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It is instructive to consider the 2006 Liberal party leadership convention, which used a system of runoff voting to select a new party leader and which, at that time, was widely touted as a model for electoral reform. Stéphane Dion, ranked third on the first ballot of the convention, won the election, garnering a majority of the votes on the fourth, and final, ballot, when he faced Michael Ignatieff.

But the fact that Dion won the final ballot does not show that a majority of the delegates preferred him to all of the other candidates. How do we know, for example, that a majority of the delegates preferred Dion to Bob Rae or to Gerard Kennedy, who were also candidates? Certainly, Dion came out ahead of Kennedy on earlier ballots, but that doesn’t prove much; after all, Ignatieff came out ahead of Dion on three ballots, but it seems that of those two candidates, a majority of delegates preferred Dion to Ignatieff. For all we know, in a contest between Dion and Rae, or between Dion and Kennedy, a majority of the delegates might have voted for the latter rather than the former. Indeed, had a majority of voters preferred Dion to all of the other candidates, there would have been no need for runoff ballots; he would have won on the first ballot.

Claiming the winner of such an election has the support of the majority is like claiming that someone got the asking price for his house after he lowered it three times

Proponents of runoff voting for parliamentary elections usually have in mind a system such as instant runoff voting, where voters rank-order their choices. When no candidate has a majority of first-choice votes, the candidate receiving the least number of such votes is eliminated, and his or her votes are redistributed according to second-choice preferences. This is repeated — the candidate with least number of first- and second-choice votes is eliminated, and so on — until one candidate achieves a majority. But, again, it is a confusion to think that because someone has garnered a majority in the last round, he or she is preferred by a majority of the voters to all of the other candidates.