If competitors aren’t willing to invest because the return on investment would be too low to make it worthwhile that’s one thing. It’s quite different from minimum efficient scale being so high that you can only efficiently have one supplier in a particular market. A local monopoly is not evidence of natural monopoly. A local monopoly has to worry about potential competition, a natural one doesn’t. Rail services in North America look like a natural oligopoly, not a natural monopoly. There are no particular welfare implications in those since if you can’t legally enforce collusion it doesn’t last. Plenty of oligopolies are competitive. Intel worries plenty about AMD.

If you search for Norfolk Southern competitors the following names come up, Union Pacific, Canadian National Railway Company, CSX Corp, Canadian Pacific Railway and Kansas City Southern[0]. Whatever that is it isn’t a natural monopoly.

Violence has high fixed costs and relatively low marginal costs. If the efficient number of states, violence monopolists, is so much greater than one why would we expect anything else to be a natural monopoly?

[0]http://financials.morningstar.com/competitors/industry-peer....