prior probability

“A bet is a tax on bullshit”

Posted on February 20, 2014 by F. E. Guerra-Pujol

Or so says Alex Tabarrok, an economics professor at George Mason University and one of our intellectual role models. (We are revisiting Alex’s previous post on bets and beliefs, given that earlier this week we offered to bet on the outcome of the upcoming Hobby Lobby case–see our blog post immediately below for details. You can also read more of Alex’s thoughts on the relation between bets and beliefs here.)

In summary, here is the core of Alex’s argument (note that when Alex wrote these words he was defending Nate Silver’s willingness to bet on the outcome of the 2012 election) —

A properly structured bet is the most credible guarantor of rigorous disinterest. In order to prove his point, Silver is not required to take the Obama side of the bet! At the odds implied by his model (currently between 3 and 4 to 1) Silver should be willing to take either side of a modest bet. Indeed, we could hold a coin toss, heads Silver takes the Obama side, tails he takes Romney.

In fact, the NYTimes should require that Silver, and other pundits, bet their beliefs. Furthermore, to remove any possibility of manipulation, the NYTimes should escrow a portion of Silver’s salary in a blind trust bet. In other words, the NYTimes should bet a portion of Silver’s salary, at the odds implied by Silver’s model, randomly choosing which side of the bet to take, only revealing to Silver the bet and its outcome after the election is over. A blind trust bet creates incentives for Silver to be disinterested in the outcome but very interested in the accuracy of the forecast.

Overall, I am for betting because I am against bullshit. Bullshit is polluting our discourse and drowning the facts. A bet costs the bullshitter more than the non-bullshitter so the willingness to bet signals honest belief. A bet is a tax on bullshit; and it is a just tax, tribute paid by the bullshitters to those with genuine knowledge.

(As an aside, please note that Nate Silver, another of our intellectual heroes and author of The Signal and the Noise, used to write for the New York Times. He has since left The Times and is now working with ESPN.)

Furthermore, notice that Alex’s argument has direct application to legal discourse and legal commentary generally as well. Shouldn’t law professors and even legal commentators on TV be required to bet their beliefs? What do you think? Would law professors and other public intellectuals be more reasonable and intellectually honest if they had to bet on their beliefs?

Posted in Uncategorized | Tagged Bets and Beliefs | 2 Comments

Hobby Lobby Case, Part 2

Posted on February 19, 2014 by F. E. Guerra-Pujol

Yesterday, Professor Scott Gaylord and I discussed the religious rights of closely-held corporations under the religion clauses of the First Amendment, one of the main legal issues in Sebelius v. Hobby Lobby Stores, Inc., an important constitutional case which will be argued before the United States Supreme Court next month (25 March, to be more precise). In summary, some family-owned businesses, such as Hobby Lobby, are objecting to the so-called “HHS mandate” under the Affordable Care Act (Obamacare). Note: “HHS” refers to the Department of Health and Human Services, a federal agency which requires all private firms with more than 50 employees to provide health plans that cover all FDA-approved contraception and sterilization procedures.

After Professor Gaylord carefully and patiently explained why the HHS mandate violates the constitutional rights of these private companies (you can read his full argument, all 70 pages of it, here), I began my talk by offering the following simple wager–I offered to bet $100 (at even odds) that the government will win the Hobby Lobby case, and I also offered to bet (at 10 to 1 odds) that the Supreme Court’s decision in favor of the government would be a unanimous decision.

Why am I so certain about the outcome of this case, so certain that I was willing to bet a small sum of my own money on its outcome?

Here’s why: The owners of the Hobby Lobby are objecting to the contraception coverage part of the HHS mandate on religious grounds. In brief, their argument is that the government is forcing them to finance immoral medical procedures that directly contradict their deeply held religious beliefs. (As an aside, they aren’t objecting to all form of contraception but only to such contraceptive products as Plan B (the morning-after pill) and Ella (the week-after pill) because these types of contraceptives don’t just prevent pregnancies; they abort actual embryos.)

The problem with this logic, however, is that some persons also object to such products like vaccines on religious grounds. Other religious persons object to blood transfusions. Yet others object to all forms of medical care. So, are those parts of the HHS mandate that cover vaccines, blood transfusions, and medical care generally (depending on the religious person doing the objecting) to be declared unconstitutional? That would be an absurd result. Hence my willingness to bet real money on the outcome of this case.

