prior probability

I wrote about my friendship with Orlando I. Martinez Garcia, who I first met in 2000 or 2001, in my previous reflection. To make a two-decade-long (and counting!) story short, Orlando’s love of mathematics and science eventually rubbed off on me and changed the entire trajectory of my research agenda. Although I continued to teach my introductory Roman law course as well as an upper-level seminar on The Federalist Papers, I became a full-fledged “legal realist” when it came to contemporary law–that is, I realized that appellate court decisions, especially in the area of constitutional law, were mostly just sloppy and shoddy ex post justifications of the judges’ own political preferences–so I wanted to find a more accurate way of modelling and predicting court decisions.

To this end, I decided to teach myself a branch of mathematics popularly known as game theory (see, for example, the image below). Among other things, I participated in an advanced research seminar on “institutional economics” at the Universitat Pompeu Fabra in Barcelona in the fall of 2005; I took Yale professor Ben Polak’s excellent online course on game theory (Econ 159) in the spring of 2007; and Orlando and I both attended NYU professor Rebecca Morton’s summer seminar on formal mathematical modelling at the University of Ljubljana in Slovenia in July and August of 2007. With these rigorous and time-consuming studies under my belt, I then began to write up a series of novel papers (two of them with Orlando Martinez himself!) applying a wide variety of mathematical methods to law. By way of example, below is a listing of my “top ten” formal papers–i.e. papers in which I thoroughly analyze an existing mathematical model (like the famous Prisoner’s Dilemma) or build a new one (like my algebraic model of the Coase theorem; see item #5):

1. A Game-Theoretic Analysis of the Puerto Rico Status Debate: Part 1 (2008)
2. A Game-Theoretic Analysis of Public-Private Partnerships in the Water Sector (2009)
3. A Game-Theoretic Analysis of the Puerto Rico Status Debate: Part 2 (2010)
4. Clones and the Coase Theorem (2011) (with Orlando)
5. Modelling the Coase Theorem (2012)
6. Modelling the Optimal Level of Rule Evasion (2013)
7. Does the Prisoner’s Dilemma Refute the Coase Theorem? (2014) (with Orlando)
8. The Poker-Litigation Game (2015)
9. The Colonel Blotto Litigation Game (2016)
10. So Long Suckers: Bargaining and Betrayal in Breaking Bad (2018)

At the same time, my interest in mathematical modelling would lead me to the wonderful world of probability theory, but that is getting ahead of my story. Rest assured, I will write about my conversion to Bayesian reasoning and subjective probability in a future “reflection” post. In my next post, however, I want to pay homage to a few of the other scholarly friends that I made while I was at the PUCPR law school in Ponce, P.R., including Jorge Cordava, Hector Cuprill, Julio Fontanet, Gustavo Gelpi, Ramon Antonio Guzman, Ruben Nigaglioni, Daniel Nina, Pedro Ortiz-Alvarez, Efren Ramos, and Carlitos del Valle.

Postscript: All ten of my papers mentioned above are available here via SSRN.

Update (1:17 pm): Since this post is dedicated to my colleague and friend Orlando I. Martinez-Garcia, I have added a picture of Orlando and I below the fold. (Orlando is on the left.)

I wrote about my transition into academia, including my sustained study of Roman Law, in my previous post in this series; today, I will write about my close friendship with Orlando Martinez Garcia, who began teaching full-time at the PUCPR law school in the fall of 2000 or 2001. Little did I suspect at the time that this new colleague would exert such a large influence on my intellectual life, for Orlando and I were complete opposites in many ways. I was quiet and shy, a lone wolf, while Orlando was always gregarious and outgoing, the life of the party. I was a meticulous planner, like a general preparing for battle. Orlando, by contrast, had a hurried-air about him; his personal credo was to “go with the flow.” At the same time, Orlando’s clothes and appearance were always impeccable (suit and tie), while I usually wore casual clothes, like cargo shorts and tennis shoes, and shaved only every other week.

