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Balkinization
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Monday, September 07, 2009
Risk, Health Care, and Red America
Frank Pasquale
I agree with Andrew Koppelman's analysis of resistance to health insurance reform. But Red America's implacable opposition to the plans now debated in Congress has deeper ideological roots in a love of risk. As Thomas Edsall has observed, "A problem for Democrats . . . is the long tradition in the US of . . . venerating risk . . . and of a deep commitment to untrammeled individualism." Saturday, September 05, 2009
You have no idea
Andrew Koppelman
One of the classic justifications for democracy is that an accountable government will do a good job of looking after people’s needs, because the voters will reward the incumbents if they do that. The present health care reform struggles cast some doubt on this theory. It turns out that government can very publicly make a lot of people a lot better off, and it will not be rewarded, and in fact may be punished. Friday, September 04, 2009
Statistical Slumps
Ian Ayres
Crosspost from Freakonomics: My dad was a box salesman and once a year he’d take me on an overnight sales trip. My daughter and I continued the tradition recently with a “dad and daughter” trip to Boston. If you are driving on I-84 to Boston, we can recommend The Traveler Restaurant (where you get to choose three free books with your yummy meal), and in Boston, we loved kayaking at Charles River Canoe and Kayak. But it was during a trip to the Boston Science Museum that I had an idea about calculating statistical slumps. The museum has an excellent example of a Galton Box, an apparatus where balls are dropped at the top at a high board and have to bounce off a grid of evenly spaced pegs. If the pegs are spaced properly, when the ball strikes a peg, it has a 50-50 chance of bouncing to the right or to the left as it travels down. Here’s a YouTube clip of one in action: The a-ha moment of the demonstration is to see that the balls end up in the bins at the bottom in piles that approximate the perfect bell-curve shape of the normal distribution. The Galton Box (also known as the Quincunx) is related to Pascal’s Triangle because the triangle tells you the number of ways to reach a particular bin: For example, if a Galton box had four rows of pegs and five bins, there would be six (equally likely) routes to reach the middle bin. But notice that there is always just one way to reach the outermost most bin. It occurred to me that it would be pretty easy to derive a statistical standard for determining when an athlete was having a “statistically significant slump.” For example, Alex Rodriguez recently went through a homerless drought of 72 at-bats. Over his career, A-Rod has averaged one homer for every 14.2 at bats — suggesting there is about a 93 percent chance that he will not homer on any individual at bat. It would be crazy to say that he was in a home-run slump after failing to homer after just a few at bats. But the question is how many homer-less at bats is enough to be a statistically significant drought? The answer is 42. There is less than a 5 percent chance that Rodriguez would go homerless 42 times in a row — so we can reject the hypothesis (at a 5 percent level of statistical significance) that he is going homer-less merely as a matter of chance. You can calculate your own drought statistics for any sporting event (for example, how many losses does Tiger have to have before he’s having a statistically significant drought?) just by using the following formula: Athlete is having a statistical significant drought if: Total consecutive number of bad events > log(.05)/log(probability of single bad event) You can copy and paste the right-hand side of this inequality into Google, plugging in the probability of a single bad event (yes, Google is a calculator): For A-Rod going homer-less, you would Google: log(.05)/log(.93). If you want to know his statistical drought number for a 1 percent level of significance, you would Google: log(.01)/log(.93). If you think Tiger Woods has a 25 percent chance of winning any individual tournament, then he would be experiencing a statistically significant drought after: log(.05)/log(.75) = 10.4 consecutive losses. The revolution of statistics in sports reporting has to date been almost exclusively an increase in descriptive statistics. But these examples show how it might be possible for reporters to usefully include some tests of statistical significance in their reporting. Even now, it would be possible to test whether reporters start using the term “drought” only after a player experiences a statistically significant number of bad events. It might be fun to do a study to back out the implicit level of statistical significance that reporters require before they use “slump” or “drought.” I’d predict that this implicit level varies with how much they like the athlete — so that they would start using the term more quickly with regard to Rodriguez than, say, Jeter. Calculating the magic numbers for statistically significant droughts is also related to the civil rights problem of the “inexorable zero.” In the landmark 1977 employment discrimination case International Brotherhood of Teamsters v. United States, the United State Supreme Court was concerned because: “Between July 2, 1965, and January 1, 1969, [out of] hundreds of line drivers [hired] systemwide . . . [n]one was a Negro.” Footnote 23 of the opinion introduced a new phrase into the civil rights lexicon: “[T]he company’s inability to rebut the inference of discrimination came not from a misuse of statistics but from ‘the inexorable zero.’” The same formula for calculating statistical droughts can be used to calculate when zero hires becomes statistically inexorable. In fact, in this old post from the Balkinization blog, I calculate when we should start to feel BOGSAT anxiety from a “bunch of guys sitting around a table.” For me, it often kicks in at five. Thursday, September 03, 2009
In the Flooded Zone
Deborah Pearlstein
Cross-posted at Opinio Juris Wednesday, September 02, 2009
The Stevens Speculation
Deborah Pearlstein
I really did intend to be on vacation this last week, but I wanted to respond at least in some form, FWIW, to all the speculation about Justice Stevens' likely plans. My former co-clerks and I have of course been reading the recent reporting about his plans with interest (see, e.g., here), and it is true that hiring only one clerk (instead of his more typical 3-4) is unusual. I honestly don't know what his plans are, but I would not be surprised if they included retirement in the near term. It's a decision that would of course be understandable. He's served with extraordinary distinction for an extraordinary length of time. For those interested in reading more, UC Davis Law Review recently sponsored a symposium event honoring Justice Stevens and reflecting on the impact of his decisions on questions of equality, liberty, and security (Chevron and the like were certainly addressed by our security panel, but were of course noted throughout). In all events, his retirement will be a sad loss for the Court and the country whenever it comes. Still, I can think of few who deserve some uninterrupted rounds of golf (and tennis and swimming) more.
