I would like to put forth a scenario to be considered by those who advocate strong property rights.

Let's take the Lockean view of property that something becomes property when someone mixes their labor with a natural resource, and after that the owner can use and trade it in whichever way he sees fit.

Now consider a farmer that comes across an unclaimed piece of land. The farmer builds a house on the land, plants crops, digs an irrigation ditch etc. Many years later all of the land around the farmer has been claimed by others, and he comes out with a 20 acre parcel of land (or however much). The farmer now dies in some accidental way. He did not specify any heir that should inherit the land, and he was the only one that worked that piece of land at all. All of the surrounding residents believe that they have as much of a right to his land as everyone else. What is a reasonable way to decide to whom the land belongs?