Unrestricted domain: Difference between revisions
→Spatial modeling
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When voting theorists create [[spatial models of voting]], they map voter opinions regarding different topics onto different dimensions in space. The most readily understood models have one, two, or three dimensions, but more dimensions are possible.
Mapping voter opinion to multi-dimensional space is tricky. When theorists choose four or more dimensions for their models, the result is difficult to visualize in a three-dimensional space. Moreover, the 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 involving many candidates, with the vast majority of election scenarios being impossible to arise.
Conversely, notwithstanding any assumptions of a spatial model, certain voting methods with arbitrary ballot restrictions may be fundamentally unable to capture the information available in an electorate.
==Ranking==
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==Examples of restricted domains==
{{Seealso|Median voter theory}}
[[Duncan Black]] defined a restriction to domains of social choice functions called ''"single-peaked preferences"''. Under this principle, all of the choices have a predetermined position along a line, giving them a linear ordering. Every voter has some special place
==References==
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