Inspired in part by Adam Bonica’s (really cool) estimates for the 112^{th} House, I’ve made my own projections for the characteristics of the House. Beyond calculating the party and chamber means, I’ve estimated the uncovered set, which relates the areas for enactable outcomes in the ideological space. I'll elaborate on the uncovered set on some later post, but for now, just consider it the median voter solution concept for two dimensional space.
This is a useful approach because it depicts what outcomes are possible for these preferences given an open agenda and simple majority rule. That is, where are outcomes likely to occur before institutional arrangements like agenda control, procedural votes, leadership pressure, etc are accounted for? From these primitives, we can then identify the magnitude of effect that institutions have on outcomes: the bigger the uncovered set, the greater the opportunity for majority party leadership to influence where an outcome occurs. If an uncovered set is quite small, the leadership has very little wiggle room to constrain outcomes.

As a baseline for comparison, consider the uncovered set for the 111^{th} House. The ideal points are calculated from all roll call votes taken in the 111^{th} House as of December 5, 2010 (accessed from Jeff Lewis’ website). I estimated W-NOMINATE scores for all legislators, omitting those who are not currently in the chamber. Both the X and Y axes are constructed so that smaller values are more liberal.

The big thing here is that the uncovered set is rather small, relatively far from any Republicans, and firmly established within the Democratic Party (some Democrats are more conservative than the most conservative end of the set).

To estimate the 112^{th} House, I’ve made a set of rather simplistic assumptions. First, with a nod to Keith “Legislators die with their ideological boots on” Poole, I’m assuming that continuing legislators will have the same ideal point coming in to the next session. Second, for those representatives who have been replaced by members of the same party, the new legislator will adopt the same voting record as the outgoing member. Third, for outgoing members who are replaced by members of the opposite party, I have adjusted scores by the coefficient from a party dummy variable when regressing legislator ideal point as a function of legislator party and district characteristics.

To be sure, each of these assumptions is problematic, but I believe that they provide a reasonable place for us to start from. Further, this baseline belief is borne out by a quick validation assessment: the party and chamber means I calculated from this simple adjustment are quite close to the ones that Bonica reports in his *really cool *estimation of ideal points based on campaign finance data.

So: what do we see? Given the polarized House and the sizeable Republican advantage, will we see a similarly small, thoroughly Republican uncovered set in the 112^{th} House? Simply, the 112^{th} House looks to be dramatically different, but not in the way that one would expect. In fact, the erosion of the moderates and the polarization of the parties actually increase the uncovered set size significantly.

Here, we see that the while the centroid of the uncovered set is quite close to the Republican party center, the uncovered set as a whole it is dramatically bigger, and actually borders some Democratic ideal points – a dramatic departure from the 111^{th} House. So how is this possible? The uncovered set (like its unidimensional cousin, the median voter) is particularly sensitive to voters in the middle of the policy space. When voters exist in the middle of the space, the uncovered set collapses around them, nearly assuring that the outcome will occur there. The erosion of the Blue Dog Caucus, and their replacement with ideological extremists, has actually dramatically increased space in which policy can be enacted.

So, what can we expect? If these projections are anything close to what the 112th House actually looks like, I think it’s going to take a lot of agenda control and procedural wrangling for John Boehner to keep the outcomes as close to the party centroid as he’d like. I’ll be watching with keen interest to see what rules the new House ratifies next month. Given all his talk about adopting a more consensus based approach, will he follow through? Or, (far more likely), will he endorse the enactment of procedural reforms necessary to keep outcomes pretty far to the right half of the uncovered set?

Either way, when the random stranger on the plane asks you what you do, and says*, “It must be a really interesting time to study politics.” You can smile and say, “Yes, it is.”

*That is, after finding out that you’re not going to be a politician, because that would be like a molecular biologist saying she wanted to be a genome.