6. [Bonus question: 1 bonus marks] A pirate ship has a captain and five crew. On
ID: 3145979 • Letter: 6
Question
6. [Bonus question: 1 bonus marks] A pirate ship has a captain and five crew. One day they raid a passing vessel and make off with a chest containing 33 gold bars. Since 33 is not a multiple of 6, they decide that a democratic way of dividing the gold is best They number themselves 1 through 6, with the captain being number 1 and the sailor who swabs the deck being nmber6. The highest numbered pirate makes a proposal about how to divide the gold, and the group votes on it. If the proposal is supported by at least half of the pirates, then the gold is divided as suggested. Otherwise, the proposer is killed and the process is repeated in the smaller group. All members of the group are awa re that (a) All pirates are greedy, and will vote against any proposal if, by waiting, they could get more gold later in the process (b) All pirates are bloodthirsty, and wll vote against any proposal in which they could get the same amount of gold later because it means the proposer is killed (c) All pirates have perfect logic skills Suppose you are pirate number 6. What do you propose? Does it matter?Explanation / Answer
Yes, it does matter and the question's answer can be proposed in such a way that if i am pirate number 6, i can get the maximum number of gold bars by passing the proposal through voting. Please find the below solution to the problem.
Since i am pirate number 6 so to understand the answer, we need to reduce this problem to only 2 pirates. So what happens if there are only 2 pirates (Pirate 1 and 2). Pirate 2 can easily propose that he should gets all the 33 gold bars. Since he constitutes 50% of the pirate, the proposal has to be accepted leaving Pirate 1 with nothing.
Now let’s look at 3 pirates situation, (Pirate 1, Pirate 2 and Pirate 3) knows that if his proposal does not get accepted, then pirate 2 will get all the gold and pirate 1 will get nothing. So he decides to bribe pirate 1 with one gold bar. Pirate 1 knows that one gold bar is better than nothing so he has to back pirate 3. Pirate 3 proposes {pirate 1, pirate 2, pirate 3} {1, 0, 32}. Since pirate 1 and 3 will vote for it, it will be accepted.
If there are 4 pirates, pirate 4 needs to get one more pirate to vote for his proposal. Pirate 4 realizes that if he dies, pirate 2 will get nothing (according to the proposal with 3 pirates) so he can easily bribe pirate 2 with one gold bar to get his vote. So the distribution will be {0, 1, 0, 32}
Pirate 5 needs 2 votes and he knows that if he dies, pirate 1 and 3 will get nothing. He can easily bribe pirates 1 and 3 with one gold bar each to get their vote. In the end, he proposes {1, 0, 1, 0, 31}. This proposal will get accepted and provide the maximum amount of gold bar to pirate 5.
Similarily, Pirate 6 (me) needs 2 votes excluding him to pass the proposal and if i die then Pirate 2 and 4 will get nothing so i will try to bribe Pirate 2 and 4 by giving 1 gold bar each and hence the distribution would be {0,1,0,1,0,31}
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