Five pirates of different ages obtain 100 gold pieces in total, and want to decide how to split them.
First each pirate, in order from youngest to oldest, makes a proposition on how to split up the gold (a proposition allocates every pirate a nonnegative integer amount of gold pieces, 100 pieces allocated in total). Then the pirates vote upon the propositions, in the opposite order as the propositions were stated (so the oldest pirate's proposition is voted upon first).
If a proposition is accepted (which requires the agreement of at least 50% of the remaining pirates), the voting procedure ends immediately and the gold is divided according to the proposition.
If a proposition is not accepted, the pirate who made the proposition is tossed overboard, and voting proceeds to the next proposition.
It is common knowledge that all pirates are perfectly intelligent, and that every pirate $X$ has the following decision criteria, in order:
- Pirate $X$ should not be tossed overboard.
- Pirate $X$ should receive as much gold as possible.
- As many pirates as possible should be tossed overboard.
- The oldest pirate should receive as little gold as possible.
- The second oldest pirate should receive as little gold as possible.
- The youngest pirate should receive as little gold as possible.
To decide between two outcomes, Pirate $X$ will go down this list and select the first criterium that distinguishes these outcomes, and select the more favourable outcome according to that criterium.
What will be the outcome of the decision procedure, and why?
The rules are changed so accepting a proposition requires the agreement of all but at most one of the remaining pirates. What will be the outcome now, and why?