# Contest : earliest written instance of economic thought

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–2nd century BCE.

The core issues in social choice theory, is the question of fair allocation, or fair collective decision. Once a proposition for a fair 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 fair allocations problems.

This is precisely the topic of chapter 3 and chapter 6 of The Nine Chapters on the Mathematical Art, which titles are respectively "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 fair allocation rule, how can we compute its solution?" at a time when the answer to this question was far from obvious).

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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