Aye, the solution depends on a number of assumptions - such as, no negotiations take place. But if negotiations DO take place, and it's possible to make deals that are based on pooling votes, bargain etc which would naturally be possible..?
What happens when the eldest mathematician says to the other six, "Look guys, I propose that I get a seventh of the loot and face the risk of standing before the guns. If I'd ask for more than 720, you'd just shoot me and get more on the average as a result so I won't. But I won't settle for less than 720 either as you would just call me an idiot for throwing money away, so I won't make an offer of a division where I get less than 720. Other than that, I'll propose to divide the other 4,320 coins any way you want - so that the two (or three) greediest get to say they want me dead, and they ones who settle for the least shares get what they ask for. For starters, let's say everyone gets an even split of 720, and start the bargaining from there. If you can come up with a split that guarantees I survive, I'll go for that, and if there are multiple such proposals I'll choose that one with the biggest share for me, propose that, you say aye, and most of us will be happy."