In a previous post, I pointed out seven of my scholarly papers that contain a question in their titles, and last week, I fed five of those questions into ChatGPT and shared the results of these AI adventures on this blog. Today, I will feature my 2016 paper “Judge Hercules or Judge Bayes?”, a purely theoretical work where I claim that the “superior Being” in Newcomb’s Problem and the mythical Judge Hercules in the late Ronald Dworkin’s (pictured below, left) theory of law are one and the same person. First off, I asked ChatGPT to “compare and contrast Dworkin’s ‘Judge Hercules’ and Guerra-Pujol’s (yours truly) ‘Judge Bayes'”; below the fold is ChatGPT’s response:

Ronald Dworkin’s “judge Hercules” is a concept from his book “A Matter of Principle” in which he describes the ideal judge as someone who is able to make moral and legal judgments that are consistent with the principles of justice. Dworkin argues that this judge, like the mythical figure Hercules, is able to distinguish right from wrong, even in difficult and complex cases.

On the other hand, “judge Bayes” is a concept proposed by Luis Guerra-Pujol in his book “Bayesian Law” which refers to the use of Bayesian probability theory as a method for legal reasoning. According to Guerra-Pujol, a judge who uses Bayesian reasoning would take into account the prior probabilities of different events and adjust them based on new information to arrive at a conclusion.

In summary, Dworkin’s “judge Hercules” is an idealized moral and legal philosopher who is able to make consistent judgments based on principles of justice, while Guerra-Pujol’s “judge Bayes” is a more technical and mathematical figure who uses probability theory to make legal decisions.

Before proceeding any further, note my name is Enrique Guerra-Pujol (not “Luis”), and there is no tome (at least not yet) called “Bayesian Law”–though that would make a great title for my next book! In any case, I asked next, “Who is more likely to solve Newcomb’s Paradox: Judge Hercules or Judge Bayes?”, and got back the following wishy-washy five-paragraph response:

It is difficult to say for certain which of Dworkin’s “judge Hercules” or Guerra-Pujol’s “judge Bayes” would be more likely to solve Newcomb’s paradox, as both approaches would likely bring different perspectives to the problem.

Newcomb’s paradox is a thought experiment in decision theory that presents a situation in which a decision maker must choose between two options, one of which offers a larger reward but is dependent on the decision of a seemingly infallible predictor. The paradox arises because the optimal decision depends on the decision maker’s beliefs about the predictor’s infallibility.

Dworkin’s “judge Hercules” might approach Newcomb’s paradox by considering the principles of justice and fairness that are at stake in the problem, and attempting to make a decision that is consistent with those principles. This approach might involve considering the rights and obligations of the decision maker, the predictor, and any other parties involved in the scenario.

On the other hand, Guerra-Pujol’s “judge Bayes” would approach the problem using Bayesian probability theory and taking into account the prior probability of the events and adjust them based on new information. This approach would likely involve a more quantitative and data-driven analysis of the problem.

In conclusion, both Judge Hercules and Judge Bayes could potentially solve Newcomb’s paradox, but they would likely approach the problem from different perspectives and use different methods to arrive at a solution.

By contrast, below is the conclusion of my 2016 paper “Judge Hercules or Judge Bayes?”:

In this paper, we have established two equivalencies between the perennial problem of hard cases in law and Newcomb’s Paradox in decision theory and philosophy. One is that Newcomb’s Problem is, in principle, a “hard case” since there are opposing solutions to the problem. The other equivalency is between the superior Being in Newcomb’s Paradox and Judge Hercules, who we have rechristened in this paper as Judge Bayes. Both ideal entities are “perfect predictors” of choices. These choices might involve the outcome of a hard case in law or deciding whether one will choose one box or two boxes in Newcomb’s Paradox, but in either case, the essential function of the superior Being and Judge Bayes is the same: prediction. Moreover, in both cases-­-­Nozick’s superior Being; our Judge Bayes-­-­we are postulating a perfect or near-­perfect predictor in order to test our intuitions about free will and determinism (in the case of Newcomb’s Problem) or our intuitions about hard cases (in the case of law).

Note: I will conclude this series in the next day or two.