I’m starting to work on a paper empirically modeling dissents on appellate panels, and was hoping you could help me with the proper way to model them.
Here’s what we can observe: 3 judges decide a case, 1 writes an opinion, and the other 2 either go along with that an opinion or write a dissent (about 10% of the time or less). In reality, the likelihood is that 2 of the three judges form a majority coalition, and then the 3rd judge decides whether to go along with them or not. However, we can’t observe the formation of this coalition, except in the (rare) cases where there is a dissent.
Here’s the problem: I want to model the individual judge’s decision whether or not to dissent. The leading work in this area treats each of the 2 judges who don’t write the opinion as separate observations, where 0 = no dissent and 1 = dissent, with standard errors clustered on cases. That it, they are essentially treating each judges’ votes as independent (except in the error terms). But this strikes me as wrong because one judge’s decision completely determines the other’s, since you can’t have 2 dissents in a case. I’m sure this issue must arise in other contexts (it’s sort of like a conditional logit problem, but not really), and there must be ways to model this properly, but can’t think of anything concrete.
My quick thought is that you want some sort of latent-data model. But I’m not quite sure what latent data you want. As Rubin says, what would you do if you have all the data? (Or, in your case, what are “all the data” that you want?) You already know how all the judges voted, right? Perhaps the latent data are the order of voting–the formation of the majority coalition. If so, you can set up a “structural model” with probabilities of each possible coalition (including unanimous 3-0 coalitions, I assume), along with a “measurement model” of the actual votes given the latent data. Such a model can then be fit using Bayes (e.g., Bugs).