In prominent voting models, expected pivotality drives voters’ turnout decisions and hence determines voting outcomes. In practice, many individuals turn out for reasons unrelated to pivotality, and their votes overwhelm the forces analyzed in pivotality-based models. Accordingly, we examine a model of large-N elections at the opposite end of the spectrum, where pivotality effects vanish and turnout is driven entirely by individuals’ direct costs and benefits from the act of voting itself. Under certain conditions, the level of turnout is irrelevant to representativeness—and thus to outcomes. Under others, anything is possible: for any distribution of underlying preferences, any other distribution of preferences in the turnout set—and thus any voting outcome—can arise. We characterize particular skews in terms of representativeness and offer limiting results. These results sharpen and in some respects redirect applied work examining voter turnout, with an emphasis on underlying determinants of representativeness.