Numerous studies have found a negative relationship between the closeness of an election, the size of the electorate and voter turnout. It is often claimed that this relationship supports the rational voter hypothesis, with closeness and size proxying for the decisiveness of a vote. We offer a different interpretation. Larger communities are more heterogeneous than smaller ones, and turnouts are inversely related to the heterogeneity of a community. We present empirical support for this hypothesis using data for voter turnouts in Norwegian school language referendums. Community size is found to have a negative effect on voter turnouts, even after accounting for the probability of a single vote being decisive and the linguistic dimension of this heterogeneity. Our findings question the adequacy of the turnout regression in testing the rational voter hypothesis, as neither a positive correlation between closeness and turnout, nor a negative correlation between size and turnout can be exclusively attributed to instrumental voting.