 A voting method is a function that assigns to each possible profile a group decision. The group decision may be a single candidate (the winning candidate), a set of candidates (when ties are allowed), or an ordering of the candidates (possibly allowing ties).  Note  that since a profile identifies the voter associated with each  ballot, a  voting method may take this information into account.  This means that  voting methods can be designed that select a winner (or winners) based only  on the ballots  of some subset of voters while ignoring all  the other voters’ ballots.    An extreme example of this  is the so-called Arrovian dictatorship for voter \(d\)   that assigns to each profile the candidate ranked first by  \(d\).   A natural way  to  rule out these types of  voting methods  is to require that    a voting method is anonymous: the group decision should   depend only on  the number of voters that chose each ballot. This means that   if two profiles are permutations of each other, then a voting method that is   anonymous must assign the same group decision to both profiles. When studying   voting methods that are anonymous, it is convenient to assume the inputs are anonymized profiles. An anonymous profile for a set of ballots \(\mathcal{B}\) is a function from \(\mathcal{B}\) to the set of integers \(\mathbb{N}\). The election scenario discussed in the previous section is an example of an anonymized profile (assuming that each ranking not displayed in the table is assigned the number 0). In the remainder of this article (unless otherwise specified), I will restrict attention to anonymized profiles.   