Chance News 43
While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will be up to, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician.
The following Forooth! is from the January 2009 RSS News
Ageing Britain: Pensioners outnumber under-16's for the first time
Gordon Lishman, of Age Concern, pointed out that not only was the average Briton getting
older, but also faced longer periods of ill health in later life.The Guradian
22 August 2008
Second thoughts about test of racial bias
In bias test, shades of gray. John Tierney, The New York Times, November 17, 2008.
A recent study showed racial bias in the way that doctors treat their patients. Or maybe not. At the heart of the study of racial bias is the I.A.T. (Implicit Association Test). This is a computerized test that measures how quickly you associate good words with faces of white subjects, bad words with faces of black subjects. If you do this more rapidly than when you associate bad words with faces of white subjects and good words with the faces of black subjects, then you have a racial bias.
The test is widely used in research, and some critics acknowledge that it’s a useful tool for detecting unconscious attitudes and studying cognitive processes. But they say it’s misleading for I.A.T. researchers to give individuals ratings like “slight,” “moderate” or “strong” — and advice on dealing with their bias — when there isn’t even that much consistency in the same person’s scores if the test is taken again.
The researchers who have developed the I.A.T. argue that the test is very useful.
In a new a meta-analysis of more than 100 studies, Dr. Greenwald, Dr. Banaji and fellow psychologists conclude that scores on I.A.T. reliably predict people’s behavior and attitudes, and that the test is a better predictor of interracial behavior than self-description.
There have been calls to try to mediate the dispute between researchers who developed the I.A.T. and those who criticize it, but these have not led to anything yet.
After all the mutual invective in the I.A.T. debate, maybe it’s unrealistic to expect the two sides to collaborate. But these social scientists are supposed to be experts in overcoming bias and promoting social harmony. If they can’t figure out how to get along with their own colleagues, how seriously should we take their advice for everyone else?
Submitted by Steve Simon
1. What is the technical term for "lack of consistency" in results if the test is taken again? Why is this a problem?
2. What is the technical term for the ability of a test to "reliably predict people's behavior and attitudes"? Why is this important?
3. Take the test yourself at implicit.harvard.edu. Do you think it accurately reflects your personal prejudices (or lack thereof)? How else might you measure your personal prejudices?
BBC 4 discusses probability
The BBC4 has a series of programs wich are described as follows: "The big ideas which form the intellectual agenda of our age are illuminated by some of the best minds. Melvyn Bragg and three guests investigate the history".
A recent program discussed probability. The guests were Marcus du Sautoy from Oxford University,Colva Roney Dougal from St. Andrews University, and Ian Stewart from Warrack University. None of these are probabilists but Ian Stewart had discussed probability in several of his very nice books and discussed probability in his popular lectures.
The discussion is quite good. Of course they have to include the birthday problem and the Monty Hall problem but towards the end they discuss more serious probability contributions such as Bolzmanns's work in statistical physics and the role of probability in quantum theory and here of course they include Einstein's famous God does not play dice. It would to have more time to spend of some of the more interesting topics. However you, your students, and your Aunt Mary or Uncle George should enjoy this discussion.
Read the comments about the program here and see what you think of the audiance reaction.
Submitted by Laurie Snell
Heaven for the Godless?
New York Times, December 26, 2008
Op Ed, By Charles M. Blow
Gaming the Vote
William Poundstone is a wonderful writer. A previous book of his, Fortune’s Formula, was reviewed admiringly twice in Chance News: here and here. His latest book, Gaming the Vote: Why Elections Arne't fair (And what we can do about it [Hill and Wang], 2008 is almost as good and that is high praise. The book is that rare beast: amusing, informative, historical and technical. Many statistics textbooks treat the subject of data manipulation but this one provides an entirely new slant on exploitation of voting systems and how the procedures have been employed in the United States and elsewhere on the globe.
Kenneth Arrow’s Impossibility Theorem here dryly “says that if the decision-making body has at least two members and at least three options to decide among, then it is impossible to design a social welfare function that satisfies all these conditions [Arrow’s axioms] at once.” In loose, lay terms, "No voting method is fair", "Every ranked voting method is flawed", or "The only voting method that isn't flawed is a dictatorship." Poundstone brings the theorem to life with examples using Condorcet’s method and Borda’s method while giving the reader the background of disdain between the two 18th century French aristocrats. “Instant runoff” and “approval voting” are also discussed at length and found wanting but for different reasons. Poundstone devotes later pages to range voting as a democratic, practical way of avoiding Arrow; in fact, range voting is already used when it comes to rating restaurants, athletes, Utube videos, and a host of other activities but never thus far in political elections.
