We test whether a voter's decision to cast a vote depends on its
probability of affecting the election outcome. Using exogenous variation
arising at population cutoffs determining council sizes in Finnish
municipal elections, we show that larger council size increases both
pivotal probabilities and turnout. These effects are statistically
significant, fairly large and robust. Finally, we use a novel instrumental variables
design to show that the jumps in the pivotal probabilities are the
likely candidate for explaining the increase in turnout, rather than the
other observed simultaneous jumps at the council size cutoffs.
Moreover, our results indicate that turnout responds only to
within-party pivotal probabilities, perhaps because they are more
salient to the voters than the between-party ones.