## Voting on Coin Distribution

Source

I got this problem from Rustan Leino, who got it from Sophia Drossopoulou.

I solved it and wrote up my solution.

Problem

100 coins are to be distributed among some number of persons, referred to by the labels A, B, C, D, .... The distribution works as follows. The person with the alphabetically highest label (for example, among 5 people, E) is called the chief. The chief gets to propose a distribution of the coins among the persons (for example, chief E may propose that everyone get 20 coins, or he may propose that he get 100 coins and the others get 0 coins). Everyone (including the chief) gets to vote yes/no on the proposed distribution. If the majority vote is yes, then that's the final distribution. If there's a tie (which there could be if the number of persons is even), then the chief gets to break the tie. If the majority vote is no, then the chief gets 0 coins and has to leave the game, the person with the alphabetically next-highest name becomes the new chief, and the process to distribute the 100 coins is repeated among the persons that remain. Suppose there are 5 persons and that every person wants to maximize the number of coins that are distributed to them. Then, what distribution should chief E propose?

Solution