prior probability

Here are some of my previous black history posts: 2014, 2015a, 2015b, 2017, and 2021.

Thus far, I have used ChatGPT to explore the research questions posed in seven of my previous papers. Below are ten additional research problems from my previous work that I may (or may not) feed into ChatGPT in the days ahead:

1. How did the English economist Ronald Coase come up with the idea that harms are a reciprocal problem? (This particular query is one that has haunted me for years; see my forthcoming paper “Coase’s Parable“.)
2. What is the optimal lifespan of a replicant? (Inspired by the original Blade Runner movie, Orlando I. Martinez-Garcia and I address this question in our 2012 paper “Clones and the Coase Theorem“.)
3. Build a game theory model of the rancher-farmer dispute used to illustrate the Coase Theorem. (See my other 2012 paper “Modelling the Coase Theorem“.)
4. Find a Bayesian solution to the “gatecrasher paradox” or to “blue bus problem” from the law of evidence. (See my 2013 paper “Visualizing Probabilistic Proof” and my 2014 follow-up blog post “The ‘Paradox of the Gatecrasher’ is not a paradox“.)
5. What was the logical contradiction that Kurt Gödel discovered when he studied the U.S. Constitution on the eve of his citizenship exam? (See, for example, my 2014 paper “Gödel’s Loophole” or this Wikipedia page.)
6. Who inspired the character of Santiago, the old fisherman in Ernest Hemingway’s Old Man and the Sea? (See my 2015 work-in-progress “Finding Santiago“.)
7. Identify possible theories of legal liability for data fabrication and other forms of “research fraud”. (See my 2017 paper “Legal Liability for Research Fraud“.)
8. What if Immanuel Kant were an 18th Century Bulgarian law professor? (See my 2019 reply to Chief Justice John Roberts and Professor Orin Kerr: “Kant on Evidence“.)
9. What is the optimal level of rule evasion? (See my 2020 work-in-progress “Tom Brady’s Footballs“.)
10. Is Chegg evil? (See my 2021 work-in-progress “The Chegg Conspiracy“.)

Bonus meta-questions: Can ChatGPT generate novel research questions on its own? Either way, will ChatGPT end up generating the equivalent of a real-life Borgesian “Library of Babel“?

Why doesn’t ChatGPT have a sense of humor? Last year, I posted an essay titled “Do Grasshoppers Dream of Impartial Spectators?”, where I review two books: Our Great Purpose: Adam Smith on Living a Better Life by Ryan Patrick Hanley and Law and the Invisible Hand: A Theory of Adam Smith’s Jurisprudence by Robin Paul Malloy. The title of my double review is a play on words of Philip K. Dick’s dystopian science fiction novel Do Androids Dream of Electric Sheep? In my case, however, the reference to “grasshoppers” is to Walt Disney’s Jiminy Cricket, who famously admonished Pinocchio to “let your conscience be your guide”, while the reference to “impartial spectators” is to Adam Smith’s imaginary internal judge who reviews the moral status of one’s actions (see here, for example). So, just for kicks, I fed the question in the title of my essay into ChatGPT and got back the following short but humorless response:

It is unlikely that grasshoppers dream, as they do not possess the necessary brain structures for dreaming. Additionally, the concept of an “impartial spectator” is a philosophical concept that likely does not apply to grasshoppers.

For the record, I also explicitly asked ChatGPT to compare and contrast Walt Disney’s Jiminy Cricket and Adam Smith’s Impartial Spectator, and the results–along with a screenshot of Disney’s famous cricket character–are pictured below. Are there any lessons to be learned from this doomed intellectual exercise? For me, the main lesson is that ChatGPT’s sense of humor is somewhat underdeveloped.

