We compare the behavior of voters, depending on whether they operate under sequential and simultaneous voting rules, when voting is costly and information is incomplete.  In many real political institutions, ranging from small committees to mass elections, voting is sequential, which allows some voters to know the choices of earlier voters.  For a stylized model, we characterize the equilibria for this rule, and compare it to simultaneous voting, and show how these equilibria vary for different voting costs.  This generates a variety of predictions about the relative efficiency and equity of these two systems, which we test using controlled laboratory experiments.  Most of the qualitative predictions are supported by the data, but there are significant departures from the predicted equilibrium strategies, in both the sequential and sumultanous voting games. We find a tradeoff between information aggregation, efficiency, and equity in sequential voting:  a sequential voting rule aggregates information better, and produces more efficient outcomes on average, compared to simultaneous voting, but sequential voting leads to significant inequities, with later voters benfitting at the expense of early voters.