Bayesian Voting (Part I)

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:

Standing Immunity
Judge #1 Yes Yes
Judge #2 Yes No
Judge #3 No No

Who wins, P or D?

It turns out that the outcome depends on the type of voting rule used to dispose of the case. (See here.) For example, if the judges decide to vote on each legal issue separately, P should win because two separate coalitions of judges agree that P has standing to sue (the coalition consisting of Judge #1 & #2) and that D may not assert the defense of sovereign immunity (the coalition consisting of Judge #2 & #3). On the other hand, if the judges follow a traditional “outcome-based” voting rule, D should win because only one judge (Judge #2) agrees that P has standing to sue and that D is not entitled to assert the defense of sovereign immunity. (By contrast, Judge #1 believes that P has standing but that D is immune, while Judge #3’s position is that P lacks standing even though D is not immune.)

Why is this judicial voting paradox worth thinking about? According to the collective choice literature, the choice of voting rule in case C is arbitrary, yet the choice of voting rule will determine the result! Moreover, although issue-by-issue voting and outcome voting produce opposite results, both voting rules are predicated on the “majority rule” principle. But what if we were to refine the majority rule principle (either issue voting and outcome voting) by introducing a simple system of “bayesian voting,” i.e. a voting system in which each judge is required to express a credence or degree of belief in his or her individual judgments? I shall explain the nuts and bolts of bayesian voting in my next blog post.

Image result for bayes

Image Credit: robotenomics.com

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3 Responses to Bayesian Voting (Part I)

  1. Pingback: Bayesian Voting (Part 2) | prior probability

  2. Pingback: Bayesian Voting (Part 3) | prior probability

  3. Pingback: Why we prefer the term “bayesian voting” | prior probability

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