  Note that  focusing on voting methods that limit the information required from   the voters  to selecting one or more of the alternatives  hides all the interesting   phenomena discussed in the previous sections, such as the existence of a Condorcet paradox.   Returning to the study of voting methods  that require voters to rank the alternatives,  the most important characterization result is Ken Arrow’s celebrated impossibility  theorem (1963). Arrow showed that there is no social welfare function (a social welfare function maps the voters’ rankings (possibly allowing ties) to a single social ranking) satisfying universal domain, unanimity, non-dictatorship (there is no voter \(d\) such that for all profiles, if \(d\) ranks \(A\) above \(B\) in the profile, then the social ordering ranks \(A\) above \(B\)) and the following key property:  