# 3-judge panels

John writes,

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).

## 3 thoughts on “3-judge panels”

1. How is writing the opinion assigned? Is it random, assigned by a chief justice of some sort, or the consequence of an initial vote (or something else)? I don't do judicial politics, but my gut says this matters.

2. Two thoughts:

First, is the phenomenon of interest dissenting (that is, actually writing a dissenting opinion) or just being in the minority? The latter is a necessary condition for the former, but many CoA judges on the wrong end of 2-1 decisions do not author dissenting opinions.

Assuming you care about the votes, not the writing/opinion, Andrew may be onto something. A CoA judge can only dissent if both other judges on the panel disagree with him/her. But agreement/disagreement is necessarily "lumpy" because it gets cast in terms of binary responses (affirm/reverse). "All the data" in this case would (hypothetically) be error-free, continuous measures of each judge's position in the case, from which some sort of natural distance/agreement metric among them could be calculated.

If the judges are A, B, and C, then Pr(A is in the minority) is then something like Pr(A and B "disagree") & Pr(A and C "disagree") & Pr(B and C "agree"). Distance-wise, this requires that D(AB)>D(BC) & D(AC)>D(BC). (There are parallel statements for judges B and C, of course). That all looks like a garden-variety logit to me, albeit one with two (rather than one) latent spaces.

This suggests that perhaps the "standard" approach isn't so bad. So long as your covariates are reasonable — and particularly so long as they include some measure(s) of "distance" among the judges on the panel — just allowing the "errors" to be correlated in each case and using Huber/grouped VCV estimates doesn't strike me as a bad idea.

3. I think that modelling dissent is a tricky topic. Judges don't decide a case based on whether they want to concur or dissent; the pick a position for one or the other side based on the merits. Each judge relatively independently decides which way she wants to rule, and the majority is formed based on where the chips lie.

If you think about the data generating process in this way, I think you see that better research questions are: do judges form cliques? Do they depend on the issue? Is one judge pivotal?