We are faced, in this case, with the prospect of minority rule in single-seat elections, such as mayor or governor. Those elected should have the support of a majority of the voting population, not simply more than each of the other candidates. Unfortunately, this promise is not guaranteed under plurality voting.
This problem is compounded when plurality voting is also used in primary elections. Party primaries often see a crowded field of candidates from across the political spectrum vying for a single nomination. This frequently leads to a party's nominee representing a large and diverse constituency in the general election, after having only garnered the support of a small fraction of the party's supporters. In a general election, this same candidate can go on to win again without a majority of voters' support. An equally likely scenario, however, is that a party's eventual nominee is not the strongest candidate that they could have endorsed for the general election.
The democratic standard ought to be majority rule; it is a fundamental principle of republican governance. So in choosing the method of electing our leaders, we should demand that it holds to the principle of majority rule. For this reason, FairVote advocates instant runoff voting (IRV), a method that produces majority winners and replaces plurality elections wherever they are used.