I was going to say the same thing as the first bullet point here—you can interpret the preference ordering as “If you were to give the agent two buttons that could cause world state 1 and world state 2 respectively, which would it choose?” (Indifference could be modeled as a third button which chooses randomly.) This gives you a definition of the full preference ordering which is complete by construction.
In practice, you only need to have utilities over world states you actually have to decide between, but I think the VNM utility theorem will apply in the same way to the world states which you actually care about.
I was going to say the same thing as the first bullet point here—you can interpret the preference ordering as “If you were to give the agent two buttons that could cause world state 1 and world state 2 respectively, which would it choose?” (Indifference could be modeled as a third button which chooses randomly.) This gives you a definition of the full preference ordering which is complete by construction.
In practice, you only need to have utilities over world states you actually have to decide between, but I think the VNM utility theorem will apply in the same way to the world states which you actually care about.