The best way to handle that situation would be to divide up the land and then divvy up the parcels by some impartial method, say by lottery. The collectivist method was tried at Plymouth and Jamestown and it led to immediate starvation.
I am not sure that the folks in Jamestown eating each other quantifies as collectivism. The trouble seemed to stem from lack of shelter, supplies, trouble with natives, living in a swamp and most of all a lack of the proper survival skills for living in a untamed place.
Eating each other is the end result of collectivism. Treat all land as common property and allowing everyone an equal share of the harvest regardless of how much they contributed to it is collectivism. That's precisely what the Jamestown settlers did. As a result, few people had any motivation to work, and they all starved as a result. The minute they discarded collectivism, they had an abundance of food. It's strange how shelter, supplies and living skills are always in short supply under collectivism.
Back to the island. I do appreciate your solution and the fact that it seems to satisfy the libertarian's moral code. I suppose a voluntary trade would solve the most obvious issue of people not getting plots that match their skill set. (e.g. fisherman gets the jungle, the hunter gets the beach) The people who received plots with no resources could either die off, making more available to the rest or could sell their labor.
since the plots would be assigned by lottery, the people who divvied them up would have a strong motivation to make sure the productive land was equally divided.
My next question is who or how would they arrive at your solution? Would it be a vote or would a natural leader emerge (perhaps the captain) and make the decision for a lottery? Also who would decide the punishment for the inevitable trespassing and theft that would occur from the people with no resources? Would there be public pathways or would everyone be landlocked?
More than likely what would actually happen would be that a leader or leaders would emerge from the 80/20 rule (followers/leaders). They would most likely try and maximize the harvest of resources based on skill sets and try and spread the knowledge and skills based on need. Only after the most basic needs seemed secure ( hierarchy of needs ) would anyone probably worry about 'property rights'.
The 80/20 rules says that on any given project 20% of the people do 80% of the work. It has nothing to do with "leadership." Apparently what you think would happen is that someone would establish a dictatorship and the rest of the population wold meekly fall into line. Of course, the dictator would be benevolent and worry about meeting other people's needs before considering his own selfish wants.
However, it really doesn't matter because your island scenario is totally unrealistic. We all know that in reality when agriculture began land was free for the taking. It had no intrinsic worth until some men learned how to make it more productive. There was no need to worry about how to divide up the land because there was far more arable land available then there was labor to plow it and sow it.
When other men saw the abundance the farmers enjoyed, they attacked the farmers, enslaved them, and forced them to hand over all their surplus production to their conquerors. That's how government came into existence.
