TADM2E 2.51

Let's start at the end and look at the process after we get to just two pirates (labeled by seniority in increasing order):

<pre> {1, 2} -> (0, 600) </pre>

since pirate 2 just takes all the money for himself and has 50% of the vote. Now, we step up to the case of three pirates where pirate 3 makes use of this fact to bribe pirate 1 to give him his vote and avoid the two pirate state where he gets nothing:

<pre> {1,2} -> (0, 600) {1,2,3} -> (1, 0, 599) </pre>

Now, we just continue this process with each pirate bribing the pirates who would get 0 in previous case until we get to the six pirate case:

<pre> {1,2} -> (0, 600) {1,2,3} -> (1, 0, 599) {1,2,3,4} -> (0, 1, 0, 599) {1,2,3,4,5} -> (1, 0, 1, 0, 598) (1,2,3,4,5,6} -> (0, 1, 0, 1, 0, 598) </pre>

Since each stage is stable then pirates 2, 4, and 6 have incentive to vote yes since the next stage is stable and would result in them receiving less ...