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Books by Balkinization Bloggers
Jack M. Balkin, Living Originalism (Harvard University Press, 2011)
Jason Mazzone, Copyfraud and Other Abuses of Intellectual Property Law (Stanford University Press, 2011)
Richard W. Garnett and Andrew Koppelman, First Amendment Stories, (Foundation Press 2011)
Jack M. Balkin, Constitutional Redemption: Political Faith in an Unjust World (Harvard University Press, 2011)
Gerard Magliocca, The Tragedy of William Jennings Bryan: Constitutional Law and the Politics of Backlash (Yale University Press, 2011)
Bernard Harcourt, The Illusion of Free Markets: Punishment and the Myth of Natural Order (Harvard University Press, 2010)
Bruce Ackerman, The Decline and Fall of the American Republic (Harvard University Press, 2010) Balkinization Symposium on The Decline and Fall of the American Republic
Ian Ayres. Carrots and Sticks: Unlock the Power of Incentives to Get Things Done (Bantam Books, 2010)
Mark Tushnet, Why the Constitution Matters (Yale University Press 2010)
Ian Ayres and Barry Nalebuff: Lifecycle Investing: A New, Safe, and Audacious Way to Improve the Performance of Your Retirement Portfolio (Basic Books, 2010)
Jack M. Balkin, The Laws of Change: I Ching and the Philosophy of Life (2d Edition, Sybil Creek Press 2009)
Brian Z. Tamanaha, Beyond the Formalist-Realist Divide: The Role of Politics in Judging (Princeton University Press 2009)
Andrew Koppelman and Tobias Barrington Wolff, A Right to Discriminate?: How the Case of Boy Scouts of America v. James Dale Warped the Law of Free Association (Yale University Press 2009)
Jack M. Balkin and Reva B. Siegel, The Constitution in 2020 (Oxford University Press 2009)
Heather K. Gerken, The Democracy Index: Why Our Election System Is Failing and How to Fix It (Princeton University Press 2009)
Mary Dudziak, Exporting American Dreams: Thurgood Marshall's African Journey (Oxford University Press 2008)
David Luban, Legal Ethics and Human Dignity (Cambridge Univ. Press 2007)
Ian Ayres, Super Crunchers: Why Thinking-By-Numbers is the New Way to be Smart (Bantam 2007)
Jack M. Balkin, James Grimmelmann, Eddan Katz, Nimrod Kozlovski, Shlomit Wagman and Tal Zarsky, eds., Cybercrime: Digital Cops in a Networked Environment (N.Y.U. Press 2007)
Jack M. Balkin and Beth Simone Noveck, The State of Play: Law, Games, and Virtual Worlds (N.Y.U. Press 2006)
Andrew Koppelman, Same Sex, Different States: When Same-Sex Marriages Cross State Lines (Yale University Press 2006)
Brian Tamanaha, Law as a Means to an End (Cambridge University Press 2006)
Sanford Levinson, Our Undemocratic Constitution (Oxford University Press 2006)
Mark Graber, Dred Scott and the Problem of Constitutional Evil (Cambridge University Press 2006)
Jack M. Balkin, ed., What Roe v. Wade Should Have Said (N.Y.U. Press 2005)
Sanford Levinson, ed., Torture: A Collection (Oxford University Press 2004) Balkin.com homepage Bibliography Conlaw.net Cultural Software Writings Opeds The Information Society Project BrownvBoard.com Useful Links Syllabi and Exams |