Five pirates on an expedition for treasure come across 100 gold coins. In order to divide up the 100 coins fairly, the five pirates draw straws in order to determine an ordering of themselves. The pirates then, in order, each propose how the 100 coins should be split up, after which all living pirates vote. If more than half of the pirates (including the pirate proposing this way of splitting the coins) approve, the coins will be divided as that pirate has proposed. If not, the pirate proposing this way of dividing coins is killed and the next pirate makes a proposal. Assume all pirates are perfect logicians (if a logical conclusion exists, they will arrive at it instantaneously). Furthermore, assume their priorities, in order, are:
- Getting as much treasure as possible
- Killing other pirates
That is to say, they will try to survive no matter what, will try to get as much treasure as possible, given that it doesn't kill them, and, given that they will survive and get no less treasure, will always try to kill more pirates. Which pirate's proposal will be accepted and how many gold coins will each receive?