Rights over found property are legal curiosities. Marine laws of salvage predate many modern legal systems, yet ships' captains scrupulously hew to their tenets. Many countries, to a greater or lesser extent, observe squatter's rights. Homesteading (or Seasteading, if you're so inclined) is a bit like claiming found property. Lost and Found bins in daycare facilities, public libraries, stores, museums, amusement parks and university bowling alleys all occur not as a function of gaseous legislators scribbling away in the halls of legislature, but as spontaneous order, as natural law. Lost and found rules operate in the secret nooks of the social labyrinth, formed from a curious blend of playground rhymes, folksy economics, tradition and intuition. In some instances, "finders keepers, losers weepers" applies. In others, found goods are held in trust and publication requirements are to be satisfied before the finder obtains a legitimate claim. In the case of mining or homesteading claims, the ball bounces on a nebulous and uncertain criterion of "property development". Adverse possession is a rather large islet in the skerries of conventional ownership, so let's pilot the taco truck through those reefs. Yes, we've converted the taco truck for maritime use--big ol' inflatable tires and an outboard.
Not only do these found-property institutions exist, but they seem to be quite robust. At the low-value end of the scale, we have playground rules: I find it, therefore it's mine. Challenges to the rule of possession can be arbitrated by Wise Adults, and ad hoc branding is typically honored. It is in this spirit that I recently had to scribble "EW" on the inside of my daughter's onesies in preparation for day care. The burden of proof here is comparatively low and very often, this is the extent that the average citizen ever has to deal with lost and found property. Forgetting an umbrella at the coffee shop is very much in this vein.
On the higher end of the scale, wars (insert your own air quotes) have been fought over cases of adverse possession (though you could easily make the case that the Pig War was over sovereign territory) and certainly, neighborhood feuds have been waged over common law easements, boundary drift and even overgrown trees. Here, established case law takes the helm and disputes can be settled (usually grudgingly) in court.
But what about the marginal cases? As we move up the scale of value from a handful of marbles to a sack of cash, what drives our intuitions about what constitutes conventional ownership? I'm quite confident that some of it is search costs. If the owner is easy to locate (like hollering, "hey, does this wallet belong to anyone?" on a subway car), the moral obligation is to restore the property to its rightful owner. That same wallet, found in the concourse of a busy international airport might be up against different odds.
And what about a distinction between cash and non-cash property? Suppose you find an envelope stuffed with concert tickets (h/t GTM) that you know you could scalp for $600. Does that envelope carry with it the same moral burden as an envelope filled with half a dozen Benjamins? More? Less? At what point is it yours?
Now, the concert ticket example is usually used to motivate opportunity cost dilemmas, but the next time you bring it up, consider to what extent found property constitutes owned property. Consider also the role of the endowment bias as it pertains to ownership of found goods. Perhaps a sense of ownership is an accumulation function. Perhaps not. I think it's an interesting exercise to pursue. Is euvoluntary exchange possible in a found-goods interregnum?
I think I may have used the word "interregnum" incorrectly just now. Sorry about that.