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Following part 5 of @Lateral fractal answer to "Handy Hints for Committing to the Beta" on the meta

"Have fun! No fun = No play. No play = No beta. I'm sure I'm not the only one to feel that a fresh private beta is like unwrapping an early Christmas present."

and in order to complement the question "What was economics like as a field before Adam Smith, the father of modern economics?", I propose the following contest:

  • Let us try to elect the "best earliest" written instance of economic thought.

Answers should contain a short description of the work at stake with proper reference and dates, and votes by users will decide of the winner.

Without a single hope of success, I suggest that people vote according to the following criterion

$$ Vote_i(answer~a) = \begin{cases} 1, \qquad \text{if } u_i(e_a,d_a) \geq T_i \\ 0, \qquad \text{if } u_i(e_a,d_a) < T_i\end{cases} $$

where $r_a$ is your subjective assessment of the degree of "economicness" of the described work, $d_a$ is the date at which the work was written, and $u_i$ and $T_i$ are a utility function and threshold of your choice.

Good luck to everyone!

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Feel free to disagree with this kind of "contest" questions. I have seen them used somehow succesfully in other SE site I am ready to be told that there is no room for them on Economics.SE in general, or in the beta in particular. (By "used successfully" I mean that they are both fun to answer and read AND that they bring about interesting answers) – Martin Van der Linden Nov 20 '14 at 18:46
+1: I like the idea! – jmbejara Nov 20 '14 at 18:48

I was recently amazed to discover instances of computational social choice in The Nine Chapters on the Mathematical Art, the Chinese counterpart of Euclid's element, written by several generations of scholars from the 10th up to the 2nd century BCE.

The core issues in social choice theory is the question of fair allocation, or fair collective decision. Once an allocation rule is devised, it remains to make it applicable. One of the topics of computational social choice is precisely to build efficient algorithm to compute the solution of allocations rules given some inputs.

This is precisely the topic of chapter 3 and chapter 6 of The Nine Chapters on the Mathematical Art, which are entitled (resp.) "Proportional Distribution" and "Fair Levies". The two fair division rules considered are the proportional division and the weighted proportional division rule. These rules are taken as given. They are not justified in any axiomatic way in the book, which would be the standard practice in modern social choice theory. Yet algorithm are proposed to apply them which in my views makes it a legitimate early instance of computational social choice ( because it answer the question "given this allocation rule, how can we compute its solution for any possible inputs?" at a time when the answer to this question was far from obvious for the allocation rules considered).

Some example problems you will find in chapter 3 :

(All the examples below are taken form the excellent commented edition of the Nine chapters by Kangshen Shen, John N. Crossley, Hui Liu Oxford University Press, 1999. This edition contains great references to instances of these problem in written sources from other civilization, such as in Euclid's Elements)

[Problem 1]

" Now Given five officials of different ranks : Dafu, Bugeng, Zanniao, Shangzao, and Gongshi jointly hunting 5 deers. Tell : how many does each get if [the deer are] distributed according to their ranks?"

[Problem 2]

"Now given a cow, a horse and a sheep have eaten up the seedlings of someone's field. The landlord demands 5 duo of millet as compensation. The shepherd says : "My sheep eats hals as much as the horse." The horse owner says : "My horse eats half as much as a cow." The compensation is to be distributed according to the rates. Tell : how much should each repay?"

An example problems you will find in chapter 9 :

[Problem 1]

"Now given the task of transporting tax millet is distributed among four counties. County A, 8 days from the tax bureau, has 10 000 households; County B, 10 days from the bureau, has 9500 households; County C, 13 days form the bureau, has 12350 households; County D, 20 days from the bureau, has 12 200 households. The total tax millet is 250000 hu needing 10000 carts. Assume the task is to be distributed in accordance with the distance from the bureau and the number of household. Tell : how much millet should each county transport? How many cart does each county employ?"

