The idea of converting 767s into tankers surfaced formally in February 2001, when Boeing proposed to convert 36 planes and sell them to the Air Force for $124.5 million each. The unsolicited bid was undercut by an Air Force study the same month -- drafted by a consulting arm of Boeing -- concluding that existing Air Force KC-135 tankers would be "viable through the year 2040" and that no new planes need be bought until after 2010.

... After the Sept. 11, 2001, terrorist attacksf Airlines had deferred commercial orders for 767s, and Boeing laid off thousands of employees at plants in Everett, Wash. But the Air Force had not even listed tankers among its "unfunded priorities" in 2001 ... The Air Force had no money to buy the tankers, so on Sept. 25, 2001, the company's top executives met with Darleen A. Druyun, then a senior Air Force acquisitions officer, at the Pentagon to work out a lease deal instead. ...

Under the contract, Boeing would produce 100 refueling tankers based on its 767-model airliner, a deal Dicks predicts would be expanded and eventually bring the giant weapons manufacturer $100 billion.

...

In December 2001, language authorizing the deal -- but providing no money -- emerged in legislation in what Hill veterans refer to as a "virgin birth," meaning it was inserted into the defense appropriations bill after the bill had passed the House and Senate ... Ted Stevens (R-Alaska), a longtime supporter of expanding federal leasing, has claimed credit for inserting the language. One month before he did so, he received $21,900 in campaign contributions from 31 Boeing executives at a fundraiser in Seattle, where Boeing has many employees.

Thirty of those contributors -- including executives from the Boeing division that makes 767s -- had not contributed to Stevens in the previous decade ... About 55 percent of the company's expected revenue of $49 billion this year will come from the federal treasury ...

"the Air Force appeared not so much to negotiate with Boeing as to advocate for it, to the point of" giving Boeing unusual control over pricing, and other terms and conditions.

In November 2001, the Air Force drafted a document spelling out what capabilities the new tankers must have. Col. Mark Donohue, an official in the air mobility office, promptly sent it to Boeing for private comment, and the company sought, and received, concessions so the requirements matched what the 767 could do. The Air Force agreed to drop a demand that the new tankers match or exceed the capabilities of the old ones.

... Boeing then strove to "prevent an AOA [analysis of alternatives] from being conducted," according to a Boeing briefing chart presented to top executives in late 2001 and other e-mails. This, too, surprised Coyle. An AOA "is done virtually every time"

... An Air Force financial consultant told Boeing at one point that it was good that attention was focused on Enron instead of "your illogical accounting posture," according to a Boeing e-mail.

... Moreover, the Institute for Defense Analyses, an independent think tank, told the Pentagon after a detailed study that the Air Force was overpaying by at least $21 million per plane and that the lease violated federal accounting rules.

... Critics of the deal have continued to complain about Air Force decisions to award Boeing a $5 billion sole-source maintenance contract for the new tankers and to permit the company to earn a 15 percent profit on the deal, or more than double what Boeing makes from commercial aircraft orders.

In New Mexico, poor families (those earning less than $13,000) pay 12.1 percent of their total income in state and local taxes compared to the richest residents (average incomes of $610,900) who pay 8.7 percent -- and only 6.3 percent after accounting for the tax savings from federal itemized deductions.

The most regressive state, according to the institute, was Washington, where poor families pay 17.6 percent of their total income in state and local taxes.

... Only eight [states] tax their wealthiest residents at rates as high as the poorest are required to pay.

Executive Summary

The human brain has evolved several mechanisms that helped us survive in the African veldt but now hinder us from understanding our world. Our brains see in terms of certainties instead of chances - we round "unlikely" to never and "likely" to now. I can observe my own brain working this way, but the evolutionary benefit is not obvious to me and I would like to read more. We see patterns when there is noise. This could be a direct result of evolution: a bias towards false positives prevents catastrophe at the cost of paranoia, which is a perfectly good tradeoff for hominids who usually die by age twenty but is not so good for, say, rational stock trading. Or, this could be a side-effect of simply having powerful pattern-recognition mechanisms. We see cause and effect when it doesn't exist. And we think in terms of natural numbers, not percentages.

Two examples of our evolutionarily triggered false conclusions: (this part is not from the book). I read a true story (in another book about risk and math, I think) in which the narrator asked a bunch of senior military leaders how many generals were "great." They conferred and said, about five percent. He then asked, how many battles does one have to win in a row to be a great general. They answered, "five in a row." If the chance of winning a battle is 50%, then the chance of winning five in a row is 1/2^5, or 1 / (2*2*2*2*2), or 1 / 32, or about 3%. In other words, there's no reason to think the typical "great" general is anything other than lucky, at least not until they rack up a bigger lead over random chance. The other example was similar, and applied to sports. The chance that purely random performance - shooting baskets, getting hits - will read to streaks during the course of a season is easily calculated, and it turns out that many or even most streaks in most sports are as frequent as you would predict from random chance. In other words, most streaks are just random chance. Since our brains are geared to recognize patterns and attribute cause to effect, we falsely see that someone is performing especially well, probably because they ate their lucky pasta before the game.

Gigerenzer outlines a number of common statistical mistakes, and I'll repeat the interesting ones here, skipping boring ones like confusing a 50% chance of rain tomorrow with the expectation of 12 hours of rain.

Risks expressed as probabilities are less understandable than risks expressed as frequencies. Compare:

  The probability that an asymptomatic woman aged 40-50 in region X
  has breast cancer is 0.8 percent.  If a woman has breast cancer, the
  probably is 90 percent that she will have a positive mammogram.  If
  a woman does not have breast cancer, the probability is 7 percent
  that she will still have a postive mammogram.  Imagine a woman who
  has a positive mammogram.  What is the probability that she actually
  has breast cancer?

  Eight of every thousand women [aged 40-50 etc] have breast cancer.
  Of these eight with breast cancer, seven will have a positive
  mammogram.  Of the remaining 992 without breast cancer, about 70
  will have a (false) positive mammogram.  Imagine a sample of women
  with positive mammograms.  How many actually have breast cancer?

It is the same problem expressed in two ways, and the second way is easier for most people. One thing that did confuse me in the book, though, is why Gigerenzer argues for physicians to use the second method instead of a third method:

  For every ten women with a positive mammogram, typically one
  actually has breast cancer.

Expression of relative risks without a base rate. Example: Mammography screening starting at age 40 reduces the risk of death by breast cancer by 25%. This seems like a convincing case for screening. However, the overall chance of dying from breast cancer is actually quite low; screening reduces the risk of death from breast cancer in the next 10 years from 0.4% to 0.3%. Once the consequences of the high rate of false positives, from stress to unnecessary surgery, is accounted for, the case for mammography screening is slim, especially if the effort put into mammography screening could instead be put into finding the real killers (i.e., smoking, poor nutrition, and lack of exercise).

Prosecutor's fallacy, confusing the chance of a match with the chance that, given a match, the defendent is not guilty. This also involves ignoring the base rate: If your DNA matches DNA found at the scene with a one in a million chance of a false match, this does not mean that the chance that you are the real killer is 999,999 in a million. If the only evidence differentiating you from the other 10 million Los Angelenos is the DNA, then there are nine other people in LA who will match, and thus only a one in ten chance that you are the right match. (And this assumes that the other links in the chain are not broken - ie, no lab error, no planted evidence, no possibility that you were at the scene and left DNA before or after the crime, or during a crime you didn't commit.)

Given a Monty Hall situation, you should switch doors.