E¢ ciency, Equity, and Timing of Voting Mechanisms1

We compare the behavior of voters under simultaneous and sequential voting rules when voting is costly and information is incomplete. In many 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 generate a variety of predictions about the relative e¢ ciency and participation 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 signi…cant departures from the predicted equilibrium strategies, in both the sequential and simultaneous voting games. We …nd a tradeo¤ between information aggregation, e¢ ciency, and equity in sequential voting: a sequential voting rule aggregates information better than simultaneous voting and is more e¢ cient in some information environments, but sequential voting is inequitable because early voters pay greater participation costs. On November 7, 2000 the polls closed in the eastern time zone portion of Florida at 7:00 p.m. At 7:49:40 p.m., while Florida voters in central time zone counties were still voting, NBC/MSNBC projected that the state was in Al Gore’s column. A few seconds later CBS and FOX also declared the state for Gore and ten minutes later ABC projected Florida for Gore, three hours before the polls closed in California [Shepard (2001)]. Most of the concerns raised after these early election calls were about the problems of inaccuracy [Thompson (2004) is a notable exception]. However, even accurate reports of early voting outcomes during an election may mean that the election is fundamentally di¤erent from one held where voters participate simultaneously in at least three ways. First, when voters participate sequentially and early results are revealed to later voters, the choices facing the voters are complex as later voters use early voting as a noisy information source and early voters try to anticipate the message their votes can send to later voters and how later voters will react to that message. These choices are even more complicated if voting is a costly act, requiring an investment of time and resources, such that some voters may choose to abstain. Second, if voters’behavior does depend on the voting mechanism, then we might expect that sequential and simultaneous voting mechanisms will di¤er in e¢ ciency. Simultaneous voting can be more informationally e¢ cient than sequential voting if in sequential voting later voters are less inclined to participate or vote to “follow the crowd”rather than their independent judgements. On the other hand, sequential voting might be more economically e¢ cient when voting is costly if the outcome of the voting is equivalent but less voters are required to participate to achieve that outcome. Finally, sequential voting can be inequitable if voters’ abstention decisions depend on when they vote and thus the costs of participation are borne unequally by early and late voters. In this paper we address these three concerns about sequential voting–strategic behavior, e¢ ciency, and participation equity–both theoretically and experimentally. Election reporting of early voters’choices during national elections in the U.S. is just