I agree with your points, but I don’t even think you need to go that far.
HowToCureYourLiberalism
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Personally, I don’t think it’s very effective to frame the issue in terms of “rights”. You say that you have the “right” to sell your labor for any amount you choose. But then a liberal can respond that everybody should have the “right” to receive a minimum amount of payment for their labor. Then you end up in a philosophical debate over “rights”.

Therefore…

“Rights” < Results

Consider this passage from the Wikipedia entry on cell signaling

Cell signaling is part of any communication process that governs basic activities of cells and coordinates all cell actions. The ability of cells to perceive and correctly respond to their microenvironment is the basis of development, tissue repair, and immunity as well as normal tissue homeostasis. Errors in signaling interactions and cellular information processing are responsible for diseases such as cancer, autoimmunity, and diabetes.

Libertarians and liberals should both agree with this. It has absolutely nothing to do with “rights” and everything to do with results.

Perceiving and correctly responding to the environment is just as important for humans as it is for cells. But in order to do so, accurate communication is necessary. Inaccurate communication results in behavior that is detrimental to the society/network.

Have you watched Sense8 on Netflix? It’s a pretty wonderful show about 8 strangers who share a psychic connection that allows them to utilize each other’s different strengths and knowledge. It’s by far the best fictional depiction of Hayek’s favorite concept of partial knowledge.

Unfortunately, Netflix recently canceled the show. Evidently the audience was too small. Netflix can see how many people watch the show, and it can also see how many people give it a thumbs up/down, but what it can’t see is the actual demand for the show. This is because Netflix is not a market.

Imagine if Netflix was a market. Subscribers could still watch all the content, but they would have the opportunity to divide their limited subscription dollars among the unlimited content. So each and every subscriber would have the opportunity to decide how to divide their $10 dollar monthly fee between Sense8 and all the other content. Then, and only then, would Netflix see and know the demand for Sense8.

Whether or not Sense8 should be canceled or continued really isn’t an issue of “rights”. Well… I doubt anybody would argue that Netflix doesn’t have the “right” to cancel its show. The real issue is… how can Netflix possibly make an informed decision when it’s entirely clueless about the amount of benefit that its subscribers derive from Sense8? In order to make a solid cost/benefit decision, you have to know both the cost and the benefit. The only way that Netflix can know the true social benefit of Sense8 is if each and every subscriber can signal this information by deciding how many of their limited subscription dollars to spend on this show.

My own environment is pretty limited. But the human environment is vast. In order to perceive and correctly respond to it, humanity needs each and every individual to use their limited dollars to accurately signal their valuation of each other’s behavior/products.

In order for Netflix to perceive and correctly respond to the environment, it has to know how relevant Sense8 is to the diverse environments of its subscribers. But the only way that Netflix can obtain this information is if the subscribers have the opportunity to use their subscription dollars to signal the relevance of Sense8 to their environment.

We have a minimum wage for the same reason that Netflix isn’t a market. It’s because people don’t perceive spending as signals. Once people perceive spending as signals, then the debate will center around accuracy rather than fairness.

I didn’t mean to imply that libertarians support the minimum wage. What I meant to convey was that most libertarians don’t truly appreciate that commerce is communication. Most libertarians don’t argue that Netflix should be a market. Here’s an example of an anarcho-capitalist who super struggles to understand why Netflix should be a market.