You are Johnny Depp 2! An extension of this question repeated below.

A band of 9 pirates have just finished their latest conquest -
  looting, killing and sinking a ship. The loot amounts to 1000 gold
  coins.
Arriving on a deserted island, they now have to split up the loot.
  You, as the captain of the band, have to propose a distribution plan
  (who gets what). What's your proposal?
Consider that this bunch is a democratic lot. If your proposal is
  accepted by half of the group, then everybody adheres to it. However,
  if folks feel you are getting greedy, and less than half of the band
  agrees to your proposal, then they kill you, and then your First Mate gets to
  make a proposal. And so it goes in decreasing order of
  hierarchy/seniority.

These pirates are unhappy with the poor definition of democratic voting and now insist that the vote must be carried by a clear majority and voting is compulsory! These are bloodthirsty pirates so life is cheap. Specifically it is worth 1 coin so the pirates criteria for accepting a proposal is (in order)


*

*They do not die

*It makes them the most money

*It allows them to kill the most pirates


How does this change the outcome?
For $n$ pirates, let $P_1$ be the last pirate, $P_2$ be the next to last and so on up to $P_n$ who is the (temporary?) leader.


*

*For $n=1$, $P_1$ takes all the money.

*For $n=2$, $P_2$ is a dead man since $P_1$ can vote no, kill $P_2$ AND get all the money.

*For $n=3$, $P_3$ can count on $P_2$ since if he votes no he is going to die.

*For $n=4$?


I will post an answer after the weekend if no one else has.
 A: Assumptions:


*

*Pirates are rational, greedy, and bloodthirsty.

*If the head pirate has multiple possible proposals in which he maximizes his profit, he will choose between them randomly, with a uniform probability distribution.

*The first two items on this list are common knowledge among pirates.


Notation:
Let $G$ be the number of gold coins.  A proposal in which $P_i$ receives $g_i$ gold coins will be denoted by $(g_n,\ldots,g_1),$ where $P_n$ is the most senior pirate.
Case $n=4$:
$P_4$ must garner the support of two other pirates to obtain a clear majority.  For the case $n=3$, $P_1$ and $P_2$ receive nothing, so a proposal of $(G-2,0,1,1)$ is accepted.
Case $n\ge 5$
A proposal of $(G+1-2\lfloor \frac{n}{2}\rfloor,0,1,g_{n-3},g_{n-4},\ldots,g_1)$ is accepted, where for $i=1,2,\ldots,n-3$, exactly $\lfloor\frac{n}{2}\rfloor-1$ of the $g_i$'s are $2$, and the rest are $0$.  First, notice that by assumption $2$, for $i=1,2,\ldots,n-3$, the expected value of the proposal for $P_i$ is
$$E_n=\frac{2\lfloor\frac{n}{2}\rfloor-2}{n-3}=\begin{cases}1&\text{if $n$ is odd}\\[.1in]\frac{n-2}{n-3}&\text{if $n$ is even}\end{cases}$$
What is most important is that $1\le E_n<2$ for $n\ge 5$.
We prove that this proposal is accepted by induction.  For the case $n=5$, the two possible proposals are $(G-3,0,1,2,0)$ and $(G-3,0,1,0,2)$.  Comparing with case $n=4$, we see that $P_5$, $P_3,$ and $P_2$ will vote for the first proposal, while $P_5$, $P_3,$ and $P_1$ will vote for the second proposal.
Now assume that the proposal holds for $n-1$ pirates, and that there are $n$ pirates.  $P_{n-2}$ receives $0$ gold coins in the case of $n-1$ pirates, so he will vote for the proposal.  Since $1\le E_n<2$, any pirate from $\{P_1,\ldots,P_{n-3}\}$ will vote for a proposal in which he receives at least $2$ coins, and will vote against a proposal in which he receives less than $2$ coins.  Thus, exactly $\lfloor\frac{n}{2}\rfloor-1$ of the pirates $P_1,\ldots,P_{n-3}$ vote for the proposal.
Remembering that $P_n$ will vote for the proposal, that makes $1+1+\lfloor\frac{n}{2}\rfloor-1=1+\lfloor\frac{n}{2}\rfloor$ votes for the proposal, so it passes.
For the case of $n=9$ and $G=1000$, $P_9$ receives $993$ coins.
Comparing this with the result of the first question, it seems that the new voting system requires that $P_n$ give up exactly $2\lfloor\frac{n}{2}\rfloor-\lfloor\frac{n-1}{2}\rfloor-1$ extra gold coins ($n\ge 5$).
Edit
If, instead of assumption $2$, we assume that the head pirate chooses between multiple possible proposals that maximize his profit by rewarding seniority, then a proposal of $(G-1-\lfloor\frac{n}{2}\rfloor,0,1,2,0,1,0,1,\ldots,\frac{1+(-1)^n}{2})$ will be accepted.  The proof is similar to the induction above.  In the case of $n=9$ and $G=1000$, we see that $P_9$ receives $995$ gold coins.