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Game Theory in the Talmud by Robert J. Aumann discusses a bankruptcy problem and a variety of fair division problems of a contested sum from the Talmud, a document written roughly between 200 and 500 CE. For example:

A fascinating discussion of bankruptcy occurs in the Babylonian Talmud 2 (Ketubot 93a). There are three creditors; the debts are 100, 200 and 300. Three cases are considered, corresponding to estates of 100, 200 and 300. The Mishna stipulates the divisions shown in Table 1. When the estate is 100, it is divided equally; since 100 is the smallest debt, this makes good sense, as pointed out above. The case in which the estate is 300 appears based on the different – and inconsistent – principle of proportional division. The figures for an estate of 200 look mysterious; but whatever they may mean, they do not fit any obvious extension of either equal or proportional division. A common rationale for all three cases is not apparent.

Behavioral Despair in the Talmud uses similar techniques on a related class of problems.

The story of King Solomon and splitting the baby (Judgment of Solomon) could be interpreted as an early example of a truthful revelation mechanism from approximately 1,000 BCE.

16 One day two women[a] came to King Solomon,

17 and one of them said: Your Majesty, this woman and I live in the same house. Not long ago my baby was born at home,

18 and three days later her baby was born. Nobody else was there with us.

19 One night while we were all asleep, she rolled over on her baby, and he died.

20 Then while I was still asleep, she got up and took my son out of my bed. She put him in her bed, then she put her dead baby next to me.

21 In the morning when I got up to feed my son, I saw that he was dead. But when I looked at him in the light, I knew he wasn’t my son.

22 “No!” the other woman shouted. “He was your son. My baby is alive!” “The dead baby is yours,” the first woman yelled. “Mine is alive!” They argued back and forth in front of Solomon,

23 until finally he said, “Both of you say this live baby is yours.

24 Someone bring me a sword.” A sword was brought, and Solomon ordered,

25 “Cut the baby in half! That way each of you can have part of him.”

26 “Please don’t kill my son,” the baby’s mother screamed. “Your Majesty, I love him very much, but give him to her. Just don’t kill him.” The other woman shouted, “Go ahead and cut him in half. Then neither of us will have the baby.”

27 Solomon said, “Don’t kill the baby.” Then he pointed to the first woman, “She is his real mother. Give the baby to her.”\

1 Kings 3:16-28 Contemporary English Version (CEV)

The book Biblical Games: Game Theory and the Hebrew Bible argues that many of the stories in the Hebrew bible can be understood as reputation games between the creator of the universe and the Jewish people. Further, in many cases the equilibrium outcomes of these games are consistent with traditional understanding of the meaning of these stories. According to the Documentary hypothesis many of the earliest such stories of the bible were written about 1,000 BCE but the earliest stories are set about 2,000 BCE or even earlier.

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I never heard of this, but it seems fascinating, thank you! – DornerA Apr 8 at 16:20

Fair division: from cake cutting to dispute resolution (Brams (1996)) claims that the following text from Hesiod’s Theogony (sometime in 750 and 650 BCE) is the earliest recorded example of an envy-free (but not regret free!) fair division problem:

For when the gods and mortal men had a dispute at Mecone, even then Prometheus was forward to cut up a great ox and set portions before them, trying to deceive the mind of Zeus. Before the rest he set flesh and inner parts thick with fat upon the hide, covering them with an ox paunch; [540] but for Zeus he put the white bones dressed up with cunning art and covered with shining fat. Then the father of men and of gods said to him: “Son of Iapetus, most glorious of all lords, good sir, how unfairly you have divided the portions!” [545] So said Zeus whose wisdom is everlasting, rebuking him. But wily Prometheus answered him, smiling softly and not forgetting his cunning trick: “Zeus, most glorious and greatest of the eternal gods, take which ever of these portions your heart within you bids.” [550] So he said, thinking trickery. But Zeus, whose wisdom is everlasting, saw and failed not to perceive the trick, and in his heart he thought mischief against mortal men which also was to be fulfilled. With both hands he took up the white fat and was angry at heart, and wrath came to his spirit [555] when he saw the white ox-bones craftily tricked out: and because of this the tribes of men upon earth burn white bones to the deathless gods upon fragrant altars. But Zeus who drives the clouds was greatly vexed and said to him: “Son of Iapetus, clever above all! [560] So, sir, you have not yet forgotten your cunning arts!” So spake Zeus in anger, whose wisdom is everlasting; and from that time he was always mindful of the trick, and would not give the power of unwearying fire to the Melian1race of mortal men who live on the earth. [565]

