The Captain's Undeniable Proposal

What was the situation?  

He can keep 98 coins! Surprised? Read how.

Let's number 5 pirates as Pirate 5, Pirate 4.....Pirate 1 as per their descending order of seniority.

Pirate 5 keeps 98 coins with him and gives 1 coin each to Pirate 3 and Pirate 1.

Now Pirate 5 i.e Captain explains his decision -

CASE 1:

 If there were only 2 pirates then Pirate 2 would have taken all 100 coins after obtaining his own vote which accounts to 50% votes (50 % of 2 = 1).

CASE 2: 

 In case of 3 pirates, the Pirate 3 would have offered 1 coin to Pirate 1 & would have kept 99 coins with him. Now Pirate 1 wouldn't have any option other than agreeing on deal with Pirate 3. That's because if he doesn't agree then Pirate 3 would be eliminated & all coins would be with Pirate 2 as explained in above (case 1) of only 2 pirates. So votes of Pirate 1 and Pirate 3 which account to 66% (2 out of 3) votes of group locks this deal and Pirate 2 would be left without any coin.

CASE 3: 

 Now in case of 4 pirates, Pirate 4 would offer coin to Pirate 2 & would keep 99 coins with him. Now, Pirate 2 know what happens if Pirate 4 gets eliminated. Pirate 3 would offer 1 coin to Pirate 1 & will take away 99 coins. So Pirate 2 would definitely accept this deal. That's how votes of Pirate 4 and Pirate 2 makes 50% (2 out of 4) votes of group to pass the proposal. Pirate 3 and Pirate 1 can't do anything in this case.

By now, Pirate 3 and Pirate 1 realizes what happens of Pirate 5 gets eliminated. They won't be getting any coin if Pirate 4 becomes captain as explained above (case 3). So they have no option other than to vote for the proposal of Pirate 5. 

This way, Pirate 5, Pirate 3 and Pirate 1 (3/5 = 60% of crew) agree on proposal of Pirate 5 where he takes away 98 coins with 1 coin each to Pirate 3 and Pirate 1.