Nevertheless, despite our outward differences and differing temperaments, I was won over by Orlando’s magnanimous personality, his can-do spirit, and his sincere and unpretentious demeanor. We soon became close friends, sharing a residence across the street from the law school, and we would often stay up late at night to discuss ideas, the crazier and more far-fetched the idea the better! One evening, for example, after dinner at our favorite local restaurant (Blankita’s), Orlando began to discuss the science of transmogrification, i.e. the instantaneous transportation of solid matter from point A to point B like in the popular science-fiction series Star Trek. True to form, we took opposing sides. I was the incredulous doubter and staunch skeptic; Orlando, the eternal optimist and resolute futurist. His face would light up and his ears twitch as he explained his wild-eyed theory to me. Suffice it to say, there we were, an unlikely pair of budding scholars debating the mechanics of transmogrification until the crack of dawn.

More importantly, our myriad late-night discussions—whether on campus, at a bar, or in his backyard—taught me the intellectual value of thought-experiments. First, a thought-experiment, especially an outrageous and far-fetched one like transmogrification, is often capable of producing the most rewarding and uncommon insights. Suppose, by way of example, that we could indeed transmogrify goods and even human beings across international borders, like in Star Trek. How would such a technological change affect law? Would immigration controls and protectionist tariffs become a thing of the past? Would the concept of the nation-state and the distinction between domestic and international law become meaningless? These were the questions that made our discussions so lively, unpredictable, and stimulating. In short, we are forced to reconsider the relationship between law and technological change.

Furthermore, who is to say that transmogrification will not become a viable method of transportation in the distant future? After all, the idea of traveling faster than the speed of sound on supersonic airplanes, the thought of supercomputers defeating chess grandmasters, and the possibility of landing men on the moon and returning them safely to Earth—were not these ideas once considered the fanciful inventions of deranged science-fiction writers? But above and beyond our late-night discussions what influenced me the most during this time (the first decade of the 2000s) was Orlando’s genuine love of mathematics and the natural sciences. To this day, he possesses more math and science books than law books, and his passion and enthusiasm for these subjects eventually rubbed off on me and my scholarly work …

 

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I will resume my reflections in my next post. For now, I just want to voice my support for cancelling or postponing the Olympics. Sorry, NBC, but public health is more important than selling ads. Also, why are so many universities (including my home institution) insisting on returning to in-person lectures in the fall? Why not wait until at least 75% of the local population is vaccinated or until we otherwise get the new “Delta variant” from India under control? In other words, if coronavirus cases are surging again, why are we letting our guard down now? What happened to “save grandma”?

I will resume my “reflections” in the next day or two; in the meantime, check out Seth’s Instagram page (@dudewithsign) here.

Thus far, I have reflected on my college and law school years and on my first few years in Old San Juan, Puerto Rico. Today, I will write about my transition into academia. At the time, I was an associate attorney at the largest law firm in Latin America, but truth be told I did not find the practice of law to be intellectually rewarding, so I was elated when in the spring of 1998 I was offered my first teaching job at the law school of the Pontificia Universidad Catolica de Puerto Rico (PUCPR), where I was assigned to teach two courses: (1) a new survey course on “The Evolution and Development of the Institutions of the Civil Law”, and (2) a two-semester course on the U.S. Constitution, and I could not have been happier! (Shout out to Charles Cuprill Oppenheimer (1916-2012), the venerable dean of the PUCPR law school, to whom I owe this happy state of affairs.)

During my first few years in academia, I decided to take an openly historical approach to my subjects. For my civil law lectures, for example I turned to the law of ancient Rome, consulting the Institutes of Gauis and the Corpus Juris Civilis. In addition to these primary Roman law sources, I read a wide variety of classics in legal history, legal theory, and anthropology, including books by Barry Nicholas, John Merryman, Oliver Wendell Holmes, Sir Henry Maine, and E. Adamson Hoebel. Summing up, like the renaissance humanists of the quattrocento, I turned to Roman Law and other bygone legal sources since the European civilian tradition and Puerto Rico’s civil law institutions can ultimately be traced back to ancient Rome. My students and I thus turned to history to discover and reconstruct the origins of the civil law in Western civilization, such as the evolution of delictal (i.e. tort) actions from the early lex talionis, to the more developed lex Aquilia of classical times, up to article 1802 of the Puerto Rico Civil Code.