Alas, my bet had no takers.

Posted in Uncategorized | Tagged Supreme Court, Wagers | 2 Comments

Hobby Lobby Case

Posted on February 18, 2014 by F. E. Guerra-Pujol

Hobby Lobby Case

All are invited to attend the Fourth Annual Professors Debate at the Dwayne O. Andreas School of Law in Orlando, Florida from 4:45 to 6 pm in Room ALC 203. Professor Scott Gaylord, Jennings Professor and Emerging Scholar at Elon University School of Law, and I will discuss the legal issues in Hobby Lobby v. Sebelius, an important constitutional law case which has been set for oral argument before the United States Supreme Court next month.

Posted in Uncategorized | Tagged Law, Religion | Leave a comment

The most dangerous road in the world

Posted on February 17, 2014 by F. E. Guerra-Pujol

According to this report in the Sunday Times, it’s Highway 1 in Afghanistan. Here is an excerpt from the Times’ report:

After spending billions of dollars upgrading and repaving Highway 1, the [US-led] military coalition is now leaving its protection almost entirely to Afghan forces like the soldiers of the Afghan Army’s Sixth Battalion, Fourth Brigade, 203rd Corps. They patrol one of the world’s most dangerous roads like beat cops, responding to domestic disputes and traffic accidents, as well as hidden explosives and sniper fire. Their struggles, which are many, offer glimpses into the road war’s new contours.

Will the Afghan forces be able to protect this vital ring road from the Taliban? If you were an advisor to Afghan President Hamid Karzai, what policies would you recommend for protecting Highway 1 from sabotage and direct attacks (e.g. electric fences, 24-hour patrols, etc.)? If you were an advisor to the Taliban, what strategy would you propose for disrupting traffic on this road (IEDs, destruction of bridges, etc.)? Remember, the Highway 1 ring road is over 2000 kilometers long, and each side in this war has limited manpower and resources, so the real question we are asking is this–how much of your resources would you invest in protecting or attacking Highway 1?

Map courtesy of the examiner.com.

Posted in Uncategorized | Tagged Arms Races, War | 1 Comment

What is the optimal speed limit on toll roads?

Posted on February 16, 2014 by F. E. Guerra-Pujol

Is it 80 mph? 90? 100? You tell me …

Posted in Uncategorized | Tagged Economics, Law | Leave a comment

A map of the largest moon in our solar system

Posted on February 14, 2014 by F. E. Guerra-Pujol

A Map of Jupiter's Moon Ganymede, Where We Might Be Able to Live

Adam Clarke Estes has posted on Gizmodo this interactive map of Ganymede, one of Jupiter’s moons, which also happens to be the largest moon in our corner of the universe. Ganymede is an extra special Jovian satellite because it has an underground ocean and is one of our solar system’s few potentially habitable environments. In the words of Mr Clarke Estes:

The map is a little intimidating at first, but once you delve into it, you’ll realize that exploring the geography of Ganymede isn’t so different from exploring the geography of Earth. Different colors represent the different elements that make up the moon’s surface creating an almost marbled look as the minerals run together. Of course, Ganymede would need a little work before we can colonize it. But let’s just hope we never have to.

So instead of Mars, should NASA or SpaceX be planning a mission for the Moon of Ganymede instead?

Posted in Uncategorized | Tagged Ganymede, Space Colonization | 1 Comment

“What if we got rid of likes?”

Posted on February 13, 2014 by F. E. Guerra-Pujol

That is the title of this provocative essay by PJ Vogt. Even WordPress, the sponsor of this blog, has a like button (see below). But “likes” are lame, right? So, why don’t we get rid of them? Here’s why, according to Mr Vogt:

There’s a million reasons why no social media platform wants to get rid of whatever version of Like it has. At its most basic, getting a Like gives you a tiny dopamine hit. It makes you want to post again. And as you notice which of your posts get more Likes, you start to write more posts like those. Which means you’re focus-grouping your dog pictures to make them grabbier. So that your friends enjoy it more. So that they stay on the site longer. So they, in turn, create more posts. And on and on. As a human though, this is kind of crappy. It’s not all that fun to have your most mundane public communications get network notes from your friends. Or rather, it’s fun in the moment, and wearying in the long run. Part of me yearns for a place where I can publicly talk to the people I know without being graded.

prior probability agrees with Mr Vogt on both counts: we love the feeling when someone “likes” what we have to say, but at the same time, it does feel like we are being graded. But what’s wrong with that?

