  We experimentally study voter turnout in two-tier elections when the
electorate consists of multiple groups, such as states. Votes are aggregated
within the groups by the winner-take-all rule or the proportional rule, and the
group-level decisions are combined to determine the winner. We observe that,
compared with the theoretical prediction, turnout is significantly lower in the
minority camp (the Titanic effect) and significantly higher in the majority
camp (the behavioral bandwagon effect), and these effects are stronger under
the proportional rule than under the winner-take-all rule. As a result, the
distribution of voter welfare becomes more unequal than theoretically
predicted, and this welfare effect is stronger under the proportional rule than
under the winner-take-all rule.
