Yes, there is a definite procedure. But you ask too much from it. They don't need to agree on the value of each item, for example, and they don't need to agree that the shares are equal. All they need to get is that each one is satisfied with his own share.
I think that any order of choosing allows for a possibility that some pirate gets less than what he perceives one fifth of the loot. This is unacceptable. They have to get definitely a satisfactory share each.
So, is there a definite procedure?
Yes. Many of those.
Yes. No probabilities.
No. All is done between the pirates.
They follow a definite procedure, and after a finite number of steps each pirate keeps a part of the loot which is at least one fifth of the total according to his own subjective evaluation.
I find many mistakes in the linked article. Take this passage, for example:
It is wrong because the numbers don't need to be prime for this result. The author used an example of 12 and 18, which coincide in 36 years. But the numbers 15 and 16, which are not prime, would coincide in 15 x 16 = 240 years, i.e., even rarer than 221.
Strictly by the pirates.
You can consider items to be small enough that they don't need to be cut or broken.
The only way to go is by the subjective value judgement of the pirates.
My former professor asks to forward this announcement to anyone interested. So, here it goes:
Subject: SC-012-2023
This is a re-announcement. Primary duties are beaver trapping.
Noel E. Myers
Noel E. Myers
State Director – South Carolina
USDA APHIS WS
400 Northeast Drive, Suite L
Columbia, SC 29203
(803) 477-3151 (o)
(803) 786-9472 (f)
SC-012-2023_reannouncement.pdf
They are not more peaceful, but more mature than children. Specifically, they don't care if another pirate got a larger share than them. Each one cares only that his share is not less than one fifth of the total, in his evaluation.
Yes, the assumption 1 is necessary. We assume that the treasure is as close to a continuum as needed. The assumed precision is the precision of their evaluation of the pieces.
I'm not sure why the other assumptions are required. For example, why there would be a conflict between who divides and/or who picks in the case of two, given the assumption 1.
Not peaceful enough
We don't want to introduce any other incentives, such as a desire not to be killed. The only criterion should be that each one is satisfied with his own portion of the treasure.
They should not be forced to accept. They should be individually satisfied.
Not by majority either. Literally, each pirate should leave satisfied.
A solution should be as good for each one of the five pirates as in the example of two pirates above.
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