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According to Wikipedia, there are some 178 breweries in Belgium, a small country about the same size as the State of Maryland … Yet it’s not just the sheer quantity of breweries in such a little country that astounds prior probability but also (from personal experience) the high quality of so many Belgian beers.
This blog is about the concept of “prior probability” and how it applies to life, love, and law. But what is a “prior probability”? Wikipedia offers the following technical definition of this concept: “… a prior probability distribution, often called simply the prior, of an uncertain quantity p … is the probability distribution that would express one’s uncertainty about p … It is meant to attribute uncertainty rather than randomness to the uncertain quantity. The unknown quantity may be a parameter or latent variable.” Here is an easier and simpler definition. Say there is some X which you are uncertain about (such as the total number of blue jelly beans in the jar below). Your prior about X represents your original or initial estimate of X. This idea is the foundation of Bayesian analysis and modern probability theory and has important implications in many different domains … Stay tuned for more.
There are reports that Major League Baseball will announce some player suspensions this Monday, 5 August. What is the probability that star player Alex Rodriguez will be suspended?
(a) No penalty
(b) Small suspension (e.g., until the end of the season)
(c) Big suspension (e.g., this season and all of next season)
(d) Lifetime ban
More importantly, where did you get your prior from and how confident are you in its accuracy?
Bonus Question: If b, c, or d occurs, what is the probability that A-Rod will appeal his suspension and still play for the Yankees this season?
This is not a mere academic or philosophical quibble. Here, for example, are various reports describing recent developments affecting the “rule of law” in Egypt, Israel, Italy, USA, and Zimbabwe. This parade of horribles is not meant to be a representative sample, but it does illustrate just how difficult it is to keep politics out of law.
Image of “Consensus Civilis” courtesy of http://www.kancelaria.info.kalisz.pl
This report in yesterday’s Times, which describes a thriving black market in China for phony receipts, begins thus:
“To begin to comprehend China’s vast underground economy, one need only visit this city’s major transportation depots and watch as peddlers openly hawk fake receipts. * * * Buyers use them to evade taxes and defraud employers. And in a country rife with corruption, they are the grease for schemes to bribe officials and business partners. Making them and using them is illegal in China … But demand is so strong that a surprising amount of deal-making takes place out in public.”
This fascinating report also raises a larger question about the relation between markets and morality. That is, just because people are trading doesn’t mean such trades are “efficient” or good for society. This is why markets need morality (and law) to work properly.
prior probability is sure you have heard of the famous placebo effect in medicine, but have you ever heard of “placebo buttons”??? Thanks (once again) to the amazing Tyler Cowen, I found this fascinating exposé of placebo buttons on David Craney’s cool blog You are not so smart:
“In many offices and cubicle farms, the thermostat on the wall isn’t connected to anything. Landlords, engineers and HVAC specialists have installed dummy thermostats for decades to keep people from costing companies money by constantly adjusting the temperature. According to a 2003 article in the Wall Street Journal, one HVAC specialist surmised that 90 percent of all office thermostats are fake (others say it’s more like 2 percent). Some companies even install noise generators to complete the illusion after you turn the knob.”
Can you think of any other possible placebos? What about law? Are hearings and other forms of legal process a kind of “legal placebo” used to fool the losing party into believing that the outcome is just?
Hat tip: Tyler Cowen of Marginal Revolution
Charles Fried, a law professor at Harvard, famously argued that a contract is a promise. We at prior probability, however, say that a contract is more like a bet.
Consider the relation between sports contracts in baseball and hitting success. When a team signs a player and pays him x dollars, there is always the risk that a player will not live up to his potential, that the x dollars (or some fraction thereof) will be misspent. (In this regard, Alex Rodriguez of the Yankees and Albert Pujols of the Angels come to mind.) This cool graphic published in today’s Times compares the level of salary (on the x-axis) with the number of hits (on the y-axis) for the ten highest-paid hitters on each Major League team. It shows that the relation between salary and success is not obvious. (It also shows the New York Yankees get the least bang for their buck.)
So, why don’t more teams use performance-based contracts to minimize this risk?
Legal positivism is an influential descriptive theory of law; its main claim, in brief, is that law and morality are separate. Along comes David Gray Carlson, a law professor at Yeshiva University, who recently published this thought-provoking paper on “Legal Positivism and Russell’s Paradox.” His paper on legal positivism is insightful, original, and non-trivial because it applies ideas from the world of mathematics–Russell’s Paradox and the axioms of Zermelo-Fränkel set theory–to the theory of legal positivism. But it was the following sentences in particular that stood out the most in my reading of his wonderful paper:
“What is positivism? In recent decades it has been difficult to say. But perhaps the core belief … is that law is not necessarily connected with morality. What is morality? Scandalously, positivim fails to provide an adequate definition beyond the claim that law is not necessarily connected with it.” (*)
Did Professor Carlson just stab the vampire-like theory of legal positivism in the heart with a stroke of his pen? (I say “vampire-like” since positivism attempts to suck morality out of the law.) At the very least Carlson has shown that legal positivism is a feeble theory of law … because without a working definition of ethics or morality, there is no way to test whether positivism is true as a descriptive matter!
(*) D.G. Carlson, “Legal Positivism and Russell’s Paradox,” Washington University Jurisprudence Review, 5(2): 257-288 (2013), p. 260 (footnote omitted). Cartoon courtesy of xkcd
Yesterday, the Committee on Energy & Natural Resources of the U.S. Senate held yet another committee meeting to hear testimony on the political status of Puerto Rico. (I say “yet another committee meeting” because Puerto Rico has been a de facto and de jure colony of the United States since the Cuban-Spanish-American War of 1898. Is there such a thing as too much due process? Why won’t Congress just vote up or down on whether to admit Puerto Rico as a State, which Congress has the power to do under Article IV of the Constitution?)
FYI, Puerto Rico has been a Commonwealth or non-State territory of the United States since 1952. A dwindling number of Puerto Ricans favor Independence, while the rest of Puerto Rico’s electorate is almost equally divided between Statehood and Commonwealth. If you love this subject as much as I do, you can watch yesterday’s 90-minute theatrical hearing here. Here is my summary of yesterday’s hearings:
In summary, supporters of Statehood and Independence want to take the current Commonwealth option off the ballot during the next political status vote. Supporters of Commonwealth cry foul, arguing that this would be a form of disenfranchisement. Statehood and Independence partisans reply in turn that the current Commonwealth status itself is a form of disenfranchisement, since the Commonwealth is territorial or colonial in nature.
prior probability‘s take is that Puerto Rico status politics is a prime example of Condorcet’s Paradox. We will be blogging more on this fascinating subject in the weeks to come, so in the meantime, tell me what you think … Should Puerto Rico become a State of the Union, remain a territorial Commonwealth, or become an independent Republic like Cuba or Panama?
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