Originally posted by TomCr
There is the additional problem, apparently not considered by some, that if less than 50% do not accept, the older brother is out, and the process starts again. This is why I disagree with 48,0,1,0,1. These are gangsters, and the problem allows for them to kick out the older brother, so the older brother should sacrifice himself to get anything at all. Cons y the most likely event is first round: reject, second round: reject, third round, accept.
Except in the second round the second oldest brother can propose 48, 0, 0, 2 and the last brother should know that if he rejects this offer then he will either get 1 or zero because the third brother will propose 49, 0, 1 and like you said if he rejects this than he will get none so I believe that the first one will be 46, 0, 0, 1, 3 since if the second youngest brother votes no he knows that he will get zero and the youngest brother knows that two is the best he can get, as per earlier in the post, if he votes no so this will be accepted. The other two brothers get zero because they will reject almost any proposal anyway....
if anybody notices there is a pattern going on here.
This debunks your theory that the second to last is advantageous... it is always advantageous to go first as you can make sure to get votes by retrograde thinking.