Sincere versus sophisticated voting when legislators vote sequentially

Elsewhere (Groseclose and Milyo 2010), we examine a game where each legislator has preferences over (i) the resulting policy and (ii) how he or she votes. The latter preferences are especially important when the legislator is not pivotal. We show that when the game follows the normal rules of legislatures—most important, that legislators can change their vote after seeing how their fellow legislators have voted—then the only possible equilibrium is one where all legislators ignore their policy preferences. That is, each legislator votes as if he or she is not pivotal. The result, consistent with empirical studies of Congress, suggests that legislators should tend to vote sincerely, rather than sophisticatedly. In this paper we examine how outcomes change if we change the rules for voting. Namely, instead of a simultaneous game, we consider a game where legislators vote sequentially in a pre-determined order. We show that, opposite to the simultaneous game, an alternative wins if and only if a majority of legislators’ policy preferences favor that alternative. Our results suggest that if Congress adopted this change in rules, then sophisticated voting would become frequent instead of rare.