(note to self: still need to add resources to this, rivers, forests, how they are maintained, etc, specifically with regards to the levels at the bottom)
Property (land, personal possesions, etc. ) is central to any currency and society. I personally believe our current treatment of it is insanely naive, out-dated, overly complicated and yet also overly simplistic. There is a plethora of arguments against property as it is now (add references sometime: Henry George, various libertarian theories, property is theft, etc...).
The main issues I have with the current view of property rights are that they are eternal and total:
Eternal, if you own property you own it forever, then you can give it to your kids and it repeats. But just because you society valued something someone did ages ago does not mean we have to value it now, perhaps a property was bought using money from the slave trade, ivory or through threat of violence. It´s ridiculous that we still have to honour this today.
Total, if you own property you own it in its entirity, say someone buys a huge swath of rainforest cheap, they can burn it if they like, doesn´t matter that many many people value that ecosystem very highly and worry that burning it may possibly push the planet closer to destruction. This is also ridiculous, just because some numbers (money) and bits of papers (property deeds) got swapped around, someone can say "screw you society, this is mine, and I´m going to use it to my own selfish ends".
I imagine a fair and just society would treat property as varying levels of privacy and use on a shared resource: Where the privacy/use would be requested by a citizen, then other members of society would then chose whether to agree to this request or not.
As a basic example: there is someone who is very lazy and who does hardly anything to help in the village analogy, he requests that he can use a large pretty field all for his own use and that no-one can enter the field. Most of the villagers would most likely not agree to this and totally ignore this request and just walk across the field as they always have done. Another Villager, an average person who helps and takes the same as any other, requests to use the field growing crops, he requests that no-one damage or walk over the crops in this time, he also requests that he can set up a tent on the side of the field where he has total privacy (no one can enter) so he can get changed in his clothes. The villagers agree to this as long as he continues to keep the same standing in the society. If he doesn´t contribute to the village or is more of a burden than a benefit then someone else may go and use the field.
In this way, we can have property (for want of a better word) or perhaps shared communal resources, that belong to no-one and everyone, require no over-arching authority and yet are maintained by all of society. Also, very importantly, the use is not permenant, you can only use it as long as society thinks it is fair that you are using it. If society thinks you are abusing it, then you will lose your right to privacy. Neither is your use total, you just look after that resource at the same time as you are tapping it.
How does this work with respect to the famous "tragedy of the commons" example: well in our case, if someone abuses a resource that is valued by society, then they will find that the society is less likely to help them. So in the "tragedy of the commons" example, If some-one maliciously lets their sheep over-graze some land, then they will eventually find that the local society does not want to deal with them, does not spin their wool, does not trade with them, walks over their vegetable garden and chases their sheep away. The conventional "tragedy of the commons" example is a misnomer, it should be the "tragedy of the free-for-all in a narrowly constructed hypothetical world where accountability does not exist" example.
So what kinds of privacy/use would we have:
Total privacy (houses, bedrooms, fenced gardens, diaries, etc), where you can reasonable expect someone not to be able to see in:
Land use (farming land, workshops, factories) where you can use the land and people have access, provided they don´t disturb what work is being done there.
Public use and preservation (parks, forests..) any one can access, but you would need a consensus before you can make a change to it.