has at least two features that were not discussed in connection with the multi-player examples. First, the moves of the players are sequential rather than simultaneous (and each player has knowledge of preceding moves). Second, there is the matter of gradation. Increases in electric current between adjacent settings are imperceptible, and therefore irrelevant to rational decision-making, but sums of a number such increases are noticeable and highly relevant. Neither of these features, however, is peculiar to one-person examples. Consider, for example, the choice between a polluting and non-polluting means of waste disposal. Each resident of a lakeside community may dump his or her garbage in the lake or use a less convenient landfill. It is reasonable to suppose that each acts in the knowledge of how others have acted before. (See “Asynchronous Moves” below.) It is also reasonable to suppose that addition of one can of garbage to the lake has no perceptible effect on water quality, and therefore no effect on the welfare of the residents. The fact that the dilemma remains suggests that PD-like situations sometimes involve something more than a conflict between individual and collective rationality. In the one-person example, our understanding that we care more about our overall well-being than that of our temporal stages does not (by itself) eliminate the argument that it is rational to continue to adjust the setting. Similarly, in the pollution example, a decision to let collective rationality override individual rationality may not eliminate the argument for excessive dumping. It seems appropriate, however, to separate this issue from that raised in the standard PD. Gradations that are imperceptible individually, but weighty en masse give rise to intransitive preferences. This is a challenge to standard accounts of rationality whether or not it arises in a PD-like setting.