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.

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.

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.”

Before you are two piles of coins. One contains 4 coins and the other contains 1. If you like, you can keep the larger pile, give me the smaller, and end the game. Or you can pass both piles to me. In that case the size of each pile doubles and I’m given the same option — I can keep the larger pile and give you the smaller one, or I can pass both piles back to you, in which case they’ll double again.

We both know that the game will end after six rounds. At that point I’ll have the coins and will win 128 coins to your 32. You’d be better off stopping the game in round 5, when you’ll have 64 coins and I have 16. But, by similar reasoning, I’d prefer round 4 to round 5, and you’d prefer round 3 to round 4 … if we rely on each other to be purely rational, it seems your best opening move is to end the game at once and keep 4 coins. This is less than you’d make in round 6, but it appears that purely rational play will never reach that round.

In practice, interestingly, human beings don’t do this — almost no one stops at the first opportunity, even after several repetitions of the game. Why they do so is not clear — possibly they’re hoping that their opponent has not reasoned through the whole game, or perhaps they’re agreeing tacitly to cultivate the pot in hopes of being the first one to cash out abruptly; perhaps the satisfaction of anticipating such a victory makes the risk worthwhile.

In lab tests in 2009, economists Ignacio Palacios-Huerta and Oscar Volij found that only 3 percent of games between students ended in the first round, but 69 percent of games between chess players did so. This rose to 100 percent when the first player was a grandmaster. They conclude that the most important factor is common knowledge of the players’ rationality, rather than altruism or social preferences.

(Ignacio Palacios-Huerta and Oscar Volij, “Field Centipedes,” American Economic Review 99 (4): 1619–1635.)