Let the robbers be called labeled with the numbers 1 -7, with 1 representing the lowest rank and 7 representing the highest rank. Given the rules set out by the OP and the additional assumption that each robber would choose staying alive and getting no money over dying and getting no money, then the money will be distributed as follows:
Robber 7 will get three bills,
Robber 6 will get zero bills,
Robber 5 will get one bill,
Robber 4 will get two bills,
Robber 3 will get three bills,
Robber 2 will get one bill, and
Robber 1 will get zero bills.
Why? Since only six robbers get to vote, Robber 7 needs only four of his companions to vote in favor of his solution. This leaves him free to give nothing to two of the robbers just so long as the other four are better off than they would be in a scenario with only six robbers. As it turns out, the distribution above is better for Robbers 2, 3, 4, and 5 than it would be if there were only six robbers because under a six robber scenario:
Robber 6 will get four bills,
Robber 5 will get zero bills,
Robber 4 will get one bill,
Robber 3 will get two bills,
Robber 2 will get zero bills, and
Robber 1 will get three bills.
Robbers 1, 3, and 4 will agree to this solution in a six robber scenario because it leaves them better off than they would be in a five robber scenario in which:
Robber 5 will get four bills,
Robber 4 will get zero bills,
Robber 3 will get one bill,
Robber 2 will get three bills, and
Robber 1 will get two bills.
Robbers 1, 2, and 3 will agree to this solution in a five robber scenario because it leaves them better off than they would in a four robber scenario in which:
Robber 4 will get seven bills,
Robber 3 will get zero bills,
Robber 2 will get two bills, and
Robber 1 will get one bill.
Robbers 1 and 2 will agree to this solution in a four robber scenario because it leaves them better off than they would be in a three robber scenario in which:
Robber 3 will get nine bills,
Robber 2 will get one bill, and
Robber 1 will get zero bills.
Robber 2 will agree to this solution in a three robber scenario because the alternative is to be the top-ranked robber in a two robber scenario. The top-ranked robber in a two robber scenario is always killed (as it allows the bottom-ranked robber to get all of the money and to kill the other robber). Therefore, no one wants to be the top-ranked robber in a two robber scenario.
However:
This solution assumes that the three robber scenario has different rules than every other scenario. If we stuck to the assumption that the solution must have at least two-thirds of the voting group to pass, then the three robber scenario would look very much like the two robber scenario. In that case, Robber 1 gets to kill both Robber 2 and Robber 3 while keeping the money for himself. This leads to a different analysis of what a four, five, six, and seven robber scenario would look like.
Why make the assumption that the rules for a three robber scenario are different? Two reasons. The first reason is that the hint we were given implies—though does not actually state—that only a two robber scenario is supposed to lead to the deaths of everyone but the bottom-ranked robber. The second reason is that there is no elegant solution if the rules are not different for a three robber scenario. Since this is supposed to be a logic problem, and since logic problems are supposed to have elegant solutions, it seems that we are warranted in assuming that the rules are different for a three robber scenario.
What, then, would the problem look like if we did not get to assume that the rules are different for a three robber scenario? A two robber scenario would proceed in the same way as above. A three robber scenario would also proceed in that way, however, meaning that Robbers 2 and 3 would both wind up dead and Robber 1 would get all the money.
This makes a four robber scenario much nicer to the top-ranked robber who can then keep all 10 bills. Robbers 2 and 3 will agree to this solution despite it leaving them with no money because the alternative is death. Thus a five robber solution allows Robber 5 to keep seven bills, while giving one each to Robbers 1, 2, and 3.
After this is where it gets inelegant. A six robber scenario would be disjunctive: Robber 6 would keep five bills for himself and give one bill to Robber 4, but he would then have to give two bills to two of Robbers 1, 2, and 3 and zero bills to the remainder. This makes the seven robber scenario even more disjunctive. Robber 7 would keep three bills for himself, give one bill to Robber 5, and two bills to Robber 4 just like in the original solution.
Robbers 1, 2, and 3, however, would have to get some distribution of three bills, one bill, and zero bills. What distribution, though? Given the disjunctive element of the six robber scenario, there would be no way for Robbers 1, 2, and 3 in the seven robber scenario to know whether they are doing better or worse than they would in a six robber scenario. As such, it would get very tricky to win their votes. Robber 6, who gets nothing in a seven robber scenario, would be smart to exploit this for his own gain. Thus perhaps Robber 7 would have to give two of them three bills each, leaving only one for himself.