Difference between revisions of "Chance News 82"

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==Martin Gardner's "mistake"==
==Martin Gardner's "mistake"==
[http://docserver.ingentaconnect.com/deliver/connect/maa/07468342/v43n1/s6.pdf?expires=1329338290&id=67229128&titleid=75000908&accname=Guest+User&checksum=00F4070339B8BAA7FC302598A2063EA7 “Martin Gardner’s Mistake”]<br>
[http://maa.publisher.ingentaconnect.com/content/maa/cmj/2012/00000043/00000001/art00006;jsessionid=yhdlpjo6p45s.alice “Martin Gardner’s Mistake”]<br>
by Tanya Khovanova, <i>The College Mathematics Journal</i>, January 2012<br>
by Tanya Khovanova, <i>The College Mathematics Journal</i>, January 2012<br>

Revision as of 02:03, 16 February 2012


"I focus on the most important form of innumeracy in everyday life, statistical innumeracy--that is, the inability to reason about uncertainties and risk."

--Gerd Gigerenzer

Submitted by Bill Peterson


“[The] ballad ‘Someone Like you’ … has risen to near-iconic status recently, due in large part to its uncanny power to elicit tears and chills from listeners. …. Last year, [scientists] at McGill University reported that emotionally intense music releases dopamine in the pleasure and reward centers of the brain, similar to the effects of food, sex and drugs. …. Measuring listeners' responses, [the] team found that the number of goose bumps observed correlated with the amount of dopamine released, even when the music was extremely sad.”

“Anatomy of a Tear-Jerker” (italics added)
The Wall Street Journal, February 11, 2012

Submitted by Margaret Cibes


Bruce Bueno de Mesquita has written a fascinating, readable book, The Predictioneer’s Game: Using the Logic of Brazen Self-Interest to See and Shape the Future. A lengthy and generally positive review of Bueno de Mesquita’s views may be found in a NYT article, Can game theory predict when Iran will get the bomb?, by Clive Thompson (12 August 2009).

His game-theory-based track record is indicated by:

For 29 years, Bueno de Mesquita has been developing and honing a computer model that predicts the outcome of any situation in which parties can be described as trying to persuade or coerce one another. Since the early 1980s, C.I.A. officials have hired him to perform more than a thousand predictions; a study by the C.I.A., now declassified, found that Bueno de Mesquita’s predictions “hit the bull’s-eye” twice as often as its own analysts did.

In the introduction to his book, Bueno de Mesquita says, “I have been predicting future events for three decades, often in print before the fact, and mostly getting them right.” Furthermore, “In my experience, government and private business want firm answers. They get plenty of wishy-washy predictions from their staff. They are looking for more than ‘On the one hand this, but on the other hand that’--and I give it to them.”


  1. In that NYT article may be found a statement shocking to the world of statistics and probability:

    Bueno de Mesquita does not express his forecasts in probabilistic terms; he says an event will transpire or it won’t.

    Why is this a shocking statement to statisticians and probabilists?

  2. In the NYT article is found the following criticism by Stephen Walt, a professor of international affairs at Harvard:

    While Bueno de Mesquita has published many predictions in academic journals, the vast majority of his forecasts have been done in secret for corporate or government clients, where no independent academics can verify them. “We have no idea if he’s right 9 times out of 10, or 9 times out of a hundred, or 9 times out of a thousand,” Walt says. Walt also isn’t impressed by Stanley Feder’s C.I.A. study showing Bueno de Mesquita’s 90 percent hit rate. “It’s one midlevel C.I.A. bureaucrat saying, ‘This was a useful tool,’ ” Walt says.

    Along these lines, suppose someone avers his hit rate is 100% when it involves forecasting a male birth, that is Prob (male predicted|male) = 1. Why might this be less than impressive?

  3. Another critic may be found here regarding a prediction about Libya.

    In February 2011 Bueno de Mesquita predicted that the unrest in the Arab world will not spread to such places as Saudia Arabia and ... Libya. Yes, Libya. Watch and listen carefully to the segment starting at 1:51 min into the interview.

