 Rankings are one type of ballot. In this article, we will see examples of other types of ballots, such as selecting a single candidate, selecting a subset of candidates or assigning grades to candidates. Given a set of ballots \(\mathcal{B}\), a profile for a set of voters specifies  the ballot selected by each voter. Formally, a profile for set of voters \(V=\{1,\ldots, n\}\) and a set of ballots \(\mathcal{B}\) is a sequence \(\bb=(b_1,\ldots, b_n)\), where for each voter \(i\), \(b_i\) is the ballot from \(\mathcal{B}\) submitted by voter \(i\). 