The theory of voting has a long and discontinuous history. Currently the theory takes individual preference rankings over alternatives as given and establishes results involving compatibility or incompatibility of various desiderata concerning ways to aggregate individual rankings into social choices or rankings. From the viewpoint of democracy, some of those desiderata are more important than others. We review some of the relevant results in this area. Since the main results are of negative nature, it makes sense to ask whether those results could be avoided if other views were to be adopted regarding the form of individual opinions.
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