Voting on how to distribute coins
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?
If he proposes equal distribution rest all will refuse so that if E leaves they can get more money.
So the above given distribution is the best.
A and B will refuse.
If D refuses, E leaves. then D will have to propose.
To stay safe he needs at least one more vote, then he’ll break the tie.
at the most he can safely propose :
if he takes any more all others will definitely refuse and he won’t get anything.
So, there’s no point in D refusing to E’s proposal.
if C is given more than what D gets, he might refuse on account of jealousy!!
though C might refuse, this is the safest possible distribution that E can come up with.
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