Tyler Cowan at Marginal Revolution responds to this question (with a very interesting consideration of robotised government):
There’s two versions of this.Leaving aside Cowan's discussion of what government means in a robotised world, isn't there a big issue with the premise of this question? The idea that state ownership of the robots is desirable? And whether 1. accurately describes how those robots will actually be owned?
1. One or a small group of entrepreneurs owns the robots.
2. The government owns the robots.
I see how we get from where we are now to 1. How would we get to 2, and is 2 better than 1?
The first point is that the robots will be an asset either of the business employing them or, assuming some sort of leasing arrangement, of a financial institution. So there may be a 'small group of entrepreneurs' owning the businesses that make the robots but the robots themselves won't be owned by those businesses (except one guesses for the robots that are making the robots that make the robots).
So the question really isn't about who owns the robots in a future economy but rather who owns the businesses that employ the robots to make and do things. This is a very different question. We can, on the basis of historical experience, dismiss the idea that state ownership of the economy is better than other forms of ownership. The Soviet Union tells us this is the case. At the same time, however, we can see that the productivity gains from the robot economy have to arrive in the pockets of regular folk for that robot economy to work.
Partly this distribution of the robot benefits comes through goods and services being cheaper (lots cheaper in some cases) thereby allowing our money to go further. But there is also the consideration that the benefits cannot simply go to a few entrepreneurs if the advantages of robots are to be realised. This is where some advocates of minimum basic income get their shtick - government taxes the robots' added value and shares it with the humans who don't have jobs any more thereby allowing those humans space to go off and do exciting, creative stuff. This does presuppose that government will not crash the robot economy so as to pay the higher basic income they promised in order to get elected. Not a presupposition I'd care to put money on.
Far better would be for us - not the government but us - to own the robots. Or, to put it another way, to own the businesses that employ the robots. And we have the models for this - mutual funds, pensions, investment funds. It would be good if (and Cowan's robot government suggests this might be so) government didn't crowd out investing in business by running huge debts funded by money that might otherwise be invested in the productive economy.
So the robot future could be very different from our presumption. Much smaller (or really much cheaper which isn't quite the same thing) government meaning that money currently taken either in taxes or spent buying government debt is available to invest in businesses that employ the robots. And a whole load of that money will belong to 'we the people' - actually belong rather than belong in some sort of romantic, wistful socialist manner. We get to own the robots.
So it's not how we get from 1. to 2. in the original question but rather how does government help us get to own those robots.