Lets get it out the way, shall we?
Negative rights place obligations on others to abstain from doing something. The most common example of a negative right is freedom of speech. My (negative) right to freedom of speech places an obligation on others (in most cases, the guvamint) to abstain from restricting my speech.
Positive rights place obligations on others to do something. For example, if I have a positive right to health care and shelter, that places obligations on others to provide it.
Self-Ownership (and Ownership) Thesis: Our rights are grounded in ownership. For example, my right to avoid harm without consent is grounded in the fact that I own my body and you're not the boss of me! My right to do with my property as I see fit is grounded in the fact that I own my property. My (negative) right to not have my property taken away or used without my consent in grounded in the fact that I freakin' own it, man! It's mine! mine! mine!
Overview of Libertarianism
Just like many broad categories it's tough to pick out exactly what defines libertarianism. Here are a couple of things that would describe most (but not all) libertarian positions:
(a) Individual rights are more important than community rights (some say there aren't any community rights) or social good. In short, appeals to social good cannot override individual rights.
(b) Strong emphasis on negative rights rather than positive rights.
(c) Strong commitment to (individual) property rights.
(d) Self-ownership as the genesis of rights; that is, your property rights (including over what happens to your own body) arise out of the fact that you own your property (including your own body).
(e) Commitment to state neutrality on conceptions of the good. That is, the state should be neutral on what sort of life people should pursue. People should be free to pursue whatever kind of life they want.
(f) People should be able to do with their property whatever they please so long as they don't harm others (without consent). Harming others is impermissible because it's a violation of their negative rights that arise from self-ownership. That is, since you don't own other people, you can't cause them any harm without their consent. It's important to add that harm is subjectively defined. Other people don't get to tell me what counts as harm to me. Only I decide if and how much something is harming me.
(g) Since rights are grounded in self-ownership they are not contingent upon considerations of social utility. In short, even though it might bring about some overall social good to harm an individual or a small group of individual, you can't do this. You can't because rights don't come and go based on utility. They are grounded in ownership and so long as you own youself or your property, you have those rights. (More on this later).
(h) There is a conspicuous absence of positive rights and positive moral duties toward others.
The Problem for Libertarianism
The problem I'm going to discuss comes from "Backing Away from Libertarian Self-Ownership" by Sobel. I've added some of my own thoughts near the end.
Often libertarian reasoning is invoked by the wealthy to provide arguments against redistributive taxation policies. "This is my money, I earned it with my body and/or mind so it's a violation of my (negative) rights for the guvamint to take it and give it to other people. Mine! Mine! Mine!"
The core principle grounding who gets to decide how property is used, recall, is the self-ownership thesis. You cannot take, use, or harm the person (i.e., body) or property of another. Ownership confers negative rights. Libertarians always be like "you can't violate harm me cuz you don't own me! I own me! Even if you cause me a mild amount of discomfort, you've violated my rights. Don't violate my rights!"
This is all fine and dandy until we look at the other side of what libertarians want to claim: unrestricted power to do with one's property as one wishes. "It's mine! mine! mine! so you can't tell me what to do with it!" This sounds fairly reasonable in many contexts. Many of us would agree that in many cases it's undesirable for the guvamint or others to legislate how we can use our property and how we can live.
The problem is when you try to combine both desires. To illustrate the problem consider the following situation. You own a widget factory. It's yours. Ain't no guvamint gonna tell you what to do with it. Being the kind-hearted libertarian that you are, you decide to produce widgets. Unfortunately, your factory emits a pollutant that will cause 1/1 000 000 000 people to get a minor skin rash.
By libertarianism's own logic, you may not produce your widgets because you are violating someone's negative rights. You don't own their body so you can't impose the harm from the rash on the 1/1 000 000. You don't have their consent to give them a rash, and so, you can't make widgets.
This is the libertarian problem: They want near absolute freedom to do whatever they want to do with their own property and life but they also want absolute prohibitions on unconsented harm. In a highly interconnected world it's pretty much impossible to do anything that isn't going to minimally harm someone in some way. So it looks like either the libertarian has to propose some sort of minimum allowable rights infractions or they're going to have to accept that their freedom to do wudever dafuk dey want is a lot more constrained than they might have thought.
There's an obvious solution. Suppose it turns out that the widgets make a significant number of people better off. Lets say, 10 000 people have their lives improved because of the new widgets. Well, there's our solution: If enough people end up better off, then surely we can allow trivial unconsented harms.
Unfortunately, the libertarian can't take this route for a few reasons. First, he is an absolutist. You cannot cause harm without consent--no matter how small. Amongst other things, that would imply that you are deciding for someone else what constitutes a trivial harm. And even if you could cause unconsented harm it couldn't be justified by an appeal to social utility. Attaching rights to social utility is exactly what libertarianism seeks to avoid. You cannot "purchase" rights violations with social utility. Rights don't depend on contingent social circumstances. Rights are grounded in ownership. So long as your ownership claim is secure, so are your rights.
Prima facia, the second method seems less problematic until we consider that wherever the minimum threshold is set, it will have to be justified on some grounds. An arbitrary threshold will lack a principled justification. Unfortunately for the libertarian, it seems like any reasonable attempt to justify a minimum will probably refer to social utility1. But, as we have seen, this is exactly what the libertarian seeks to avoid. Rights, argues the libertarian, are not contingent upon social utility. Doh!
A Proposal Libertarians Will Hate
I've been thinking about a way out for the libertarian that is consistent with their commitments, except they probably won't like it. Too bad. I'm the boss of me! I'm working on developing a view that allows shared ownership rights. If the community is a partial owner in all things, including the individuals who make it up then libertarian reasoning allows appeals to community interests (because rights are grounded in ownership). If community interests can be involved then we can return to something like the ratio view above but this time it will be consistent with libertarian logic.
Very briefly, here's how I think it might be accomplished: the libertarian
There's an obvious objection here. Yes, we are parts of groups and groups might even be "real" things but ownership requires agency and only individuals have agency. Perhaps, but most of us already accept that groups can own things. This idea isn't crazy. For example, families, couples, and shareholders can all have shared ownership in property. The proponent of the agency view would have to show why families can't own things. Maybe they're right. I'm not sure.
Anyhow, for my theory to work, I need to develop a concept of identity that is dualistic: we are individuals but we are also parts of a whole. Both individuals and groups have ownership claims to the bodies that make them up. If the community ownership claim can be established via a dual identity theory, then libertarians can appeal to social good to resolve pollution-type cases because communities have rights in what happens to individuals (and their property) via their shared ownership claims.
I think this dual identity/ownership theory can also explain many of our intuitive judgments. For example, the reason you can just simply use me for your own purposes or steal my things is because they are mine. But we also think it's OK to use the property of others to produce a certain degree of social good. It's OK to use your stuff because you are also a part of a whole. You are part of that whole that benefits.
Anyway, like I said, it's a work in progress. It may go nowhere and I've already thought of a couple obstacles. Meh, we'll see.