That can't be correct as written because if I could magically extract everyone's scalar utility function from their minds, a mixture of utility functions would satisfy those three criteria.
You need an additional requirement, "The citizen's true ordering of preferences is the only data presented to the algorithm." In other words the algorithm can't access the scalar utility function, only the ordering, and every similar ordering has to result in the same social ordering - no mixture of utility functions will satisfy this, obviously. If you want to prevent "strategic voting" that would impose other requirements as well.
Impossibility theorems often aren't as impossible as they look, and indeed Arrow's Impossibility Theorem makes a good illustration of that, especially as the evasive answer is pretty obvious if you walk around thinking of expected utility maximizers all day long. Doesn't work for non-mind-reading applications because of the strategic voting problem, but in terms of whether it's possible for a society to aggregate the true utilities of its citizens, no sweat.