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Democratic distribution of wealth

A crew of 100 pirates have captured 100 laptops. The pirates are ranked 1 through 100, with pirate 100 being the pirate king. Captured booty is distributed as follows.

  1. The pirate king proposes a distribution of booty.

  2. The pirates, including the king, vote to adopt or reject the king's proposal. In case of a tie, the proposal is adopted.

  3. If the proposal is adopted, then the matter is settled. Otherwise, the pirate king is forced to walk the plank (he dies), the next highest ranked pirate becomes king, and we repeat from step 1.

Pirates all excel at mathematics. They each vote with the following ordered priorities.

  1. Stay alive!

  2. Get as many laptops as possible.

  3. Make as many other pirates walk the plank as possible.

The pirates cannot trust each other. They can only expect each other to follow these three priorities. E.g. if pirate 99 attempted to undermine pirate 100's proposal by making campaign promises of certain numbers of laptops, to buy votes, then the other pirates could not trust these promises.

a) Who lives, who dies, and how are the laptops ultimately distributed?

b) What if there are n pirates with 100 laptops, with n > 200?

Source: folklore




Induct on the number of pirates, not on the number of laptops.