Charles M. Cameron and Lewis A. Kornhauser (Princeton University - Woodrow Wilson School of Public and International Affairs and Department of Politics and New York University - School of Law) have posted Modeling Collegial Courts (3): Judicial Objectives, Opinion Content, Voting and Adjudication Equilibria on SSRN. Here is the abstract:
We present a formal game theoretic model of adjudication by a collegial court. Distinctively, the model incorporates dispute resolution as well as judicial policy making and indicates the relationship between the two. It explicitly addresses joins, concurrences and dissents, and assumes judicial rather than legislative or electoral objectives by the actors. The model makes clear predictions about the plurality opinion's location in policy space; the case's disposition; and the size and composition of the disposition-coalition, the join-coalition, and the concurrence-coalition. These elements of adjudication equilibrium vary with the identity of the opinion writer and with the location of the case. In general, the opinion is not located at the ideal policy of the median judge. The model suggests new directions for empirical work on judicial politics.
And from the paper:
We have highlighted three features of adjudication in particular:
• First, adjudication jointly determines a case disposition and “policy” or opinion content. Although case dispositions must be compatible with opinion content, the linkage between the two is complex. For example, a majority, indeed a unanimous, view on case disposition does not imply majority (or unanimous) agreement on policy. In fact, in the United States, adjudicatory institutions do not require that any opinion receive majority support. Moreover, the joint production of case dispositions and policy outcomes may present a judge with difficult tradeoffs between the better case disposition and the best rule on offer.
• Second, the rules used to choose policies are radically different from those used in legislatures or elections. There is no amendment agenda. There is no paired comparison of alternatives. There is no vote pitting alternatives against the status quo. There is no run‐off between tied alternatives. There is free entry of opinions. Voters may abstain from endorsing any opinion, and doing so is consequential for the clarity of the Court’s voice.
• Third, in light of the procedures employed to determine outcomes, judicial motivations are apt to be critical in determining case dispositions and policy. Doing the right thing, announcing the best rule, and achieving clarity in the law may be as or more important than triumphing over competitors.
We have taken some tentative steps towards incorporating these features in a formal, game theoretic model of adjudication. First, the model incorporates joint production of case dispositions and policy outcomes and links the two. Second, the model incorporates some of the distinctive procedures used to choose policy. For example, we model joins, dissents, and concurrences. Third, we posit distinctively judicial preferences, including preferences for case dispositions and preferences for policy, and desires by opinion writers to achieve clarity in the law. We have not considered free entry of opinions nor competition between potential majority opinions, though we believe the model can be extended to address them. We believe most of the reported results will remain.
The model predicts behavior that is clearly at odds with the median justice model and the “median of the majority” model. For many parameter values, the location of an opinion depends critically on the entire distribution of ideal points, not simply on the location of the median justice. Dense clusters of ideal points tend to exert a “gravitational pull” on opinions. In courts with a strong center, outcomes may resemble median outcomes. In general, though, the model is an “author influence” model and for some parameter values is a “monopoly author” model. As such, the model suggests the importance of opinion assignment and strategic calculations by the Chief Justice. Other critical parameters affecting opinion locations and join decisions include the costs of writing separately and judicial valuations of a correct disposition and legal “