Why did so many would-be Roman emperors refuse to update their priors? Hat tip to Flibidi via reddit (DataIsBeautiful).
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The geography of love
We found this fascinating romantic census of the United States via The New York Times. (Hat tip to Marginal Revolution for the pointer.) According to Hilarie Sheets of the Times, R. Luke DuBois became obsessed with the words people use to describe themselves in their online dating profiles. He joined 21 dating sites in every ZIP code in America, downloaded 19 million profiles, and algorithmically determined the most common word in each location, which he then inserted in place of the city names on his maps. “New York is ‘Now,’ Seattle is ‘Heartbreak,’ Atlanta is ‘God.’ Upper Peninsula of Michigan is dotted with ‘Masochist,’ ‘Depression,’ ‘Futile,’ ‘Rustic,’ ‘Fairytale.'”
The “Paradox of the Gatecrasher” is not a paradox
There is a sizable scholarly literature discussing the so-called “Paradox of the Gatecrasher,” a simple thought experiment introduced many years ago by British philosopher L. Jonathan Cohen, an evidence problem designed to test the proper role of statistics in law. (For a survey of this legal literature, see footnote 8 of our latest paper “Visualizing Probabilistic Proof.”) Briefly, Wikipedia presents the gatecrasher problem as follows:
Statistical syllogisms may be used as legal evidence but it is usually believed that a legal decision should not be based solely on them. For example, in L. Jonathan Cohen‘s “gatecrasher paradox”, 499 tickets to a rodeo have been sold and 1000 people are observed in the stands. The rodeo operator sues a random attendee for non-payment of the entrance fee. The statistical syllogism:
- 501 of the 1000 attendees have not paid
- The defendant is an attendee
- Therefore, on the balance of probabilities, the defendant has not paid
is a sound one, but it is felt to be unjust to burden a defendant with membership of a class, without evidence that bears directly on the defendant.
Notice, however, that Professor Cohen’s Gatecrasher Paradox is not really a paradox in the true sense of the word. In fact, it’s not even a mildly interesting problem, if you are a good Bayesian, that is. Why not? Because the statistical syllogism above only establishes a Bayesian prior, i.e. the initial probability that a randomly-selected attendee snuck in the rodeo without paying for his or her ticket. We still have to update our prior! Accordingly, let’s assume that the randomly-selected rodeo attendee in the example above is a man (let’s call him Mr X) and that our hypothetical Bayesian inquisitor is a woman (let’s call her Miss B). After finding her Bayesian prior, Miss B, our Bayesian puzzle-solver, would also ask Mr X to produce some scrap of evidence or proof that he paid for his rodeo ticket — a receipt, a ticket stub, a witness, etc. — and our Bayesian sleuth would then update her prior in a manner consistent with the evidence, including the lack of any evidence if that were the case.
Let’s solve the case of the gatecrasher
Shades of slavery (circa 1861)
According to Gareth Cook’s fascinating essay on the history of “infographics,” this was President’s Lincoln favorite map. Here is the opening paragraph of Mr Cook’s essay (emphasis ours):
Near the end of 1861, with the American Union crumbling, President Abraham Lincoln became obsessed with an unusual document. Nearly three feet in length, it appeared at first to be a map of the southern states. But it was covered with finely rendered shading, with the darkness of each county reflecting the number of slaves who lived there. South Carolina, the first to secede from the Union, featured a particularly dark coastline. Yet other parts of the South (like western Virginia) appeared as islands of lightness.
By the way, is the word “infographic” a useful or helpful term? Isn’t every map or image an “infographic” to a lesser or greater extent, depending on the purpose of the person who created it?
How easy is it to fix an NFL game?
Match fixing has occurred in soccer leagues around the world, so why should the NFL (or college football, for that matter) be any different? In fact, according to this devious report by Brian “The-Fix-Is-In” Touhy, it is much easier to “fix” or tamper with a North American football game than you might think. From a potential fixer’s point of view, the main problem for the fixer is finding a place where to place one’s bet, or in the words of Mr Tuohy: Continue reading
Posted in Deception, Economics, Law, Questions Rarely Asked, Sports
Tagged bets, Match-fixing
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All proof is probabilistic
That is the premise of our latest paper “Visualizing Probabilistic Proof.” (We’ve blogged about this paper before, but the latest draft of our paper is available on SSRN here and will be published in an upcoming volume of The Washington University Jurisprudence Review. By the way, our paper is full of diagrams and is “only” 37 pages long, which is short by law review standards!) In brief, in our probabilistic proof paper, we try to solve the Blue Bus Problem, a hypothetical puzzle often presented by law professors when they teach Evidence. Unlike most treatments of the Blue Bus Problem, however, our solution uses Bayesian methods. In a future post, we will talk about a related problem known as the Gatecrasher Paradox.
Annals of recursion
Hat tip: LargeCoinPurse, via reddit.
Infinite regress, bias, and the Coase theorem
In their paper “Motive attribution asymmetry for love vs. hate drives intractable conflict,” Adam Waytz, Liane Young and Jeremy Ginge appear to extend the logic of the Coase Theorem into the domain of politics. Specifically, Waytz, Young, and Ginge study the problem of “motive attribution asymmetry,” i.e., the belief that people who disagree with you have motives that are bad. Among other things, they found that “offering Democrats and Republicans financial incentives for accuracy in evaluating the opposing party can mitigate this bias …” This is an exciting and promising research agenda, but if we can pay people to be less biased, couldn’t we also pay people to be more biased as well? Consider, in addition, this hypothetical scenario, courtesy of Sandeep Baliga (emphasis by us): Continue reading
Posted in Economics, Law, Philosophy, Politics
Tagged Bias, Coase Theorem, Infinite Regress
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Chess piece survival rates
Someone on digg posted a variant of this question on Quora: “What are the chances of survival of individual chess pieces on average.” In reply, Oliver Brennan, a
Image credit: Oliver Brennan
Update (25 Oct. 2014): The excellent Ada Swanson interprets this probabilistic chess board as follows (emphasis ours):
The kings have the highest survival rate … because they can’t be taken. Rooks also tend to be hardy because they spend a lot of time at the back of the board and are generally more active in endgames. The knights and central pawns have the lowest survival rates. Many popular openings involve d and e pawns undertaking suicide missions, which are sometimes counter-attacked with c pawns. The wing pawns have a higher survival rate, prompting one forum user to comment …, “If you can’t be the king, be the little guy hiding in the corner.”
