Bayesian voting is easy

In this blog post, I will address the practicality objection to bayesian voting by judges. First, I concede that, in the judicial context, cardinal or utilitarian methods of voting–like my method of bayesian voting–are marginally more costly and cumbersome than the traditional, i.e. binary, method of voting that appellate judges already use (e.g. affirm or reverse). Nevertheless, I will make two replies to this objection. My first reply is that all ordinal methods of voting have serious flaws and drawbacks, i.e. any ordinal system of voting can be manipulated in one way or another. (See, e.g., Frank H. Easterbrook, “Ways of criticizing the court,” Harvard Law Review, Vol. 95, No. 4 (1982), pp. 802-832; Saul Levmore, “Parliamentary law, majority decisionmaking, and the voting paradox,” Virginia Law Review, Vol. 75, No. 5 (1989), pp. 971-1044; William H. Riker, Liberalism against populism: a confrontation between the theory of democracy and the theory of social choice, chapter 4, 1988.) As a result, it’s not enough to point out that bayesian voting is costly or cumbersome. Instead, one must compare the costs of bayesian voting (the switching costs of implementing a new method of voting for appellate courts) with the potential benefits of bayesian voting (accuracy, coherence, and fairness). So, to the extent bayesian methods of voting are harder to manipulate than ordinal or traditional (binary) methods of voting are, the costs might be worth trading off.

In any case, my next point regarding the practicality of bayesian voting is that such a method is, in fact, not all that hard to understand or complicated to use. We engage in a form of bayesian voting whenever we rank or review products on Amazon, rate movies on Netflix or Rotten Tomatoes (see image below), or decide how much money to place on a bet. All of these mundane activities are everyday examples of bayesian voting: subjective expressions of a voter’s personal preferences. The more you like a product or movie, the higher score the product or movie should receive, and conversely, the less you like the product or movie, the lower the score you will assign it. (The same bayesian logic applies to bets: the more confident you are in the outcome of a bet, the more money you should be willing place on the bet.) A cardinal ranking thus conveys more information than a simple binary choice does. (As an aside, many Netflix users have criticized Netflix’s recent decision to replace its five-star rating system with a binary “thumbs up” and “thumbs down” system. One user referred to the new binary system as “quite literally the most useless rating system I have ever seen across any form of media.” See Paul Tassi, “Netflix’s thumb-based rankings system is the epitome of uselessness,” Forbes (26 Jun 2017). For a defense of Netflix’s new binary method of ranking movies, see David Sims, “Netflix believes in the power of thumbs,” The Atlantic (21 Mar 2017).)

To sum up, given the accuracy, simplicity, and usefulness of bayesian voting, there is no reason why the logic of bayesian voting cannot be applied to appellate judicial procedure as well. Instead of voting up or down (e.g. affirm or reverse), under bayesian voting each judge would simply assign a number reflecting the strength of his belief (i.e. his credence or degree of belief) in a given legal proposition or a legal outcome. But this opens up a new objection: the problem of incommensurability. Since the credences of each judge are entirely subjective, should we be allowed to aggregate such subjective values? I will address this objection in my next blog post.

Image result for amazon netflix rotten tomatoes rating

About F. E. Guerra-Pujol

When I’m not blogging, I am a business law professor at the University of Central Florida.
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3 Responses to Bayesian voting is easy

  1. Pingback: Three objections to bayesian voting | prior probability

  2. Pingback: Digression: Netflix’s binary voting system | prior probability

  3. Pingback: Bayesian voting is subjective; so what? | prior probability

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