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:

I won’t have much to say about Chapter 2 of Tom Bingham’s book Rule of Law (available here), which surveys several “historical milestones” in Anglo-American legal history, beginning with the Magna Carta of 1215 and concluding with the Universal Declaration of Human Rights of 1948. (Judge Bingham does include one “foreign” (i.e. non-English-language) milestone in his survey: the “The French Declaration of the Rights of Man and the Citizen“, which was adopted by France’s National Assembly in the summer of 1789 during the start of the French Revolution.) Alas, Bingham’s short history of the rule of law contains many omissions. He fails to explain, for example, why the ill-fated French Declaration of Rights was such an ineffectual legal document, one that failed to curb the violence of the Reign of Terror (1792-94) or prevent Napoleon’s consolidation of power in 1799, nor does Bingham have much to say–at least not in Chapters 1 or 2 of his book–about the English jury system, the hallmark of the English common law tradition and perhaps the single-most important aspect of the rule of law. Suffice it to say that, next time, I will not assign Chapter 2 to my students. Instead, I will assign John Langbein’s “The four epochs of jury trial in England” (available here) or his essay on “The English criminal trial jury on the eve of the French Revolution” (here). (Full disclosure: John Langbein was my favorite professor when I was his student at the Yale Law School.)

Back in 2015 I published a paper with the title “Why don’t juries try range voting?” In brief, range voting, also known as score voting, is a voting method in which voters give a score or rank to each candidate or issue, rather than just voting for a single candidate from a menu of candidates or voting up or down on each issue. The candidate with the highest average score is elected. (See, for example, the sample ballot pictured below.) If voters are voting on an issue, the issue is considered approved if the average score crosses a pre-determined threshold.

To cut to the chase, I asked ChapGPT: “Why don’t juries try range voting?” and got back the following well-reasoned response:

Juries in the United States typically use a form of majority voting called “unanimity voting” in which all jurors must agree on a verdict. Range voting is not currently used in jury deliberation because it is seen as more complex and time-consuming than the traditional voting methods used by juries. It may also be more difficult for jurors to understand and agree on a method for scoring or ranking the defendants or options. Additionally, the legal system generally favors clear and definite verdicts, and range voting may not provide such clear results.

My 2015 paper, by contrast, makes the case in favor of score voting in jury trials!

The Prisoner’s Dilemma and the Coase Theorem are two widely-cited ideas in economics and law. As it happens, one of my papers is titled “Does the Prisoner’s Dilemma Refute the Coase Theorem?,” which I co-wrote with my colleague and friend Orlando I. Martinez-Garcia back in 2014. We therefore fed the same question in the title of our paper into ChatGPT and got back this super-formal and uncreative response (see below) telling us that these two concepts are not directly related:

The Prisoner’s Dilemma and the Coase Theorem are two different concepts in economics. The Prisoner’s Dilemma is a game theory scenario in which two individuals must decide whether to cooperate or defect, with the outcome depending on the decisions of both players. The Coase Theorem, on the other hand, states that if property rights are well-defined and transaction costs are low, the allocation of resources in a market will be efficient regardless of the initial distribution of property rights. The two concepts are not directly related, and the Prisoner’s Dilemma does not refute the Coase Theorem. However, the presence of externalities, public goods, and the absence of well-defined property rights, the Coase Theorem doesn’t hold.

Unhappy with this answer, we then posed the following question to ChatGPT: “Could the prisoners in the Prisoner’s Dilemma avoid defecting if they could bargain with each other?” (i.e. if the prisoners could engage in Coasian bargaining) and got back a different answer:

If the prisoners in the prisoner’s dilemma are able to communicate and negotiate with each other, it is possible that they may be able to come to an agreement to not defect and cooperate with each other instead. However, this outcome would depend on the specific details of the situation, such as the level of trust between the prisoners and their willingness to cooperate. In some cases, the prisoners may still defect even if they can communicate, if they feel that the benefits of defecting outweigh the benefits of cooperating.

Note the last line of ChatGPT’s response: “In some cases, the prisoners may still defect even if they can communicate, if they feel that the benefits of defecting outweigh the benefits of cooperating.” By comparison, our 2014 paper concludes that “even when the prisoners are allowed to communicate and bargain with each other, there is some positive probability that they might not strike a Coasean bargain” and more specifically that “the probability of defection is a function of various factors, including such things as uncertainty, exponential discounting, and elasticity.”

In my next post, we will see how ChatGPT responds to an esoteric question about jury voting that I posed in the title of another paper of mine: “Why don’t juries try range voting?“

That is the title of my 2008 applied game theory paper in which I model the impasse over Puerto Rico’s political status as a three-person duel (or “truel”) and the question I fed into ChatGPT last night. Below the fold is the chat bot’s one-paragraph reply: