 I conclude this section with a few comments on the relationship between the ballots in a profile and the voters’ opinions about the candidates. Two issues are important to keep in mind. First, the ballots used by a voting method are intended to reflect some aspect of the voters’ opinions about the candidates. Voters may choose a ballot that best expresses their personal preference about the set of candidates or their judgements about the relative strengths of the candidates. A common assumption in the voting theory literature is that a ranking of the set of candidates expresses a voter’s ordinal preference ordering over the set of candidates (see the entry on preferences, Hansson and Grüne-Yanoff 2009, for an extended discussion of issues surrounding the formal modeling of preferences). Other types of ballots represent information that cannot be inferred directly from a voter’s ordinal preference ordering, for example, by describing the intensity of a preference for a particular candidate (see Section 2.3). Second, it is important to be precise about the type of considerations voters take into account when selecting a ballot. One approach is to assume that voters choose sincerely by selecting the ballot that best reflects their opinion about the the different candidates. A second approach assumes that the voters choose strategically. In this case, a voter selects a ballot that she expects to lead to her most desired outcome given the information she has about how the other members of the group will vote. Strategic voting is an important topic in voting theory and social choice theory (see Taylor 2005 and Section 3.3 of List 2013 for a discussion and pointers to the  literature), but in this article, unless otherwise stated, I assume  that voters choose sincerely (cf. Section 4.1).