prior probability

Moritz Stefaner is an artist specializing in data visualizations. Here is a description of one of his data art projects (see also the video summary below): “Today, we collectively and continuously document our city experience on social media platforms, shaping a virtual city image. Multiplicity reveals a novel view of this photographic landscape of attention and interests. How does Paris look as seen through the lens of thousands of photographers? What are the hotspots of attraction, what are the neglected corners? What are recurring poses and tropes? And how well do the published pictures reflect your personal view of the city?” Check out Mr Stefaner’s “Truth & Beauty Operations” website here.

We need to update our priors again! We have been reading Victor Goldberg’s 2006 book “Framing Contract Law” and have already posted some positive reviews of various chapters of his book. (See here, for example.) One of the major themes in the book is Professor Goldberg’s disdain (if not utter contempt) for “the good faith standard” in contract cases. To summarize Professor Goldberg’s position, courts do not apply the good faith standard evenly, for “good faith” is too vague a rule to police contract disputes. Initially, we agreed with Professor Goldberg’s devastating critique of the good faith standard, but the more we think about his critique, the more we realize that it is Goldberg who is wrong, not the judges! It turns out many contract disputes involve some form of “post-contractual opportunism.” (Indeed, there is an extensive academic literature about this problem. See image below for an example.) So, as good Bayesians, we are updating our position on the good faith standard and our review of Goldberg’s book. To the extent that opportunism is a genuine problem in many contractual relationships (and the reported cases confirm this observation), the good faith standard (though vague) is probably a good second-best judicial solution in response to the problem of post-contractual opportunism.

Credit: Carmella Merritt

Via The Economist (circa 2015): Continue reading →

For the convenience of any of our followers who are as fascinated by the legal doctrine of stare decisis as we are, below are links to our six-part extended review of Randy Kozel’s excellent new book “Settled Versus Right“:

1. Introduction
2. The Brandeis Problem
3. Pros and Cons of Stare Decisis
4. The Problem with Precedent
5. Second-Best Stare Decisis
6. Bayesian Stare Decisis?

Credit: Martina Green

Rather than end our extended review of Randy Kozel’s excellent new book on precedent (“Settled Versus Right”) on a negative note, we shall conclude our review by stating our points of agreement with Kozel and then offering an alternative solution to the Brandeis problem. Let’s start with the following points of agreement:

1. Interpretive pluralism. To begin with, we agree with Kozel that “interpretive pluralism” is unavoidable. Judges and justices have competing views of the Constitution and how the Constitution should be interpreted. [As an aside, in the context of judging and judicial disagreement in close cases, this fact is why we reject the common prior assumption in the “agreeing to disagree” literature initiated by R. J. Aumann, Annals of Statistics, Vol. 4, no. 6 (1976), pp. 1236-1239.]

2. Tail-wags-dog argument. Next, we also agree with Kozel that stare decisis is a feeble constraint at best in constitutional cases. Specifically, when a court is considering its own previous decisions, the judges of that court will measure the strength and scope of those “horizontal precedents” in light of their own individual priors. In other words, each judge’s priors, not precedent, are what decide the case.

3. Second-best theory. Lastly, although we are skeptical about Kozel’s various solutions to the Brandeis problem, we agree with him that this problem is a real one, not a pseudo-problem, and we admire his valiant effort to develop a “second-best theory” of precedent, especially his idea of “supermajority stare decisis.” The main question is, can we develop a better second-best solution to the Brandeis problem?

We will give it a try. For starters, like Kozel we will take interpretive pluralism as a given, but unlike Kozel, we would extend the domain of interpretive pluralism to include the evaluation and interpretation of horizontal precedent as well. That is, we take judicial disagreement over the strength and scope of precedent as a given.

As such, instead of trying to find a way of minimizing or working around such precedential disagreements (as Kozel does), a hopeless task in any case, we would propose the following thought-experiment in place of a supermajority rule: why not ask judges to use some alternative voting procedure, one that requires them to openly disclose their subjective views regarding a previously decided case. Specifically, imagine a world in which judges, when deciding whether a precedent applies (the question of scope) or whether to follow or overturn a precedent (the question of strength), would openly disclose their subjective evaluations of the precedent by ranking its scope and strength on some fixed scale, such as the [0, 1] interval.

We call this alternative judicial world “Bayesian judging,” or in the context of precedent, “Bayesian stare decisis.” Our approach recognizes the inherently subjective nature of constitutional interpretation, and it can be used to test both the scope of a precedent and its strength. A judge could just as well rank a precedent’s strength or its scope, i.e. whether statement x is holding or dicta. Either way, each judge would assign a numerical score reflecting his or her relative degree of belief or “credence” in the precedent under review. To keep things simple, this degree of belief could be expressed in numerical terms anywhere in the range from 0 to 1, 0 to 9 (see image below, for example), or some other uniform scale. The higher the score, the greater the judge’s credence or degree of belief. A score above 0.5, for example, indicates that the precedent is a strong one and should dispose of the case, while a score below 0.5 means that the precedent is weak or should even be overturned. (A score of 0.5 means the judge is undecided about the precedent’s precedential value.)

Under this alternative system of Bayesian stare decisis, a precedent would be affirmed if the sum of the judges’ or justices’ individual scores divided by the number of judges exceeded some threshold value, say .5; by contrast, a precedent would be overturned only if the sum of their individual scores divided by the number of judges went below .5. (In the event the sum of the judges’ individual scores divided by the number of judges were exactly .5, the court could require a rehearing of the case.)

In fairness to Kozel, Bayesian stare decisis is open to the same objections we identified over supermajority voting; namely, why would judges themselves ever agree to implement such an unorthodox reform? That said, my immediate purpose here is not to change the procedures of appellate practice and judging in the short term. My purpose is simply to question the traditional nature of judicial voting (majority rule) and demonstrate the subjective nature of stare decisis in close cases. [We have painted our alternative approach to precedent with a broad brush in this blog post, but we do delve into the details of Bayesian judging and the possibility of Bayesian verdicts in these two papers: The Case for Bayesian Voting (2017), and Why Don’t Juries Try Range Voting (2015).]

FYI: We will conclude our review of Randy Kozel’s book “Settled Versus Right” on 15 May. (In other words, we’re taking Monday off.)

H/T: Brian Leiter. Happy Mother’s Day!