Justice Confused

Suppose that a house is robbed and police find a strand of the burglar’s hair at the scene of the crime. A suspect is in custody, and tests show that the strand matches his hair. A forensic scientist testifies that the chance of a random person producing such a match is 1/2000. Does this mean that there’s a 1999/2000 chance that the suspect is guilty?

No, it doesn’t. In a city of 5 million there will be 1/2000 × 5,000,000 = 2,500 people who produce a match, so on the basis of this evidence alone the probability that the suspect is guilty is only 1/2500.

In a 1987 article, William Thomson and Edward Schumann dubbed this “prosecutor’s fallacy.” Unfortunately, it’s matched by the “defense attorney’s fallacy,” which holds that the hair-match evidence is worthless because it increases the likelihood of the suspect’s guilt by a negligible amount, 1/2500. In fact it drastically narrows the range of possible suspects, from 5 million to 2,500, while failing to exclude the defendant, hardly cause for confidence.

Worryingly, Thompson and Schumann found an experienced prosecutor who insisted that if a defendant and a perpetrator match on a blood type found in 10 percent of the population, then there’s a 10 percent chance that the defendant would have this blood type if he were innocent and hence a 90 percent chance that he’s guilty. “If a prosecutor falls victim to this error,” they write, “it is possible that jurors do as well.”

(William C. Thompson and Edward L. Schumann, “Interpretation of Statistical Evidence in Criminal Trials,” Law and Human Behavior, 11:3 [September 1987], 167-187)

Fixing Dates

In 1899, British statistician Moses B. Cotsworth noted that recordkeeping could be greatly simplified if each month contained a uniform number of whole weeks. He proposed an “international fixed calendar” containing 13 months of 28 days each:

international fixed calendar

This makes everything easier. The 26th of every month falls reliably on a Thursday, for example, and statistical comparisons between months are made more accurate, as each month contains four tidy weeks with four weekends. (Unfortunately for the superstitious, every one of the 13 months contains a Friday the 13th.) A new month, called Sol, would be wedged between June and July, and an extra day, “Year Day,” would be added at the end of the year, but it would be independent of any month (as would Leap Day).

In 1922 the League of Nations chose Cotsworth’s plan as the most promising of 130 proposed calendar reforms, but the public, as always, resisted the unfamiliar, and by 1937 the International Fixed Calendar League had closed its doors. It left one curious legacy, though: George Eastman, the founder of Eastman Kodak, was so pleased with Cotsworth’s scheme that he adopted it as his company’s official calendar — and it remained so until 1989.

A Penny Saved


Ben Franklin’s “necessary hints to those that would be rich,” written around 1730:

  • The use of money is all the advantage there is in having money.
  • For six pounds a year you may have the use of one hundred pounds, provided you are a man of known prudence and honesty.
  • He that spends a groat a day idly, spends idly above six pounds a year, which is the price for the use of one hundred pounds.
  • He that wastes idly a groat’s worth of his time per day, one day with another, wastes the privilege of using one hundred pounds each day.
  • He that idly loses five shillings worth of time, loses five shillings, and might as prudently throw five shillings into the sea.
  • He that loses five shillings, not only loses that sum, but all the advantages that might be made by turning it in dealing, which, by the time that a young man becomes old, will amount to a considerable sum of money.
  • Again: he that sells upon credit, asks a price for what he sells equivalent to the principal and interest of his money for the time he is to be kept out of it; therefore, he that buys upon credit, pays interest for what he buys, and he that pays ready money, might let that money out to use: so that he that possesses any thing he has bought, pays interest for the use of it.
  • Yet, in buying goods, it is best to pay ready money, because he that sells upon credit expects to lose five per cent by bad debts; therefore he charges, on all he sells upon credit, an advance, that shall make up that deficiency.
  • Those who pay for what they buy upon credit, pay their share of this advance.
  • He that pays ready money, escapes, or may escape, that charge.
  • A penny sav’d is two-pence clear, A pin a day’s a groat a year.


From a letter from Benjamin Franklin to Samuel Mather, May 12, 1784:

You mention your being in your seventy-eighth year; I am in my seventy-ninth; we are grown old together. It is now more than sixty years since I left Boston, but I remember well both your father and grandfather, having heard them both in the pulpit and seen them in their houses. The last time I saw your father [Cotton Mather] was in the beginning of 1724, when I visited him after my first trip to Pennsylvania. He received me in his library, and on my taking leave showed me a shorter way out of the house through a narrow passage, which was crossed by a beam overhead. We were still talking as I withdrew, he accompanying me behind, and I turning partly towards him, when he said hastily, ‘Stoop, stoop!’ I did not understand him, till I felt my head hit against the beam. He was a man that never missed any occasion of giving instruction, and upon this he said to me, ‘You are young, and have the world before you; STOOP as you go through it, and you will miss many hard thumps.’ This advice, thus beat into my head, has frequently been of use to me; and I often think of it, when I see pride mortified, and misfortunes brought upon people by their carrying their heads too high.

B. Franklin.

Looking Up

Planetary economy will be a determining factor in the change of diet which the coming century must inevitably witness. Such a wasteful food as animal flesh cannot survive: and even apart from the moral necessity which will compel mankind, for its own preservation, to abandon the use of alcohol, the direct and indirect wastefulness of alcohol will make it impossible for beverages containing it to be tolerated. Very likely tobacco will follow it.

— T. Baron Russell, A Hundred Years Hence, 1905

Good Boy

Image: Wikimedia Commons

An epitaph in the Pine Forest cemetery in Wilmington, N.C., reads:

BORN SEPT. 24, 1894
DIED MAY 18, 1904


Actually, dogs commonly attended services in former times. Indeed, until the 19th century, they could be so numerous that churches employed “dog whippers” to remove unruly dogs during services. The Great Church of St. Bavo in Haarlem, the Netherlands, contains a carving of the hondenslager at work (above).

