The Desert Island Problem

The ss Minnow was a little cruise ship manned by a small crew and several groups of passengers. It was caught in a tropical cyclone which blew it thousands of miles off course for several days. In the second day of the storm, the radio and all communication means were destroyed after the ship had sent out a distress call, expressing the fear that the ship would go down. Many days later, after the ship had been tossed through the South Pacific, the ship ran aground on an island which the Captain realised was a remote and uncharted and probably undiscovered new volcanic island. The implication of all this is that eventual rescue is remote but cannot be ruled out if they survive long enough: search and rescue would be based on the last plotted position thousands of miles away on the belief that the ship may have sunk at that point; the island is not near any trade route. This is before the days of GPS and satellite tracking.
The Hapsburg family (a group of six) has lots of money, gold, jewellery, and are willing to offer these for anything they want. The Doonesbury clan (all twenty of them) brought their own canned food, which will last them a couple of weeks with careful hoarding. The dozen Klungs have, upon coming aground and realizing their situation, enterprisingly gathered all the coconuts on the very small island, and now hold the monopoly on them. The ten Corleone brothers broke into the ship’s store and grabbed all the ship’s food, which will last them two week if they do not share them. The Rotweilers (husband and wife) have a shotgun between them, which can be used to hunt birds for food but which they are threatening to use to hold up the others if they do not get the lion’s share of the available food. They have enough buckshot for three dozen rounds which means that they can kill many of the others but not even half of them. The Clements are the largest group, equal to everyone else put together, but have nothing. The Captain and his trusty First Mate,