prior probability

Thus far, we have identified a voting paradox in law and proposed a system of “bayesian voting” by judges in multi-member panels. There are, however, at least three major objections to my proposed system of bayesian voting:

1. Practicality (operational objection): Bayesian voting is much more cumbersome and complicated than traditional forms of voting.

2. Incommensurability (logical objection): Since each voter’s credence is subjective, it is meaningless to combine or aggregate such subjective and incommensurable values.

3. Anti-majoritarianism (ethical objection): Bayesian voting can produce anti-majoritarian outcomes.

Due to time constraints and other commitments this weekend, we will address each of these objections in future blog posts, i.e. during the last week of July.

In our 7/17 blog post, we described a voting paradox in law and presented a simple model of bayesian voting, and in our 7/18 blog post, we showed how bayesian voting might work in practice. In that post, however, we assumed judges’ votes were sincere. In this post, by contrast, we will assume that all three judges are strategic actors (see image below); that is, all three judges are going to choose extreme values, i.e. inflate or deflate their degrees of belief as the case may be, in order to achieve their preferred outcome. I am making this assumption because I want to test whether my system of bayesian voting can be successfully manipulated or gamed. Continue reading →

July 19 is the 200th day of the year, so we interrupt our series of blog posts on Bayesian voting to wish our loyal followers good tidings. What will the next 100 days bring? In the meantime, enjoy …

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.

Continue reading →

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 →