ABSTRACT
A social ranking function is a function that inputs a voter profile and outputs a complete ranking (permitting ties) of the candidates. Where a social choice function chooses winners, a social ranking function ranks all candidates. A social ranking function can be thought of as a method for taking the preference lists of all the voters and producing a composite preference list representing the entire electorate. But note: Ties are forbidden on voter preference lists, even though ties are expressly permitted on the social preference list. For example, if the set of candidates is {A ,B ,C ,D ,E ,F ,G}, a typical output might be described by a notation like C > D = G > A = E = F > B to describe the electorate’s view that candidate C is best, candidates D and G are tied for second best, candidates A, E, and F come next and are equally regarded, and candidate B is worst.