The text is dense, but what is happening is the classic solution to the fair division among two players where one (Prometheus) of the payers divides the cake (here an ox) and the other (Zeus) chooses which half he prefers.

Another Greek example from Mechanism design comes from A Toolbox for Economic Design

During the Classical Period in Athens (479—322 BCE) direct government taxation was not feasible, and the city-state of Athens resorted to the private provision of some important public goods, such as the fleet necessary for the defense of the city. The Athenians devised the liturgical system to deal with this, a system that deserves to be much better known especially in the world of economics. The New Oxford American Dictionary offers this as its second entry for the word liturgy. “(in ancient Athens) a public office or duty performed voluntarily by a rich Athenian.”

At the center of the liturgical system was the trierarchy, which meant the “command, outfitting, and maintenance of a war ship for one year’ ‘ (Kaiser, 2007, page 445) . The war ship this refers to is the trireme, a fast galley with three banks of oars that proved very effective in the Battle of Salamis against the Persian Navy, which Persian king Xerxes had to watch being destroyed from a nearby hill in 479 BC. This battle was decisive in repelling the Persian threat to what is now mainland Greece, and it is no accident that the Classical Period is taken to start in the year of the Battle of Salamis. The intrigue that the trierarchy holds for us is not the same as for history buffs. It was a remarkable institution that maintained a high level of support for the Athenian fleet by wealthy Athenians for a long time by giving them the right incentives.

The burden and honor of the trierarchy fell on the members of the landowning classes. These individuals had visible wealth, self-proclaimed wealth, and actual wealth, to use categories relevant for the trierarchy. There was a strong incentive to hide part of one’s wealth. This could easily allow wealthy citizens to shirk their liturgical duties. The institution of trierarchy was an early example of a mechanism, a concept we discuss in this chapter and formally define in section 2 . Its purpose was to make the true wealth of citizens become apparent so they would not be able to shirk their duties. Athens was governed then by the boule, a council chosen randomly from the population of citizens. The council did not observe the true wealth of citizens, it only observed visible wealth, such as land holdings, slaves, and mines. Once it identified the wealthiest citizens, it imposed trierarchy duties on them. If an individual was assigned such a duty, he could either perform the duty or attempt the antidosis challenge. This challenge meant that the citizen charged with the trierarchy duty could point his finger to another citizen and say that the latter is wealthier and hence more fit to carry out the duty than himself. The challenged citizen had three options: (a) agree that he is wealthier than the challenger and take on the trierarchy duty; (b) disagree that he is wealthier than the challenger and offer to swap his visible wealth for the challenger’s visible wealth so that the challenger would perform the duty but with the challenged individual’s wealth at his disposal; or (c) disagree that he is wealthier than the challenger and let the court decide, based on the court’s subsequent investigation of the wealth of the challenger and the challenged.

This system had a purpose: in modern economic terms, it was aimed at securing the efficient provision of the public good of national defense. It was also sophisticated in that it took account of the incentives of individuals to free-ride, and actively counteracted them. The study of social goals and institutionalized incentive systems to achieve the goals is at the heart of this book. We turn now to a more general discussion of social goals and incentives embodied in institutions as an introduction to our methodical investigation of the topic in the rest of the book. Rest assured that we will return to the fascinating antidosis challenge system for the trierarchy when we have developed enough of the necessary theoretical tools to see how it provided incentives for people to perform their duties.

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