Unrestricted domain: Difference between revisions
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It was stated by Kenneth Arrow as part of his [[Arrow's impossibility theorem|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|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 [[dimensional limitations of the spatial model|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, with the vast majority of election scenarios being impossible, and that certain voting methods with arbitrary ballot restrictions may be fundamentally unable to capture the information available in an electorate.
[[Category:Voting system criteria]]
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