We apply formal, statistical measurement models to the Polity indicators, used widely in studies of international relations to measure democracy. In so doing, we make explicit the hitherto implicit assumptions underlying scales built using the Polity indicators. Modeling democracy as a latent variable allows us to assess the "noise" (measurement error) in the resulting measure. We show that this measurement error is considerable and has substantive consequences when using a measure of democracy as an independent variable in cross-national statistical analyses. Our analysis suggests that skepticism as to the precision of the Polity democracy scale is well founded and that many researchers have been overly sanguine about the properties of the Polity democracy scale in applied statistical work.

Given the increasingly polarized nature of American politics, renewed attention has been focused on the ideological nature of the mass public. Using Bayesian Item Response Theory (IRT), we examine the contemporary contours of policy attitudes as they relate to ideological identity and we consider the implications for the way scholars conceptualize, measure, and use political ideology in empirical research. Although political rhetoric today is clearly organized by a single ideological dimension, we find that the belief systems of the mass public remain multidimensional, with many in the electorate holding liberal preferences on one dimension and conservative preferences on another. These crosspressured individuals tend to self-identify as moderate (or say "Don't Know") in response to the standard liberal-conservative scale, thereby jeopardizing the validity of this commonly used measure. Our analysis further shows that failing to account for the multidimensional nature of ideological preferences can produce inaccurate predictions about the voting behavior of the American public. There appears to be a consensus among scholars and political observers that U.S. political elites have grown more polarized in recent decades. Democrats and Republicans in Congress more consistently oppose each other on legislation (McCarty, Poole, and Rosenthal 2006), the party platforms are more ideologically extreme (Layman 1999), and issue activists are more committed to one political party or the other (Stone 1991). In contemporary American

Although estimating the revealed preferences of members of Congress is straightforward, estimating the position of the president relative to Congress is not. Current estimates place the president as considerably more ideologically extreme than one would expect. These estimates, however, are very sensitive to the set of presidential positions used in the roll call analyses for the 103rd through 109th Congresses. The president often obtains more moderate ideal point estimates relative to Congress when including positions based on signing bills into law.

Conventional accounts of the Federal Convention of 1787 point to the many different compromises made at the convention, specifically the Great Compromise on representation and the Three-Fifths Compromise on slavery. Often these compromises are treated as separate events, the result of deliberation leading to moderation of delegate positions (presumably among the key states of Massachusetts and North Carolina). However, by applying the techniques of roll-call analysis, we find this traditional account is at best incomplete and probably misleading. While the Massachusetts delegation's behavior seems consistent with a moderation hypothesis, we find evidence that the other crucial vote for the Great Compromise-from North Carolina-is inconsistent with moderation, but can be linked through the agenda to the Three-Fifths Compromise over slavery, taxation, and representation. We conclude by arguing that this reconsideration of some of the convention's key votes should cause political scientists and historians to reevaluate how they see the compromises at the convention.