[This problem was communicated to me by Sophia Drossopoulou.]

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?

[This problem and its solution caused my niece Sarah Brown to send me the following article from The Economist, which considers a human aspect of situations like these.]

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