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How did you determine that? It seems to be an ideological conviction with some popularity in the steemit circles, but is that really a fact and if so, how was this established as fact? I find the first point especially unconvincing.

Competition drives innovation.
Governments are monopolies, so don't need to compete for market share within their borders.
They have no incentive to take risks or embrace efficiencies.

The way I see it, those are still assertions and I'm not sure there is actual evidence to prove those. I personally haven't found any evidence to convince me that this is really the case.

What would you accept as evidence? What would qualify?

Some facts I guess. Any data that would support these particular views. There is a wide variety of evidence that could potentially be convincing. A good place to start might be your reason to believe that this is the case.

How much time do you have? :)
Let's be specific. Which is the important service you see as least likely to be provided properly by the market, in the theoretical absence of the state?

Oh, I have time, especially if you are going to spend the time to go into detail, I will always be willing to read, digest and discuss. After all this is the idea here anyway, right? ;)

I think the market is going to have a hard time with safety, dealing with crime or undesirable and harmful behaviors, infrastructure, things like nature reserves and so on.