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):

{1, 2}     -> (0, 600)

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:

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

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:

{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)

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 ...