Likewise, for my course on the United States Constitution, I began to read such classics as The Federalist Papers, Alexis de Tocqueville’s Democracy in America, and the judicial opinions of Chief Justice John Marshall. I also read the works of leading contemporary constitutional scholars, including Akhil Amar’s The Bill of Rights: Creation and Reconstruction, John Hart Ely’s Democracy and Distrust, and José Trías Monge’s masterful four-volume constitutional history of Puerto Rico. Moreover, instead of organizing my “conlaw” course around Supreme Court cases (as most conlaw professors do), I organized my course around the major historical events in U.S. history: the Revolution, the Founding, the Whiskey Rebellion, the Louisiana Purchase, the Seminole Wars, the Treaty of Guadalupe Hidalgo, etc.

Though this was only a beginning, it was a fairly productive period in my intellectual life. All told, I had devoured dozens of scholarly books and hundreds of academic articles, and I had prepared detailed and meticulous lecture notes and course outlines. Furthermore, it was only a matter of time before I moved from legal history to history qua history and to give serious and sustained thought to the problems of historical analysis. I eventually discovered a wonderful book entitled The Historian’s Craft, written by the French historian Marc Bloch, who was brutally executed by the Nazis in 1942. His was the most thoughtful book I had read about the work of the historian. He treated such eternal problems as subjectivity, historical causation, and historical time itself with such a degree of humility and humanity that his ideas have left a lasting impression on me.

Now that I look back on this transition, I cannot help but notice that, because of my historical focus, I hardly read any contemporary law cases, but little did I know that my most important intellectual development was yet to come, for I had yet to meet Orlando I. Martínez-Garcia, a future colleague and friend who would gently nudge me in a different direction …

I wrote about my college and law school years (1986 to 1993) in my previous two posts in this series; today, I will reflect on my first few years of “island life” in the Commonwealth of Puerto Rico (1993 to 1995). During that first fateful summer after law school (the summer of ’93), I bought my first car (a dark blue Jeep Wrangler with manual transmission), studied the intricacies of the Puerto Rico Civil Code and other areas of P.R. law at the University of Puerto Rico, where I took Professor Ernesto Chiesa’s excellent “JTS” bar review course (I passed the notoriously difficult P.R. bar exam on my first try), and began my legal career as an associate attorney at the prestigious firm of McConnell Valdes, the largest law firm in Latin America. But what I remember the most are not my material possessions or my early professional accomplishments. What I cherish the most from this time are my memories of the walled city of Viejo San Juan, one of the most romantic and magical places in the world. Like a moth attracted to light, I made my way to the old city as soon as I graduated from law school and checked in at the Gallery Inn on Norzagaray Street, overlooking the ocean-side neighborhood of La Perla. The legendary proprietress of the Gallery Inn, the artist Jan D’Esopo, put me in touch with a local realtor, Merce Roca, and that is how I somehow ended up renting the first floor of Ms Rosa’s charming colonial-era building on Calle Caleta de San Juan #58, between the Cathedral and La Puerta de San Juan, where I lived for the next 24 months. Ms Roca’s first-floor apartment had tall ceilings and was furnished with many pieces of Caribbean art–paintings, sculptures, even an old-fashioned barber’s chair–and the tall doors of the main living room and the small colonial-style kitchen all opened out into a garden. Moreover, I had to walk through the garden to reach the bedroom, which was nestled in a small cozy room behind the garden, where tiny tree frogs (the famed coqui) would sing their two-note lullabies late at night. Alas, all good things must come to an end. I eventually left Old San Juan behind when I bought my own place in the historic neighborhood of Miramar and began my academic career at the Catholic University of Puerto Rico, but my metaphorical heart will always belong to Old San Juan …

I will resume my “reflections” series in my next post; in the meantime, here are some of my favorite summer songs; enjoy …

I talked about my college years at UCSB in my previous “reflection”; today, I will talk about my Yale Law School years (1990 to 1993). Beyond the wonderful friendships I made during my three years of law school, several highlights stand out in my mind: (1) reading “The Problem of Social Cost” and being exposed to the “Coase theorem” for the first time in Guido Calabresi’s torts class; (2) finding out that most private property in the world is held in common (I discovered this fact while I was editing a large chunk of Bob Ellickson’s “Property in Land” law review article for Volume 102 of the Yale Law Journal); and (3) attending, along with a small handful of other Yalies, a Herbie Hancock concert as well as a guest lecture by the great Mexican writer and thinker Octavio Paz. (I had previously written my senior honors thesis in Spanish about one of Paz’s works.) In addition to these intellectual and cultural experiences, I twice had the privilege of being one of Steven M. Gillon’s teaching assistants for his survey U.S. history course. As part of my duties, I attended all of Professor Gillon’s excellent lectures and led two discussion sections every week. More importantly, that’s when I knew for sure that I wanted to become a college professor myself!

