If there are two places that one could go to, then I’d, if there is one person, want our state to build two roads taking the person to whichever place he wants to go. So state, for our present purposes, is a collection of two roads. A state-of-affairs with only one road is unsatisfactory; the person, then, can go to only one of the two places to which he could potentially go. States are supposed to be small: we do not want a state with more than 2 roads; then there will be more than 1 road to a place and our fictitious person would have to choose (which calls for consciousness and then there is the Buridan’s ass story).
What if there are more people? How big does the state have to be (say, after limiting peoples aspirations to 2 places)? Pareto liberalism wants everybody to go wherever they want to go (irrespective of where others go). So if we have two people, how many roads, then, do we need? One to take both to place 1, one to take both to place 2, one more to take person 1 to place 1 and person 2 to place 2, and one last one to take person 1 to place 2 and person 2 to place 1. Remember state is for all–there are no roads which take some people places and leave others–we in this together.
Given people and the places they want to go, is there a way to build a state (just the right-size) that lets them?
I’ll be back after studying map objects (Conceptual Mathematics, page 313).