But, the choice is not to eliminate these library's and watching identical private ones pop up, it's between having them and not, and by having them I benefit more than it costs me for them to be there.

Second, how much crime is prevented by libraries? Is this the cheapest way to prevent crime? Or would it be cheaper to devote the money to a few more beat cops?

Is it the cheapest way to prevent crime? Is a leading question. Where I live we spend a lot of money on a wide range of things from beat cops to parks and street lights that prevent crime. And library's provide many other services than just crime prevention.

A more realistic question might be; Assume 10% of their useful function to me was crime prevention would reallocating 10% of their funding to something else above and beyond what we already spend on it prevent more crime? And the answer to that question is no.

PS: In theory we might be able to say use subliminal messages to prevent crime more cheaply. But, of the options that are actually being considered Library's are surprisingly cost effective.

The cost/benefit to evaluate public subsidies is (public benefits) / (public costs). If 90% of the benefits of a library are gained by the users, then it's highly likely that this will be negative.

In such cases, a mixed model is best - i.e., if 10% of the benefits are public, 90% private, then a 10% subsidy for libraries might be justified.

Cost and benefit are also independent. It possible for a Polio vaccine to provide 100,000 times the public benefit relative to it's cost (eliminating a disease for all time can easily be worth vaccinating people on the other side of the planet). Research can also easily have that magnitude benefit ratio's.

And (public benefits) / (public costs) is only negative if public benefits or public costs are negative you might be thinking Benefits - Costs but that does not really fit the rest of your equations either. Anyway, the idea that public subsidy's should not exceed the ratio of (individual benefit) / (public benefit) sounds good until the public benefit exceeds the cost at which point there is little for an individual to pay the costs.

PS: There is a reason people get PHD's in economics it's a lot more complex than you might think. Just consider adding different levels of diminishing returns to all of those cost benefit equations and your still barely scratching the surface.

That actually made me feel sorry for you.

Are you really this much of an island, or do you just enjoy trolling? Is there no possible benefit for me that you might have learned something, or that perhaps you might now be able to tell me something I didn't know before? Is there no benefit to me that perhaps because someone in a library showed you how to apply for your housing benefit online you didn't feel the need to break into my car?

And yes, much crime like theft can be related to drugs. But a significant proportion can also be tied back to poverty.

You're like a parody of all that's bad about the libertarian ethos. Or whatever you think you are.

You are moving the goalposts. I asserted there is no "massive positive externality", not that there is no possible external externality.

I do concede that maybe people who spend time in the library are more interesting conversationalists. I just don't consider this benefit to be "massive". Do you?

I don't think I've seen anyone argue for a truly nihilist position as earnestly as you have here.

Do we have different definitions of "sole" and "private" - those words feel fairly absolute to me.

Sure it may not be a massive positive and direct benefit to you, but I find it hard to understand how you think there's no possible benefit at all. Do you feel the same way about teaching people to read, write and count?