Honestly a stateless society probably wouldn't look terribly differant on small scale, from the outside, though there would be some significant "larger scale" differances. You'd still have entites which fight crime, convict criminals, engage in defense, etc etc.
The main differance would be that instead of one monolithic government handling these things VERY poorly and filled with corruption, you'd have hundreds of them in competition with one another who all have to turn a profit in order to survive. Turning a profit means pleasing customers. Companies who survive on "insurance" would probably replace the majority of government functions.
But first, a realistic compairison in the differance between a "government" and a "company":
Government: A group of humans who band together for a purpose. They take the money they need by force or via printing press from other humans. They need only please their "subjects" just enough to keep them from revolting. You cannot get rid of them as votes are rigged, and your money is taken by force from you.
Company or Contractor: A group of humans who band together for a purpose. They only get money by providing a valuable service that other humans willingly pay for. They must continue to please their customers by remaining competitive with the best product. If they fail to do so, you can get rid of them by choosing to spend your money on their competitor instead.
So as an example; Defense & Military: Is given money taken by force from individuals. Must over-spend in order to recieve "more" money the next year. Losses nothing by loosing assets, as the products of its industry are paid for with tax money and it has no "customer" to please. Therefore the more useless armaments it builds and then destroys, the richer it becomes by extorting more money from individuals.
Defense contracter in stateless society: Is one of many local companies who must find a way to win the business of large groups of individuals in order to stay in business. In order to remain competitive, must offer the best product for the best price. Builds its own armaments FROM its own savings, and is therefore extremely cautious about wasting its weapons. A successful defense contractor is one who will have to expend its assets the least, there is no incentives for waging pointless conflict. They are far better served by maintaining peace as a company. If one defense contractor decides to use its armaments to take people's lives and property by force, there are dozens of ambitious defense contractors who, wanting to win a larger market share would jump at the chance to stop the rogue company and restore the peace.
Department of Justice: One monolithic organization who "is" the source of law, and thus can break any law it pleases without fear of an authority above them to stop their corruption. Eric Canter anyone?
Stateless system of arbitors and justice: Again, competition. Who is going to pay into a system that is known for favoring the rich dispite clear law, or who makes unfair decisions on behalf of investors/private prisons? Corrupt arbitors will be trampled by those with an excellent reputation for distributing fair and just rulings in all disputes.
The basic answer to your quary is: Competition in a free market makes "Everything" better. Competition leads to lower prices, and better service, every time. Monopoly "always" leads to higher prices and poorer service. Without a state to pick winners and loosers, there are no monopolies.
As for nukes, its hard to say, save that when we no longer have massive gangs (governments) fighting over turf and resources; when you no longer have "this" nation and "that" nation, but instead just have private property and people trading with one another an enjoying the massive fruits and prosperity of an unbridled free market, what's the point in using a weapon like a nuke to attack.... who? Those people over there who have no identifiable feature that makes them differant than these people over here? Since most companies will have profitable ventures all over the place, why would they want to engage in destroying customers which would cut into their profits?
Also, in a free market without government lies, we'll stop pretending that platonium is dangerous to humans and realize that spent uranium is a near infinite source of clean and safe energy for everyone. The truth is finally getting out, thanks to the internet that radiation isn't nearly as deadly as we have been told by our monopolizing, cartel-running pack of thieves in government. You could go for a swim in a nuclear cooling pool or drink water out of it with no ill effects. After 3 years in a cooling pool, peaces of uranium can be used to power tiny power plants that could, for example, power a neighborhood.
The "value" of platonium for this purpose would almost certainly lead to a world wide dismantling of nukes as savy investors quickly realized they make a hell of a lot more money converting weaponized uranium and depleating it, then selling it across the world as an energy source than they ever could be stockpiling useless weapons which no longer serve a purpose in a world without "nationalistic" boarders.
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