Unrestricted domain

The Universality criterion requires that a system give unique results for a given set of ranked ballots, i.e., that any set of ranked ballots should be viable as a valid set in the domain of the social choice function.

It was stated by Kenneth Arrow as part of his impossibility theorem, and it is such a basic criterion that it's satisfied by all non-random ranked systems. However, since it was defined by Kenneth Arrow before there had been theoretical analysis of rated voting systems, it does not apply to rated ballots, and so all rated systems technically violate universality. This is why some rated systems, such as MCA-P, can appear to violate Arrow's theorem by satisfying all of his more-interesting criteria such as monotonicity and independence of irrelevant alternatives. When not combined with (ranked) universality, those other criteria are not incompatible.

In the spatial model of voting, the choice of dimension for the latent space of voter opinions imposes fundamental limitations on the set of allowed elections, depending on the number of candidates, as there may be insufficient room in the space for all ranked ballots to occur. This geometric result implies that violations of unrestricted domain are common in low-dimensional simulations, and that certain voting methods with arbitrary ballot restrictions may be fundamentally unable to capture the information available in an electorate.