Team Players

In human societies, if some individuals fail to cooperate in joint enterprises, there’s often an institution that imposes sanctions on them. If there isn’t, people seem to be willing to punish them directly, even at a cost to themselves. How does that behavior get started? How does a cooperative society “get off the ground”?

In 2007, researchers from Harvard University and the University of Vienna created a model in which individuals can choose either to receive a secure income or to play a risky game. Those who choose to play the game can either pay a fee or choose not to. The fee supports an investment, the proceeds of which are distributed among all the players. If enough of the players pay the fee, then everyone benefits. But if too many players opt out of paying the fee, then the remaining donors suffer.

In order to avoid that situation, the donors are allowed to impose a penalty on the freeloaders, but this incurs a cost for them, so not every donor will choose to enforce it. So overall there are four strategies: nonparticipants don’t play the game at all; freeloaders play but choose not to pay the fee; contributors pay the fee but choose not to impose penalties on the freeloaders; and enforcers play the game and punish the freeloaders.

After many rounds of computer simulation, the researchers were surprised to find that when participation in the game was mandatory, most of the players became freeloaders, and the game fell apart because no one was willing to pay the fees. Adding enforcers at this point couldn’t save the game — they could make no headway against the freeloaders.

But when opting out of the game was permitted — when players could choose to receive a secure income instead of playing the game — many of the freeloaders simply withdrew, leaving behind contributors, enforcers, and a few freeloaders. And now the resulting game was stablest if the enforcers dominated the group, since they ensured that everyone cooperated. If contributors began to outnumber enforcers — that is, if the group became unwilling to punish freeloaders — then the freeloaders took over and everything fell apart again.

“The paradoxical result is that cooperation can be enforced by penalizing freeloaders, but only if participation in the community is voluntary,” writes George Szpiro in A Mathematical Medley. “This reminds us that discipline in the dreaded foreign legion, which legionnaires join of their own free will, is legendary. In the compulsory army, on the other hand, it is often in rather short supply.”

(Christoph Hauert et al., “Via Freedom to Coercion: The Emergence of Costly Punishment,” Science 316:5833 [2007], 1905-1907, via George Szpiro, A Mathematical Medley, 2010.)

| Society

Math Notes

Andrew Bremner devised a magic square that expresses 652 as the sum of three squares in six different ways (the sum of each row and column):

152 202 602
362 482 252
522 392 02

(From Edward Barbeau, Power Play, 1997.)

| Science & Math

Autumnal

There was a young fellow called Hall,
Who fell in the spring in the fall;
‘Twould have been a sad thing
Had he died in the spring,
But he didn’t, he died in the fall.

— Anonymous

| Poems

Duet

In 1924 cellist Beatrice Harrison was playing to the birds in her Oxted garden when “I suddenly stopped and thought, ‘Why should I be the only being to have the joy of hearing the nightingale and the cello sing together? If only it were possible for people, even at the other end of the world, to hear him, those who have never heard the most exquisite bird sing.'”

The BBC resisted her idea at first — no wild bird had ever been broadcast before — but on May 19 they arranged a live performance in the garden, and “the nightingale burst into song as I continued to play. … I shall never forget his voice that night, or his trills, nor the way he followed the cello so blissfully. It was a miracle to have caught his song and to know that it was going, with the cello, to the ends of the earth.”

The broadcast was heard by about a million people; those who had radios relayed it by telephone to friends who didn’t. She played again the following week, and again the following year, and received thousands of letters, some addressed to “The Lady of the Nightingales” or “The Garden of the Nightingales, England.”

The only listener who remained unimpressed was her gardener. “I loves your music, Miss,” he told her, “but I do wish it didn’t attract them birds the way it do. They eats up all the fruit, something cruel.”

(From her 1985 autobiography, The Cello and the Nightingales.)

| Art · Technology

An Army of Two

https://books.google.com/books?id=6GA9AAAAYAAJ&pg=PA9

Doubtful but interesting: In June 1814 two British warships marauded Scituate Harbor in Massachusetts, burning and capturing American vessels. Militia member Simeon Bates fired cannon shots after them from his lighthouse on Cedar Point. When a ship returned in September, only Bates’ wife and daughters were at the lighthouse, so 21-year-old Rebecca grabbed 17-year-old Abigail, took up a fife and drum that the militia stored there, ran behind a range of cedars, and played “Yankee Doodle” to suggest that the militia was returning. The British withdrew.

The story is supported only by the two sisters’ recollection, and Rebecca identified the ship as La Hogue, which turns out not to have been near Scituate at the time. “But Rebecca might have simply misidentified the ship, and she and her sister swore the story was true, even signing affidavits to that effect,” writes Eric Jay Dolin in Brilliant Beacons. “Many locals, siding with the two intrepid sisters, believed it too.”

(“Along the South Shore,” Harper’s New Monthly Magazine 337:57 [June 1878], 1-14.)

| History

Two Quizzes

King William’s College, on the Isle of Man, has posted the 2018 edition of its General Knowledge Paper, “The World’s Most Difficult Quiz.”

“The King William’s College General Knowledge Paper (GKP) has been frustrating and intriguing a select group of quiz connoisseurs since 1904. The paper consists of 18 sets of 10 questions, each set covering a particular theme, which in many cases is far from obvious. Cracking the theme has long been one of the attractions to devotees of the GKP.”

Answers will be published on the school website at the end of January. A warning: “A Latin phrase is always printed at the top of the quiz: Scire ubi aliquid invenire possis ea demum maxima pars eruditionis est. Freely translated, this means ‘The greatest part of knowledge is knowing where to find something’. However, be warned — using Google or a similar search engine may not always deliver the expected results!”

At the same time, the Royal Statistical Society has released its annual Christmas Quiz.

“For the last quarter-century, the Royal Statistical Society has published a fiendishly difficult Christmas quiz to entertain puzzle fans over the festive break – and this year’s special 25th anniversary edition, devised by Dr Tim Paulden, is sure to get the cogs spinning after a glass or two of mulled wine. Cracking the 15 problems below will require a potent mix of general knowledge, logic, and lateral thinking – but, as usual, no specialist mathematical knowledge is needed.” The entrant or team that scores the most points wins a subscription to the society’s magazine, Significance.

(Via MetaFilter.)

| Puzzles

Oh

These three riddles have the same answer. What is it?

He who with his hands puts it together will not be poor, and he who buys it, does not wish to use it, and he who uses it, does not know it: now you guess what it is.

— Johannes Secundus (1511-1536)

There was a man bespake a thing
Which when the owner home did bring,
He that made it did refuse it:
And he that brought it would not use it,
And he that hath it doth not know
Whether he hath it yea or no.

— Sir John Davies (1569-1626)

There was a man who bought a thing,
The thing he bought, he did not want,
The man who sold it, could not use it,
The man who used it, did not know it.

— Every Other Saturday: A Journal of Select Reading, New and Old, April 26, 1884

Click for Answer
| Puzzles