Ideal Points 

 One of the goals of this blog is to promote dialog between people working in different social science disciplines.  As part of that, we have been posting reports from the Political Methodology conference in Tallahassee.  Of course, even though we may all speak the same statistical language, we often speak it with distinct accents; similar concepts and methods often go by different names in different fields.  For example, it turns out that estimating the ideal points of political actors is similar in many ways to the problem of estimating the difficulty of question on standardized tests, a commonality that has only been exploited in the last few years. 

 First things first, however; what exactly is an ideal point?  People have long thought about politics in spatial terms: "left" and "right" have been used to describe political preferences since at least the French Revolution, when royalists sat on the right and radicals on the left in the Legislative Assembly.  Ideal point models attempt to estimate the position of each legislator on the left-right or other dimensions using the votes that they cast on legislation.  Basically, the models assume that a legislator will vote in favor of a motion if it moves policy outcomes closer to their most preferred policy.  The resulting estimates from these models provide a descriptive summary of the distribution of preferences within a legislature.  They are also important parameters in many formal models of legislative behavior. 

 Much of the recent work in the area of ideal point estimation has drawn on earlier research by education scholars.  Item response theory studies the relationship between the ability (and other characteristics) of test subjects and the answers they give to particular test questions.  The general idea is that every test question has an associated ability cutpoint; those with ability above the cutpoint will answer correctly on average.  In a typical testing situation, the authors will attempt to include questions with an array of cutpoints in order to estimate the ability of the test takers.   

 The analogy between ability estimation and ideal point estimation is close; votes in the legislature correspond to questions on the test.  One difference is that, in the item response context, the researcher will typically know the correct answer and can therefore associate those responses with higher estimated ability.  In the ideal point context, it is not always clear whether a proposal moves policy left or right.  Several recent articles have addressed this and other problems in translating item response models to the political context, including work by Harvard's own Kevin Quinn with Andrew Martin   (Martin and Quinn 2002)  ,   Clinton, Jackman, and Rivers (2004) , and   Bafumi, Gelman, Park, and Kaplan (2005) .  Dan Hopkins described some recent work on ideal point estimation in an   earlier post .