Posted in Uncategorized | Tagged "Likes", Social Media | 2 Comments

Pascal’s Wager 101

Posted on February 11, 2014 by F. E. Guerra-Pujol

Did you know that Blaise Pascal’s most important contribution to the theory of probability is the notion of expectation value? Briefly, the expected value of any given wager is the value of the prize multiplied by the probability of winning the prize. The earliest, and perhaps the most ingenious, illustration of this idea appears in Pascal’s quixotic philosophical treatise, Pensées (Penguin edition, pp. 123-124). In one of his essays, Pascal offers a rational argument (as opposed to purely religious or faith-based reasons) for believing in God.

In summary, Pascal’s famous wager can be expressed mathematically as follows: consider a strategy set (S) containing two choices: one can either believe in God (S₁) or be an Atheist (S₂). Now, let p be the probability that God exists, and 1 – p the probability that God does not exist. In essence, belief in God is like a bet or a coin toss, and given the structure of this game, there are four possible scenarios or outcomes:

(1) You choose strategy S₁ (i.e., you bet on God’s existence), and God does, in fact, exist. Under this happy scenario, you will be rewarded handsomely with eternal life in Heaven and infinite joy and happiness. We further assume that the value of this heavenly reward approaches infinity (∞).

(2) You choose strategy S₁, but it turns out that there is no God. Given this state of affairs, you obtain a negative payoff –c. We assume that c is a negative value, lesser than 0, because of all the lost time one may have wasted during one’s lifetime praying to a non-existent God.

(3) You choose strategy S₂ (i.e., you bet against God, so to speak), but it turns out that God does exist, after all. Under these circumstances, you will be punished with eternal damnation and misery for betting against God, with a value of negative infinity (–∞).

(4) You choose strategy S₂ and there is no God. Given these conditions, one will obtain a reward b in which b is greater than 0 but less than infinity (0 < b < ∞). We assume that b has a positive value, since instead of wasting your time on prayers, one was able to engage in other, more productive pursuits.

Given these payoffs, we can express the expectation value (EV) of believing in God as follows:

EV(S₁) = (p)(∞) + (1 – p)( –c)

And similarly, the expectation value of the Atheist is as follows:

EV(S₂) = (p)( –∞) + (1 – p)(b)

If p is zero, then it pays to be an Atheist, since b is greater than –c. The problem, however, is that no one knows with mathematical certainty whether there is a God, and even if the probability that God exists is miniscule, the expected value of believing in God is infinity. Therefore, according to the logic Pascal’s Wager, the safe or rational bet is to believe in God.

Of course, there is just one small problem with Pascal’s brilliant analysis–it assumes there is just one true God. But what if the Christian God is not the same as the Jewish God or Moslem one? What if, in short, there is more than one possible God? Which one should you worship or believe in?

Posted in Uncategorized | Tagged Expectation Value, God, Probability | 6 Comments

Trust and collaboration

Posted on February 10, 2014 by F. E. Guerra-Pujol

Why do most elite colleges and institutions of higher learning (including law schools) resort to proctors and complex rules to prevent cheating on exams? Why don’t we trust our students to do the right thing, like they do at Caltech? (*) According to this fascinating report, for example, undergraduate exams at Caltech are regularly taken at home and are never supervised or proctored.

Caltech’s “Honor Code” is short and simple — “No member of the Caltech community shall take unfair advantage of any other member of the Caltech community” — and Caltech students are routinely given 24-hour access to labs, workshops, and other facilities on campus. Moreover, Caltech tells its undergraduates from day one that “collaboration on homework and other assignments is not just encouraged, it’s practically essential for success.”

The report mentioned above also features some interesting remarks by Markus Meister, a professor of biology at Caltech. According to Professor Meister, “The expectation is that students will follow the rules without being proctored. Proctoring is not part of the repertoire — many of the finals are take-home.” Professor Meister was himself a Caltech student 30 years ago, and he remembers the huge degree of trust placed in him and his fellow students. “I took a lot of take-home exams – it is a challenge to complete stuff in three hours and usually you don’t finish, so you draw a line and say ‘this is where I got to in three hours’ and then you continue. The teaching fellow might only give you credit for what you did in the three hours.”