The regularity of mass killings breeds familiarity. [….] Those who live in America, or visit it, might do best to regard them the way one regards air pollution in China: an endemic local health hazard which, for deep-rooted cultural, social, economic and political reasons, the country is incapable of addressing. This may, however, be a bit unfair. China seems to be making progress on pollution.
After posting about The Prosecutor’s Fallacy I recalled a similar case with the Defense in the O.J. Simpson trial. The issue was summarized in What is your favorite problem for an introduction to probability?:
… one of Simpson’s lawyers, Alan Dershowitz, noted that even though Simpson beat
his wife, that hardly mattered, because in the United States, four million women are
battered every year by their male partners, yet only one in 2,500 is ultimately
murdered by her partner (1 in 1000), so, by the ‘reasonable doubt’ criterion, this is
irrelevant. The jury found that argument persuasive, but it’s spurious. The relevant
question was what percentage of all battered women who are murdered are killed by
their abusers, which ain’t 1 in 1000, but rather 9 in 10.
For a clear explanation of the details see Chances Are, by Steven Strogatz, which is reprinted in his excellent book, The Joy of x: A Guided Tour of Math, from One to Infinity.
Notation: Prob(A) means “the probability of event A” and Prob(A|B) is “the probability of event A, given that event B has happened.”
Bayes’ Theorem: Prob(A|B)xProb(B) = Prob(B|A)xProb(A)
Now, Prob(A|B) and Prob(B|A) are often confused by even the most intelligent of people. The confusion often appears in legal cases and is sometimes called the Prosecutor’s Fallacy. Bayes’ Theorem relates these two distinct conditional probabilities.
Followed by a straightforward example of why this really matters.
Note the first “tip:”
01. Fake data nobody ever expects to see. If you’re going to make things up, you won’t have any original data to produce when someone asks to see it. The simplest way to avoid this awkward situation is to make sure that nobody ever asks. You can do this in several ways, but the easiest is to work only with humans. Most institutions require a long and painful approval process before anyone gets to work directly with human subjects. To protect patient privacy, any records are usually completely anonymized, so no one can ever trace them back to individual patients.
I have often wondered if such a thing would be possible, and what the consequences would be.
After being snowbound for 40 hours we were finally able to get out late Sunday morning. The first event: A family trip to a bookstore. There I found and bought a copy of The Big Con: The Story of the Confidence Man. I had read it decades ago, back in college or even high school. The author, David W. Maurer was a long time friend and colleague of my parents. When I saw The Sting a few years later I immediately noticed how closely it followed Maurer’s book and mentioned that to my father. Dad agreed, but that was done with without Maurer’s permission or any acknowledgement of his work. As noted here, a lawsuit followed.