Puzzle worm Sandi Sandman sent me this simple yet interesting puzzle. Interesting because it offers a model, even if overly simplistic, of how a self serving politician in a seemingly democratic set up can end up impoverishing others while enriching themselves. 

Jack Sparrow and his crew of 129 pirates have 1 gold coin each (130 coins in total). As captain, Sparrow can propose changes to matters on his ship including coin redistribution. But as a democratic bunch, they always vote on proposals. However, votes for Sparrow’s proposals are only cast by the 129 pirates; Sparrow himself never gets to vote as he is the one always making the proposals.
A pirate votes in favor of a Sparrow proposal if he gains by it (with certainty), and votes against it if he loses due to it (again with certainty). If a pirate will neither gain nor lose with a proposal, he abstains from voting. If there are more votes in favor of a proposal than against it, then the proposal is accepted by everyone, otherwise it is rejected.

Question: Can Sparrow end up with more than the single gold coin he started with, and if yes, what’s the maximum number of coins he can appropriate? Note – a coin cannot be broken up into fractions.

*spoiler alert*  solution and answer follow in the expandable sections below.