The 18th-century zoologist Carl Linnaeus used to attend mass with his dog Pompe. Linnaeus always left after an hour, regardless of whether the sermon was finished. It’s said that when he was sick Pompe would arrive at the service alone, stay for the customary hour, and depart.

“Heaven goes by favor,” wrote Mark Twain. “If it went by merit, you would stay out and your dog would go in.”

Box Scores


“It is probable that television drama of high caliber and produced by first-rate artists will materially raise the level of dramatic taste of the nation.” — RCA president David Sarnoff, 1939

“Television? The word is half Greek and half Latin. No good can come of it.” — Manchester Guardian editor C.P. Scott, 1928

“Television won’t matter in your lifetime or mine.” — Rex Lambert, The Listener, 1936

“Television won’t last because people will soon get tired of staring at a plywood box every night.” — movie producer Darryl Zanuck, 1946

“Television won’t last. It’s a flash in the pan.” — BBC school broadcasting director Mary Somerville, 1948

“How can you put out a meaningful drama or documentary that is adult, incisive, probing, when every fifteen minutes the proceedings are interrupted by twelve dancing rabbits with toilet paper?” — Rod Serling, 1974

“I hate television. I hate it as much as peanuts. But I can’t stop eating peanuts.” — Orson Welles, 1956

Skin Deep

Image: Wikimedia Commons

During the filming of Planet of the Apes in 1967, Charlton Heston noted “an instinctive segregation on the set. Not only would the apes eat together, but the chimpanzees ate with the chimpanzees, the gorillas ate with the gorillas, the orangutans ate with the orangutans, and the humans would eat off by themselves. It was quite spooky.”

James Franciscus noticed the same thing filming Beneath the Planet of the Apes in 1969. “During lunch I looked up and realized, ‘My God, here is the universe,’ because at one table were all the orangutans eating, at another table were the apes, and at another table were the humans. The orangutan characters would not eat or mix with the ape characters, and the humans wouldn’t sit down and eat with any one of them.

“I remember saying, ‘Look around — do you realize what’s happening here? This is a little isolated microcosm of probably what’s bugging the whole world. Call it prejudice or whatever you want to call it. Whatever’s different is to be shunned or it’s frightening or so forth.’ Nobody was intermingling, even though they were all humans underneath the masks. The masks were enough to bring out our own little genetic natures of fear and prejudice. It was startling.”

(From Joe Russo and Larry Landsman, Planet of the Apes Revisited, 2001.)

Addition and Subtraction


In Mathematical Applications of Political Science, University of Minnesota political scientist William Riker describes a worrisome voting paradox that unfolded in the U.S. House of Representatives in 1956. At issue was a bill calling for federal aid for school construction; an amendment was proposed that would have offered this aid only to states whose schools were integrated. The House was divided into three interest groups:

  • Republicans opposed federal aid in general but supported integration. They would have preferred no bill at all but favored the amended bill to the original.
  • Northern Democrats wanted the amended bill but would accept the original bill rather than have no bill at all.
  • Southern Democrats, whose schools were segregated, favored the original bill but would prefer to have no bill rather than accept the amendment.

education bill bloc preferences

Clearly the original bill would have passed, as the Democrats as a group preferred it to having no bill at all. But, following procedure, the House voted first on whether to accept the amendment, and here the Republicans and the northern Democrats combined to support it, since both preferred the amended bill to the original bill. The second vote addressed whether to accept the now-amended bill, and now the Republicans and the southern Democrats united to kill it, since both preferred no bill to the amended bill.

So the original bill was popular, and the proposed amendment was popular, but combining them led to the bill’s defeat. “As if it were not enough that the choice may depend on the voting order, this fact can be used to twist the outcome of the legislative process,” Riker writes. “It may be possible to create a voting paradox such that no action is taken by the legislature even though a proposed bill would have passed prior to the creation of the paradox. A legislator could introduce an amendment to create such a paradox, and if the voting order were just right, the amended proposal would then be defeated.”

Apportionment Paradoxes


Until 1911, the U.S. House of Representatives grew along with the country. Accordingly, when the 1880 census showed an increase in population, C.W. Seaton, chief clerk of the census office, worked out apportionments for all House sizes between 275 and 350, in order to see which states would get the new seats.

He was in for a surprise. The method was straightforward: Take the total U.S. population and divide it by the proposed number of seats in the House, rounding all fractions down. This would dispose of most of the seats; any leftover seats would be awarded to the states whose fractional remainders had been highest. But Seaton discovered an oddity:

alabama paradox

If the House had 299 seats, Alabama would get 8 representatives (because its remainder, .646, was higher than that of Texas or Illinois). But if the House had 300 seats it would get only 7 (the extra representative would now go to Illinois, whose remainder had surpassed Alabama’s). The problem is that the “fair share” of a large state increases more quickly than that of a small state.

Seaton called this the Alabama paradox. A related problem is the population paradox: If the method above had been used in 1901 to reallocate 386 seats in the House, Virginia would have lost a seat to Maine even though the ratio of their populations had increased from 2.67 to 2.68:

population paradox

Here, even though the size of the House has not changed, a fast-growing state receives fewer representatives than a slow-growing one.

In 1982 mathematicians Michel Balinski and Peyton Young showed that if each party gets one of the two numbers closest to its fair share of seats, then any system of apportionment will run into one of these paradoxes. The solution, it seems clear, is to start cutting legislators into pieces.

(These data are from Hannu Nurmi’s Voting Paradoxes and How to Deal With Them, 1999. Balinski and Young’s book is Fair Representation: Meeting the Ideal of One Man, One Vote.)