This is a post I made at the progress.org geoist forum. It was part of a conversation about homesteading, in response to being asked "Why does specifying the FIRST owner matter so much?"
Political philosophy is all about specifying some principles/rules for determining who owns what. That is, who has ultimate decision-making jurisdiction over scarce objects. The reason we humans developed the concept of rights and ownership and laws is so that when a conflict occurs over a scarce object, we can determine, in some non-arbitrary way, ideally based on some well-thought-out principles, who is 'in the right' and who is 'in the wrong' in any dispute.
That is, we as a species learned that order (as opposed to chaos) comes when you have a system of ownership, where specific scarce objects are associated with specific individuals. That way, when a dispute arises over a scarce object, one need only ask 'who owns that object' in order to know who is in the right, and who is in the wrong, and then a resolution to conflict can be proposed.
For example, take this beer can in front of me. Suppose someone else now grabs it and starts drinking it without my consent. We have a dispute over a scarce object: a can of beer. We might resolve this dispute peacefully or we might get violent about it. Those are our two choices. Violence would be costly and risky for both of us, so we'll negotiate and try to reach some settlement. If we can't resolve this peacefully among ourselves, we might ask a third-party to help us resolve it. This third-party would be carrying out the role of judge.
The first thing the judge will want to know is: who rightfully owns the beer can? Whose will, in this dispute over how the beer is to be used, ought to prevail? Because if I owned the beer can, then I have ultimate decision-making jurisdiction over it, so clearly my co-disputant is 'in the wrong' because he initiated coercion against me. In the opinion of a judge that decides I was the rightful owner, I now 'have the right' to use coercion, if necessary, to take my beer can back. Another judge might decide the other way: that my co-disputant owned the beer can, so he was 'within his rights' to grab it from me. Then I was 'in the wrong' for using the beer can without his consent and trying to prevent him using it when he wanted to.
All conflicts can be shown to be ultimately about property rights, about who owns which scarce objects. The task of the political philosopher is to come up with some set of principles for determining who rightfully owns what. That is, political philosophy is about devising a set of principles for associating particular scarce objects to particular individuals, and those individuals are then considered (by that political philosopher) to rightfully have ultimate decision-making jurisdiction, or ownership, over those scarce objects.
So who does rightfully own the beer can in front of me? It depends on what political philosophy you subscribe to.
The facts of the case are that I personally bought the beer can from a supermarket. Most political philosophers have no objection to voluntary exchanges, so they would say that I am the rightful owner of it, so long as the supermarket was the rightful owner of it before that exchange took place.
The next question is obviously: was the supermarket the rightful owner? The supermarket also acquired it through a voluntary exchange, and so did several suppliers in the chain before them. This chain stops at the FIRST holder/user of the beer can. In this case, the producer of it. Only if he is considered the rightful first owner of the beer am I now considered the rightful owner of it, and rightfully able to defend it from anyone who might try to take it from me.
Most political philosophers would agree that the producer of the beer can was the rightful owner of it, so long as he was also the rightful owner, or had permission to use, the factors of production that went into producing it. Factors of production can be classed into three types: capital, nature and labor. But capital goods are themselves previously produced goods, so there are only two ultimate factors of production: nature and labor. So the task of the political philosopher boils down to determining who rightfully FIRST owns the products of each individual's labor, and who rightfully FIRST owns the scarce items of nature. Then, should conflicts about those items of nature occur, we can determine who acted 'in the right' and who acted 'in the wrong'.
Libertarianism and geo-libertarianism are unusual in political philosophy in that they both support, unequivocally, the principle that the product of a person's labor belongs to the laborer himself. Anyone who supports income taxes and most other forms of taxes demonstrates that he does not fully support the principle that one own's the products of one's labor.
Where we differ is of course land, i.e. determining first owners of scarce items of nature, although even here there are similarities. For libertarians it is simple enough: the first owner ought to be the individual identified as the homesteader. Thereafter, so long as he does not abandon that scarce item of land, this individual is the rightful owner and can use it as he pleases, exclude other people from it, keep any rental income or gain in capital value he derives from it, and sell it to others as he pleases.
You retain Locke's proviso, and interpret this as meaning that some part of the scarce items of nature always remain 'commonly owned', namely the rental income derived from the scarce items of nature. So the homesteader is thieving from the rest of the community by keeping the income attributable to the scarce item of nature which he is excluding others from.
Maybe this facet of scarce items of nature could be commonly owned - and the land rental income distributed equally - and there would be no conflicts, just like when a path through a small village might be commonly owned with no conflicts over usage occurring. But what if there is a conflict? What if, say, the homesteader(s) of a particular scarce item of nature tries to homestead and keep for himself also the income he derives from it, which is supposed to remain forever commonly owned? We have a dispute. And so the judge of the dispute turns to his political philosophy for some guidance on whether party A, the homesteader, or party B, who may be acting as a representative for 'the community', ought to have ultimate decision-making jurisdiction over what happens to the income derived from that scarce item of nature.
A libertarian judge would always support party A's right to keep the land rent income, and his right to use force to defend it from aggressors if necessary. This would follow from the homesteading principle without the proviso.
A geoist judge would, not always, but certainly sometimes, support party B's right to collect the land rent income, and his right to use force to collect it if necessary. The decision would depend on the identity of A and B and the opinion of the judge about whether the land rental income being claimed by B is truly the fair amount of land rental income owed by A, and is not excessive. This would involve calculating land values and separating income derived from land rent from other sources of income, such as income derived from the improvements on the land, or from the genuine entrepreneurial skill of the homesteader in his particular use of the land.
Libertarians believe that the income derived from excluding others from all scarce items of nature should be considered a private good, while geo-libertarians believe that the income derived from excluding others from certain scarce items of nature rightfully remains forever a common good which ought to be redistributed equally in the community.
So, to finally get around to answering your question directly, specifying who the first owner ought to be is crucial whenever we're talking about a private good. When we're talking about a common good, it doesn't make sense to talk about first owners, of course, because it is always owned in common by everyone.
Going back to your "rule" of "whoever pays the most" determining first owner... if you're really talking about common property, then you don't need any rule in the first place, because common property is harmonious by definition. Everything starts off being common property; things are only privatized as a means to avoid/resolve/reduce conflicts.
You only need a rule when you're talking about private goods, which are, by definition, associated with particular individuals - not all - rather than being owned in common.
A perversion of the idea of common property is public property, which is de facto ownership by a small group of individuals nominally acting on behalf of all individuals, and no one may divest themselves of their share of ownership. Public property is neither private property nor common property. In practice however, when a scarce item is deliberately designated as common property, when private property is preferable due to regular intolerable disputes over usage, it becomes public property. Then a small group of individuals, usually a State, manages that scarce item of nature and you have the problem known as the "tragedy of the commons" but which should really be called the "tragedy of the managed commons" or the "tragedy of public property".
So it seems to me you have a few options at this point:
1. You could make the case that the income derived from land rent can successfully be considered common property. You will have to argue that conflicts will not occur over it, i.e. that no one objects to the collection of it, or that conflicts will be less than when the income derived from land rent is a private good, and in particular a private good which is first owned by the homesteader(s) of the use of the scarce item of nature.
2. You could make the case that the income derived from land rent should be considered public property and managed (collected & redistributed) by a small group nominally on behalf of all citizens, who are not allowed to divest themselves of their share of ownership.
3. You could make the case that the income derived from land rent should be considered private property. Then you would have to specify a rule for deciding who the first private owner of that scarce item ought to be. Your rule can then be compared directly against the libertarian rule for deciding first private owner.