King Solomon, thought by some to be the wisest man who ever lived, anticipated the economists concept of separating equilibria by about 3,000 years. In his most famous case, he proposed cutting a baby in half to separate the true mother and the false mother. The true mother said: “No, give him to the other woman,” whereas the claimed mother accepted the proposed deal. Not only did Solomon perceive a difference in risk preferences — he knew the true mother would not accept even a small chance of slicing the baby in half — but he anticipated that the false mother would not figure out how to pose as the true mother. The baby was placed in the true mother’s arms.
Recent archaeological discoveries have unearthed a lost scroll that detailed another separation decision by Solomon, where, once again, he uses risk to gauge preference intensity.
One day a wealthy man came to Solomon for advice. He observed: “I have two sons, X and Y. They are both fine boys, and help me administer my business. I do not spoil them, but they both receive an adequate income. Alas, the great sadness of my life is that they do not get along, and I must keep them apart so they do not quarrel. When I die, and fortunately my health is still good, one must get my business. The other will receive my worldly possessions, but alas the division will be unequal. The business is worth far more, and the burden to run it is not great. I cannot rely on either to provide an income interest to the other.
My sons are equally capable, and I love them equally. Today, knowing what the future portends, they both spend what they receive. But I know that some people receive more pleasure from consumption expenditures than do others. I would like to leave my business to the son who receives the greater pleasure. However, when I ask them, they both say their pleasure is immense. How shall I decide?”
Solomon responded. “The day after the second new moon, bring your sons to me, and we shall resolve this problem. I have but one constraint. You must let me resolve this problem, and you must remain silent as I do so.”
The man agreed and at the appointed day and time, the wealthy man and his two sons appeared before the king.
Solomon spoke to the sons. “Alas, the two of you do not get along. When your father passes from this Earth, his wish is that one of you receive his business, and the other his worldly possessions. You will then have no need for further contact with each other.
“But wonderful things do not come without sacrifice. You see before you a large jar with a scorpion and some leaves. One of you will place his hand in this jar for a period of time to risk his sting. The scorpion may not see your hand for a while. But even when seen, it will not look like his natural prey; it may be ignored. But should the scorpion sting, it will be intensely painful, and perhaps worse. I have a papyrus scroll for each of you. You will each go to a corner of the room and write down how many minutes you are willing to leave your hand in the jar to be the one who inherits the business.”
Solomon then explained how he would conduct this as a second-price auction, and the virtues of that method. The father was sad, because he did not want either son to risk the scorpion’s sting, but he got false succor from the second-price auction, thinking that it would lead to less time at risk. But most important, as promised, he remained silent.
The sons returned with their answer. X had written 2 minutes on his scroll. Y had written 30 minutes. Solomon, after looking at the responses, decreed: “The business shall go to Y upon your father’s death, because he is the son I have determined would reap greater benefits from the excess income that would offer. Moreover, Y need not place his arm within the scorpion’s bottle. That would be a deadweight loss, conceivably in the literal sense of that term. I was confident that neither of you would decipher this game. Just as I had no intention of dividing the baby in an earlier decision, I had no intention of forcing either of you to take a dreaded risk.”
Solomon continued: “Unlike judges in the democracies of future centuries, I do not have time to write down and justify my opinion. But I will explain to the court scribes the principles underlying my decision, so they may be recorded and available to future generations.“
The father failed to understand what happened but maintained his promise. When he died, Y took his business, X the worldly possessions.
Solomon’s Reasoning
King Solomon observed: “My job was to find a way to identify which of two sons would derive greater utility from a substantially increased income. I have spent many years receiving my many subjects, from rich, moderate and poor circumstances. I have struggled to perceive their levels of satisfaction. I have concluded that life in moderate or poor circumstances is much the same for all. But having riches separates men. Some are possessed of exquisite taste, and turn their riches to great consumptive pleasures, both for themselves and with their celebrations for the community. Others, alas, turn riches into little of value. They purchase ostentatiously to impress, and impress no one, not even themselves.
I label these groups connoisseurs and boors. A connoisseur benefits greatly from securing riches, and this possibility is, therefore, worth making great sacrifices for. Hardly so for the boor. My test was a simple one. Son Y showed himself to be a connoisseur by his willingness to take a substantial risk to win the business; son X gave away his boorish nature when he answered a mere two minutes.
I would like to claim originality for my method, but any fairy tale king who sent suitors into battle against dragons before they could claim his daughter’s hand understood the underlying principle: Any hopeful dragon slayer faced a 20% chance of death, with only an 80% chance of blissful marriage to the princess.
(History is written by the victors, which is why traditional accounts suggest better odds.) The fairy tale king in anticipating von Neumann and Morgenstern recognized the implicit requirement: .8U(marriage to princess) > U(status quo) – 2U(death)
Only the deeply devoted would have such a utility for marriage to the princess.”
If you’re interested in learning more about the reasoning, read the full paper.