    Other incorrect predictions made by Bueno de Mesquita are also noted on this web site, including what this author calls “The n factorial debacle” whereby Bueno de Mesquita misconstrues the number of possible interactions between n individuals (game participants). This web site also brings up the issue of the so-called “black swans” when it comes to predicting outcomes of the game. What is a black swan and why does a black swan have an impact on prediction?

  4. Brazen Self-Interest and its mathematical logic rest on game theory which asserts that morality or any other nicety is counter productive to achieving success. Bueno de Mesquita’s particular computer model starts with data of expert opinion and then somehow via simulation iterates to a conclusion. Comment on the problem of local minimums/maximums.
  5. Health care is in the news today as it was back in the 1990s. The NYT article notes that “In early 1993, a corporate client asked him to forecast whether the Clinton administration’s health care plan would pass, and he said it would.” The black swan in this instance was Congressman Daniel Rostenkowski who [page 125] “was the key to getting health care legislation through Congress.” Google Daniel Rostenkowski to see why Rostenkowski was a black swan and “contrary to my expectations, nothing passed through Congress.”

Submitted by Paul Alper

Flood of data means flood of job opportunities

The Age of Big Data, Steve Lohr, The New York Times, February 11, 2012.

If you like working with data, you have great career opportunities ahead of you. We are seeing an

an explosion of data, Web traffic and social network comments, as well as software and sensors that monitor shipments, suppliers and customer

This means a big deal for the job market.

A report last year by the McKinsey Global Institute, the research arm of the consulting firm, projected that the United States needs 140,000 to 190,000 more workers with “deep analytical” expertise and 1.5 million more data-literate managers, whether retrained or hired.

It is a trend that occurs in more than business. This article cites major changes in Political Science and Public Health. The article introduces a term "big data" which it defines as

shorthand for advancing trends in technology that open the door to a new approach to understanding the world and making decisions.

While the article extols the virtues of data analysis, for the most part, there are some cautionary statements.

Big Data has its perils, to be sure. With huge data sets and fine-grained measurement, statisticians and computer scientists note, there is increased risk of “false discoveries.” The trouble with seeking a meaningful needle in massive haystacks of data, says Trevor Hastie, a statistics professor at Stanford, is that 'many bits of straw look like needles.'

Now data analysis demanding more attention from business circles and more.

Veteran data analysts tell of friends who were long bored by discussions of their work but now are suddenly curious. “Moneyball” helped, they say, but things have gone way beyond that. “The culture has changed,” says Andrew Gelman, a statistician and political scientist at Columbia University. “There is this idea that numbers and statistics are interesting and fun. It’s cool now.”

Submitted by Steve Simon

Martin Gardner's "mistake"

“Martin Gardner’s Mistake”
by Tanya Khovanova, The College Mathematics Journal, January 2012

Martin Gardner first discussed the following problem in 1959:

Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

His answer at that time follows:

If Smith has two children, at least one of which is a boy, we have three equally probable cases: boy-boy, boy-girl, girl-boy. In only one case are both children boys, so the probability that both are boys is 1/3.

Gardner later wrote a "correction" to his original solution, indicating that “the answer depends on the procedure by which the information is ‘at least one is a boy’ is obtained.”

He suggested two potential procedures.

(i) Pick all the families with two children, one of which is a boy. If Mr. Smith is chosen randomly from this list, then the answer is 1/3.

(ii) Pick a random family with two children; suppose the father is Mr. Smith. Then if the family has two boys, Mr. Smith says, “At least one of them is a boy.” If he has two girls, he says, “At least one of them is a girl.” If he has a boy and a girl he flips a coin to choose one or another of those two sentences. In this case the probability that both children are the same sex is 1/2.

Khovanova discusses a number of other scenarios related to being given both the sex and the day of the week on which the given child was born. The results may surprise students - and/or probability amateurs like this Chance contributor.

The pdf file containing this article is accessible to all and contains active links to her references, which include two 2010 articles by Keith Devlin, both discussing day-of-the-week scenarios and real-life cultural differences which might impact solutions: “Probability Can Bite” and “The Problem with Word Problems”


Do you think that Gardner made a mistake? Why or why not?

Submitted by Margaret Cibes