Go here to see short videos of him discussing the general ideas of his book.
1. Statisticians are quick to despair over the lack of statistical literacy on the part of the lay public but rarely concern themselves with their own lack of historical literacy. On page 65 can be found this surprising table regarding the presidential election of 1860:
Popular Vote (%)
What percentage of Chance News readers and contributors knew that Breckinridge and Bell each received more electoral votes than Douglas? What percentage of Chance News readers and contributors knew that Breckinridge and Bell together received a larger popular vote than Douglas? Does anyone know the first names of Breckinridge and Bell? According to here “At least five U.S. presidential elections have been won by the second most popular candidate. The reason was a ‘spoiler’—a minor candidate who takes enough votes away from the most popular candidate to tip the election to someone else. The spoiler effect is more than a glitch.” What where those five elections?
2. Facing off two at a time is known as Condorcet voting because of its 18th century advocate, Marquis de Condorcet, Marie Jean Antoine Nicolas de Caritat Condorcet, and makes perfect sense as in: if A is taller than B and B is taller than C, then A is taller than C. Unfortunately, while the concept of “taller than” always has this property of transitivity, “preferable to” often lacks transitivity and can thus, lead to the so-called Condorcet cycle. Find some common examples in life where transitivity is violated.
3. There is also the problem of the irrelevant alternative, an excellent example of which is found on page 50. When faced with the choice of apple pie vs. blueberry pie only, the customer chooses apple. However, moments later the waiter comes back and says cherry pie is also available and the customer switches to blueberry. Why does this sound totally irrational? Poundstone also has a real example from an ice skating competition where the gold and silver medal winners were forced to exchange places due to a subsequent skater finishing sixth. Conjure up a defense of these seemingly unreasonable switches.
4. Borda count is another way of voting. “The voter ranks all the candidates, from most to least preferred. This can be done by putting numbers next to the names on the ballot.” You merely “add up the numerical rankings given each candidate on all the ballots.” It turns out that the Borda count “may be better known to sports fans than to voters. The ’voters’ are sportswriters and the ‘candidates’ are players” and this method is used to determine trophies and standings in university as well as professional sports. Borda counts are, unfortunately, subject to “burying.” His example of burying is the Kennedy/Nixon race if there were a Nazi candidate as well. Democrats would have the following ranking in order to bury Nixon:
Republicans would have the following ranking in order to bury Kennedy:
If all the Republicans and Democrats engaged in burying, there is a good chance that Schickelgruber could win. Naturally, not all Democrats and Republicans will vote dishonestly, that is, “bury” the closest opposition, but Poundstone points out that the winner is “likely to be the major candidate whose supporters are less honest.” Justify the disheartening conclusion of that last sentence.
5. If you find this these results counterintuitive, indeed weird, note that a century after Condorcet and Borda, Charles Dodgson on his own reinvented each of the procedures because of his intense dislike of Henry George Liddell—the father of the eponymous Alice. To make matters even more bizarre, most of the animosity was due to the choice of the architectural design of a new belfry at Oxford’s Christ Church College.
6. Range voting” is not covered by Arrow’s theorem because it doesn’t deal with ranks and hence, at least in Poundstone’s evaluation, is a voting scheme which “captures voter sentiments admirably when everyone is completely honest. The surprising thing is that it also works well when people ‘cheat’.” Each candidate is given a score and rather like an American instructor who grades rather than ranks his students so that conceivably, all can get the top marks or all can get failing grades—highly unlikely should the instructor want to keep his job—or anything in between. Another supposed advantage of range voting is that it “can be run on every voting machine presently in use in America.” He adds, “Perhaps the most surprising thing about range voting is that no one seems (yet) to have found anything dreadfully wrong with it. The main concern you hear is that it is difficult.” Go to here for the latest regarding the on-going, interminable U.S. Senate election recount in Minnesota and the unfair comparison to Florida’s 2000 presidential vote. Now, what are your views on the difficulty—for the voter and for the machine—of range voting?
Submitted by Paul Alper