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. The rational-choice literature on Congress identifies two types of voting behavior, sincere and sophisticated. “Sophisticated voting” essentially means that legislators vote rationally, based on their preferences for policy. Thus, faced with a complex agenda involving a bill, amendments, a substitute bill, substitute amendments and the like, a sophisticated voter looks down the game tree and employs backward induction to inform each vote cast in the legislative process. In contrast, a “sincere voter” treats each roll call as if it were an isolated one-shot game, regardless of the subsequent implications that this choice may have for the final outcome of the legislative process. This behavioral assumption is typically justified as embodying the constraint that unsophisticated constituents impose on a reelection maximizing legislator; in other words, naive constituents induce legislators to act on “position-taking” preferences that may conflict with their “outcome preferences.” Put this way, sophisticated voting is consistent with forward-looking and rational behavior among all political actors and so, not surprisingly, has been the favored approach to modeling legislative behavior among rational choice theorists. However, Groseclose and Milyo (2010) conduct an extensive review of the empirical literature on Congressional voting and identify only a handful of isolated roll-call votes that plausibly indicate instances of sophisticated voting. Meanwhile, more systematic tests (Lahda, 1994, Poole and Rosenthal, 1997, and Wilkerson, 1999) decidedly conclude that sophisticated voting is very rare. Groseclose and Milyo (2010) propose a solution to this apparent puzzle by making note of a previously ignored institutional feature of roll call voting in Congress: the prohibition against “quick gavels.” The common practice in both the U.S. House and Senate is that roll call votes end only when no legislator desires to change his or her vote. The rule thus requires that every roll-call vote must be part of a pure-strategy Nash Equilibrium. Given this, Groseclose and Milyo demonstrate that the only possible equilibrium is for each legislator to vote sincerely. In this paper we show, however, that if the rules of the game are altered slightly, then outcomes will change greatly. Namely, instead of voting simultaneously, suppose that legis-