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)
" 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?"
"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 :
"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?"