A book called Structures of Social Life: The Four Elementary Forms of Human Relations by Alan Page Fiske explores some possible answers to the question of what social/ political structures are humans naturally inclined to form, though it does not cover a specific scenario of people isolated on an island.
The four forms are summarised in this Forbes article by Rawn Shah, quoting a paper by Fiske, as being:
Authority Ranking (AR) –relationships are based on asymmetry ordered in some form of hierarchy. The people involved in this context have some rank understand on some level, whether implicit or explicit. Think of hierarchy in any company or in the military.
Communal Sharing (CS) – relationships are based on a bounded group of people who consider themselves generally undifferentiated from each other. Their focus is common beliefs, and they think it natural to be kind and altruistic to other people of their own group. They do not separate the notion of one person having more than another because in thought everyone shares the same things.
Equality Matching (EM) – relationships are based on maintaining balance between members of the group. The direction and magnitude of any imbalance is meaningful and noticed by others. People can keep track on some level of how far out of balance the relationship may be, although they may not do so based simply on altruistic bases. Think of the balance of and exchange of favors, or even unformed relationships—notice how upset people get when a single person car improperly uses the car pool lane.
Market Pricing (MP) – relationships are based on setting an explicit basis of value in ratios or rates on the interaction (e.g., just about every retail sales transaction is set on a common basis of currency value). The explicit exchange rate is rational –even if it seems outrageous at times – based on some balance of supply and demand.