**Mike Kellermann**

We have talked a bit on the blog (here and here) about estimating the ideal points of legislators in different political systems. I've been doing some work on this problem in the United Kingdom, adapting an existing Bayesian ideal point model in an attempt to obtain plausible estimates of the preferences of British legislators.

The basic Bayesian ideal point model assumes that politicians have quadratic preferences over policy outcomes; this implies that they will support a proposal if it implements a policy closer to their ideal point than the status quo. Let q_{i} be the ideal point of legislator i, m_{j} be the location of proposal j, and s_{j} be the location of the status quo that proposal j seeks to overturn. The (random) utility for legislator i of voting for proposal j can thus be written as:

s_{j}^{2} - m_{j}^{2} + 2q_{i}(m_{j} - s_{j}) + e_{ij}

Or re-written as

a_{j} + b_{j}q_{i} + e_{ij}

With the appropriate assumptions on the stochastic component, this is just a probit model with missing data in which the legislator votes in favor of the proposal when the random utility is positive and against when the random utility is negative. Fitting a Bayesian model with this sampling density is pretty easy, given some restrictions on the priors.

Unfortunately, applying this model to voting data in the British House of Commons produces results that lack face validity. The estimates for MPs known to be radical left-wingers are located in the middle of the political spectrum. Party discipline is the problem; the influence of the party whips (which is missing from the model) overwhelms the policy utility.

I try to address this problem by moving to a different source of information about legislative preferences. Early Day Motions allow MPs to express their opinions without being subject to the whips. EDMs are not binding, and can be introduced by any legislator. Other legislators can sign the EDM to indicate their support. There are well over 1000 EDMs introduced every year, which greatly exceeds the number of votes in the Commons.

We can't just apply the standard ideal point model to EDM data, however, because there is no way for MPs to indicate opposition to the policy proposed in an EDM. Instead of 'yea' and 'nay', one observes 'yea' or nothing. In particular, it is clear that some Members of Parliament are less likely to sign EDMs, regardless of their policy content. I model this by adding a cost term c_{i} to legislator i's random utility.

s_{j}^{2} - m_{j}^{2} + 2q_{i}(m_{j} - s_{j}) + c_{i} + e_{ij}

This is a more realistic model of the decision facing legislators in the House of Commons. In this model, the proposal parameters are unidentified; I restrict the posterior distribution for these parameters by assuming a prior distribution that assumes the sponsors of EDMs make proposals that are close to their ideal points.

I'm still finalizing the results using data from the 1997-2001 Parliament, but the results on a subset of the data seem promising; left-wingers are on the left, right-wingers are on the right, and the (supposed) centrists are in the center. These estimates have much greater face validity than those generated from voting data.

If you are interested in this topic, I am going to be presenting my preliminary results at the G1-G2 Political Economy Workshop today (Friday, November 18) at noon in room N401. By convention, it is grad students only, so I hope there are not too many disappointed faculty out there (sure...).

Posted by Mike Kellermann at November 18, 2005 3:09 AM