Starting today, I will be reflecting on some of the milestones in my life, beginning with my college years at UC Santa Barbara (1986 to 1990), the happiest time of my life! I took daily walks or bike rides along the beach and expanded my intellectual and cultural horizons, double-majoring in International Relations and Spanish Literature, and I also had the opportunity to live abroad two summers in Cuernavaca, Mexico. Suffice it to say I fell in love with Mexican culture and history and henceforth considered myself to be an honorary citizen of Mexico!

(As a postscript, looking back now, one of the most amazing aspects of my college years is the fact that, outside high-level military research circles, none of us had cell phones or email accounts, and furthermore, e-books and “learning management systems” like Canvas and Blackboard did not yet exist. What bliss!)

Below is the last (for now) but most important part of my Conspiracy Theory Betting Market proposal from my forthcoming paper “Betting on Conspiracies” (footnotes below the fold):

One practical objection to my proposal is that conspiracy theories generally refer to past events, like the JFK assassination, 9/11, or the election of 2020. The objection here is that one cannot use a market to “predict” a past event. In reality, though, betting markets are versatile and can be used for a wide variety of purposes beyond forecasting. Among other things, betting markets can provide financial services such as risk-management and the funding of public goods.[1] In addition, betting markets can be used to detect lies, encourage and protect whistleblowers, and provide decision makers with honest advice.[2] In principle, then, we should be able to extend betting markets to conspiracy theories as well.

The most serious practical objection to my proposal, however, is the “Who Decides?” question. Simply put, who decides whether a particular conspiracy theory is true or whether a particular claim or allegation is “fake news”? To the point, what separates actual or true conspiracies, like the assassination of the President of Haiti on July 7, 2021,[3] from improbable or far-fetched conspiracy theories, like Gödel’s “Leibniz Conspiracy”? In short, where should we draw the line, and how should we draw it? [Note to my readers: I devote the first two parts of my paper to Kurt Gödel’s “Leibniz Conspiracy”.]

To solve this dilemma, I would consider the creation a special “conspiracy court”–perhaps consisting of retired judges as well as randomly-selected citizen-jurors–and turn to the actual law of conspiracy.[4] This court would hold hearings and allow anyone to make arguments or present evidence. The court would then have to decide, does the alleged conspiracy theory satisfy the elements of conspiracy law?, perhaps using “the preponderance of the evidence” or “more likely than not” standard used in civil cases. That is, instead of asking whether a given conspiracy theory is simple or falsifiable or questioning the mental health of conspiracy proponents, we should be asking a series of practical or legal questions: (1) Is the agreement an illicit one? (2) Which conspirator has performed an overt act in furtherance of the conspiracy? And (3) which standard of proof should apply to the previous two questions?

By way of example, the general federal conspiracy statute, which is codified at 18 U.S.C. § 371,[5] defines a conspiracy as follows:

If two or more persons conspire either to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner or for any purpose, and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined under this title or imprisoned not more than five years, or both.

In other words, the crime of conspiracy refers to an illicit agreement between two or more persons, i.e. an agreement to commit a crime or a civil offense, such as common law fraud.[6] The conspirators must intend to achieve the goal of the conspiracy, and at least one of the conspirators must commit an “overt act” in furtherance of the conspiracy.[7] As an aside, it is worth noting here that a conspiracy need not be successful in order to constitute a crime; it is the illicit agreement itself that it is illegal, regardless of whether the conspiracy is successfully carried out beyond the commission of an overt act in furtherance of the conspiracy.[8] Given this well-developed body of law, a specially-constituted “conspiracy court,” as I have outlined here, could turn out to be an ideal neutral party that could be trusted with resolving the specific claims underlying the bets in my proposed market.[9] People will participate in a betting market only to the extent they trust that the methods and processes used to resolve bets are fair, accurate, and unbiased. A special “conspiracy court,” staffed with experienced judges and randomly-selected citizen-jurors and basing its decisions on the law of conspiracy, would go a long way to building and cultivating this trust.

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