That the last half-century has seen increased polarization in Washington is clear. Holders of most key posts and key votes just a few decades back, conservative Democrats and liberal Republicans are now few and far between, so much so that one scribe recently referred to the former as "endangered species" and the latter as "essentially extinct" (Roll Call, October 27, 2005). Replacing these moderates have been resolute ideologues and loyal partisans (Fleisher and Bond 2004; McCarty, Poole, and Rosenthal 2006; Poole and Rosenthal 1984; 1997; Sinclair 2006; Theriault 2008). Plainly, Jim Hightower's aphorism that "There's nothing in the middle of the road but yellow stripes and dead armadillos" remains instructive, and more so with each passing year.
In light of Congress's increasingly polarized character, a burgeoning literature has sought to uncover the causes and consequences. While a myriad of factors have been identified as contributing to congressional polarization (Brady and Han 2007; Carson et al. 2007; Fleisher and Bond 2004; Jacobson 2000; Ladewig 2010; McCarty, Poole, and Rosenthal 2006; Poole and Rosenthal 1997; Sinclair 2006; Stonecash, Brewer, and Mariani 2003; Theriault 2008), the hypothesized effect is comparatively clear: legislative gridlock. Partisan polarization (via divided government) is thought to engender gridlock by promoting posturing over compromising (Gilmour 1995; Groseclose and McCarty 2001; Lee 2009; Sinclair 2006), and ideological polarization is predicted to encourage gridlock by reducing the range of status quos that can be beat by a coalition preferring something else (Brady and Volden 1998; Krehbiel 1998).
But, of course, gridlock is not an all-or-nothing proposition. Although polarization certainly inhibits lawmaking (Barrett et al. 1997; Binder 1999, 2003; Coleman 1999; Howell et al. 2000; Jones 2001; Kelly 1993), significant laws continue to pass-underunified and divided government, and even in the face of substantial polarization (see esp. Mayhew 2005). This article considers these exceptions to the general rule. Specifically, building on Snyder (1991) (see also, Beckmann and McGann 2008; Groseclose and Snyder 1996) we develop a simple game-theoretic model in which the president allocates scarce political capital to induce changes in senators' votes and, in turn, show how a polarized chamber, compared to one with more homogenous preferences, can actually improve a president's prospects for winning important roll-call votes and passing preferred legislation. We test this hypothesis against data on presidents' success on key Senate roll-call votes from 1953 to 2008. (1)
Polarization as a Presidential Opportunity
To investigate the relationship between polarization, presidents, and policy making, let us consider a simple, complete information game-theoretic model with two player-types. The first of these is the president, P, who has an ideal policy preference, p. Building on Neustadt's (1960) seminal insight that presidential power turns on informal persuasion (rather than formal prerogatives), we assume the president is exogenous to the lawmaking game per se but wields "political capital" he can allocate to lobby lawmakers. (2) The president values both the policy outcome and his political capital; his utility can be given as
[u.sub.P] = -A x [(y - p).sup.2] - B; B [less than or equal to] [W.sub.P] (1)
[FIGURE 1 OMITTED]
Here, y is the policy outcome, B the investment of political capital needed to get legislators (3) to adopt the president's proposal, and A is a coefficient indicating the weight the president assigns to prevailing on the policy versus preserving his political capital. Because our interest is assessing presidents' potential influence in Congress, we assume a nontrivial A--that is, the president is willing to invest some political capital in order to achieve a policy outcome nearer his ideal.
The second player-type in our game are lawmakers, organized along a continuum, with a pivotal (median) voter, m. …