The Winner’s Curse

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In 1983, Max Bazerman and William Samuelson asked M.B.A. students in 12 Boston University microeconomics classes to estimate the value of each of four commodities: jars containing 800 pennies, 160 nickels, 200 large paper clips each worth 4 cents, and 400 small paper clips each worth 2 cents. Thus each jar had a value of $8.00, though the students didn’t know this. They asked the students to bid on the value of each commodity. The student whose bid came closest to the true value in each auction would win a $2 prize.

The average estimated value of all the commodities was $5.13, $2.87 less than the true value. But the average winning bid was $10.01, resulting in an average loss to the winner of $2.01. The average winning bid produced a loss in more than half of all the auctions.

This is the “winner’s curse”: The winner of an auction tends to be one of those who form the highest estimate of an item’s value — and hence one of those most at risk of overpaying.

“If an individual assumes that his or her bid will win the auction, this piece of data should indicate that the bidder has probably overestimated the value of the commodity in comparison to other competitors,” write Bazerman and Samuelson. “When the correct inference is drawn, the bidder should revise the estimate of the true value of the item downward and lower the bid accordingly. By failing to take this inference into account, the winning bidder risks paying too much for the ‘prize.'”

(Max Bazerman and William Samuelson, “I Won the Auction But Don’t Want the Prize,” Journal of Conflict Resolution 27:4 [December 1983], 618-634.)

| Society

Round Numbers

A curiosity attributed to a Professor E. Ducci in the 1930s:

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Arrange four nonnegative integers in a circle, as above. Now construct further “cyclic quadruples” of integers by subtracting consecutive pairs, always subtracting the smaller number from the larger. So the quadruple above would produce 22, 8, 38, 8, then 14, 30, 30, 14, and so on.

Ducci found that eventually four equal numbers will occur.

A proof appears in Ross Honsberger’s Ingenuity in Mathematics (1970).

| Science & Math

There and Back Again

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John and Mary drive from Westville to Eastville. John drives the first 40 miles, and Mary drives the rest of the way. That afternoon they return by the same route, with John driving the first leg and Mary driving the last 50 miles. Who drives the farthest, and by what distance?

Click for Answer
| Puzzles

Turn, Turn, Turn

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Image: Flickr

The Hoover Dam contains a star map depicting the sky of the Northern Hemisphere as it appeared at the moment that Franklin Roosevelt dedicated the dam. Artist Oskar Hansen imagined that the massive structure might outlive our civilization, and that the map could help future astronomers to calculate the date of its creation. The center star on the map, Alcyone, is the brightest star in the Pleiades, and our sun occupies a position at the center of a flagpole. The whole map traces a complete sidereal revolution of the equinox, a period of 25,694 of our years, and marks the point of the dam’s dedication in that period.

“Man has always sought to express and preserve the magnitude of his exploits in symbols,” Hansen said in 1935. “The written words are symbols arranged so as to preserve in objectified form the thought of man and to record his variant states, both mental and physical. All other arts are similar as to their symbolic significance. They take their place among the category of human endeavor simply as the interpreter of life to itself. They serve as an outer object typifying the inner process. They form the connecting link between the spiritual and the material world. They are the shadows cast by the realities of the soul.”

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Image: Wikimedia Commons
| Science & Math

Naming Change

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When Canada introduced its 1-dollar coin in 1987, it became known as the “loonie” for the loon on its back.

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When the Royal Canadian Mint introduced the 2-dollar coin in 1996, Canadians tried hard to find a comparable nickname. Though “toonie” or “twoonie” eventually won out, the list of failed suggestions included “doubloonie,” “doozie,” and the charming “moonie.”

Why moonie? Because the coin depicts the queen “with a bear behind.”

(Thanks, Ethan.)

| Language

Misc

  • Juneau, Alaska, is larger than Rhode Island.
  • After reading Coleridge’s Biographia Literaria, Byron said, “I wish he would explain his explanation.”
  • If A + B + C = 180°, then tan A + tan B + tan C = (tan A)(tan B)(tan C).
  • Five counties meet in the middle of Lake Okeechobee.
  • “Life resembles a novel more often than novels resemble life.” — George Sand

No one knows whether Andrew Jackson was born in North Carolina or South Carolina. The border hadn’t been surveyed well at the time.

| History · Literature · Quotations · Science & Math · Trivia

Vision

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In short my dear Friend you and I have been indefatigable Labourers through our whole Lives for a Cause which will be thrown away in the next generation, upon the Vanity and Foppery of Persons of whom we do not now know the Names perhaps. — The War that is now breaking out will render our Country, whether she is forced into it, or not, rich, great and powerful in comparison of what she now is, and Riches Grandeur and Power will have the same effect upon American as it has upon European minds.

— John Adams, letter to Thomas Jefferson, Oct. 9, 1787

| History

A Head for Letters

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On June 29, 1851, phrenologist J.P. Browne examined a subject he knew only as a “gentlewoman”:

In its intellectual development this head is very remarkable. The forehead is at once very large and well formed. It bears the stamp of deep thoughtfulness and comprehensive understanding. … This lady possesses a fine organ of language, and can, if she has done her talents justice by exercise, express her sentiments with clearness, precision, and force — sufficiently eloquent but not verbose. In learning a language she would investigate its spirit and structure. … In analyzing the motives of human conduct, this lady would display originality and power.

The subject was Charlotte Brontë. She had attended the reading with George Smith, presenting themselves as “Mr. and Miss Fraser.” Phrenology was fashionable at the time, and Charlotte, like many others, was willing to overlook its failures to appreciate its successes. Smith’s reading said, “He is an admirer of the fair sex. He is very kind to children. … Is active and practical though not hustling or contentious.” Smith found this “not so happy,” but Charlotte said, “It is a sort of miracle — like — like — like as the very life itself.”

| Literature