prior probability

In my previous blog post, I showed how the outcome of an appeal can depend on the type of voting rule appellate courts use to decide cases, and I mentioned a possible solution to this paradox: bayesian voting. In brief, bayesian voting would not change the way the parties make their arguments. The party with the burden of persuasion on a given legal issue would continue to write legal memoranda, submit legal briefs, and present arguments to the court, and the opposing party would also have the opportunity to do the same things, but bayesian voting would change the way appellate judges decide cases.

Specifically, instead of voting up or down on the outcome of an issue, judges using bayesian voting would have to disclose how strongly or weakly they believed in each side’s arguments. For this method to work, however, judges would have to vote sincerely (a big if, as we shall see in our next blog post), and they would have to use the same numerical scale. By way of example, see the image below, depicting a sliding scale starting at 0 (meaning complete disbelief in the arguments made by a party) and going up to 1 (meaning complete belief in a party’s arguments). So long as the judges use the same scale, it’s okay if each judge uses his own criteria to evaluate the strength of each party’s arguments. After all, the assignment of probabilities is a subjective activity; bayesian voting just makes this fact explicit.

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Imagine a case or controversy C presenting two separate legal issues: standing and sovereign immunity. Specifically, (1) does plaintiff P have standing to sue, and (2) is defendant D (a governmental entity) entitled to assert the defense of sovereign immunity, either under the Eleventh Amendment or under the act of state doctrine? Further assume the case is being decided by a panel of three impartial judges: J-1, J-2, and J-3. After deliberations, a set of individual judgments emerges as follows: Continue reading →

Instructions, via Dexter See: “Form a circle with Skittles on a plate (colours should be in repeated order, preferably according to colours of the rainbow e.g. purple, green, yellow, orange, red), then pour hot water over them.” (Hat tip: The Amazing Cliff Pickover.)

The entry in Wikipedia for “single-peaked preferences” explains this concept in three different ways: in words, then using formal mathematical notation, and then with a simple image. First, the concept is defined in words:  Continue reading →

Compelling stories all share a similar structure (see image below), even stories as radically different as the simple plot line in the movie Trolls or the complex one in the series Breaking Bad. For more, check out this essay by Cristina Wodtke titled “The Shape of Story.”

Credit: Cristina Wodtke (tip of the hat to Cliff Pickover)

Shout out to our student Nathalies Amitie! During this morning’s Summer B lecture, she posed a great question about JAY-Z and Beyoncé’s decision to trademark the names of their newborn twins (Rumi and Sir, for the record). After all, why get a trademark when the common law already creates legal rights to one’s name, likeness, and image? We did some research and found this report by Kenza Moller. According to Ms Miller: “there are legitimate reasons for celebrities to want to trademark their children’s names. In fact, Beyoncé and JAY-Z’s company — BGK Trademark Holdings — didn’t even try trademarking Blue Ivy’s name until a couple of other individuals and companies attempted to do so first. One individual reportedly tried to trademark the name ‘BLUE IVY CARTER NYC’ for a children’s clothing company, while a Long Island company registered ‘BLUE IVY CARTER GLORY IV’ as a name for fragrances.” In other words, Beyonce and JAY-Z may have decided to trademark the names of their children for defensive reasons: to keep other people and firms from trying to profit off of their names.

The burden of proof is a key feature of legal trials. In brief, in order to secure a conviction in a criminal case or an award of money damages in a civil case, the moving party must produce sufficient evidence or proof that his allegations are true. (In the Anglo-American legal tradition, the burden is “proof beyond a reasonable doubt” in criminal cases, while the “preponderance of the evidence” standard is used in most civil cases.) This concept is relevant to many areas of life beyond law as well. Here is Google Scholar; below is a partial lit review:

J. P. McBaine, Burden of proof: degrees of belief, California Law Review, Vol. 32, No. 3 (1944), pp. 242-268, available here. This law review article contains proposed jury instructions for various burdens of proof (i.e. preponderance of the evidence, clear & convincing proof, and proof beyond a reasonable doubt.

Rita James Simon & Linda Mahan, Quantifying burdens of proof: a view from the bench, the jury, and the classroom, Law & Society Review, Vol. 5, No. 3 (1971), pp. 319-330, available here. This paper presents the results of several experiments conducted on sociology students at the University of Illinois and on judges and jurors in Champaign County Court. Specifically, the researchers attempt to measure how students, judges, and jurors translate legal burdens of proof into numerical probability estimates.

Louis Kaplow, Burden of proof, Yale Law Journal, Vol. 121, No. 4 (2012), pp. 738-859, available here. This book-length “paper” (consisting of 122 pages and 218 footnotes) explores the burden of proof from an economic perspective.

As a follow up to a recent series of blog posts by our colleague and friend Eric Posner (see: “Twenty theses about Twitter” and “Twitter is a slot machine composed of humans“), we would argue that Twitter is mostly just a repository of memes and wisecracks. But at the same time, Twitter can be an excellent “random knowledge generator.” In particular, if you are selective and strategic about who (whom?) you follow, then Twitter can be a great place to discover new ideas. By way of example, here are three links we found scrolling down our Twitter feed today (8 July):

1. Modelling fish stocks by Murray Bourne, via @mathematicsprof.

2. Undefined behavior in 2017 by Pascal Cuoq and John Regeher, via @CompSciFact.

3. The myth of the apolitical Montaigne by Robert Minto, via @PhilosophyMttrs.