These IRV opponents argue that there is a failure to produce a "real" majority under IRV because they use the total number of votes in the first round to compute a majority, not the total number of votes cast in the instant runoff. Sometimes the number of exhausted ballots - that is, ballots that don't rank any of the remaining candidates in the final instant runoff - can mean that neither of the two finalists has more than 50% of the votes cast in the first round.
The mayoral election in Burlington (VT) in 2009 is used as an example of this "failure." In the first round of that election, the results were:
Kurt Wright 2,951
Bob Kiss 2,585
Andy Montroll 2,063
Dan Smith 1,306
James Simpson 35
(With four invalid ballots, three of which were later found to be valid in a partial recount.)
In the final result of the election, the results were:
Bob Kiss 4,313
Kurt Wright 4,061
(with 602 exhausted ballots and the 4 invalid ballots)
IRV opponents argue that although Kiss won a majority of the valid ballots in the final round of voting, he failed to win a "real" majority because his final round votes were only 48% of the votes case in the first round.
IRV advocates point out that the result was due to some voters exercising their option to abstain from a choice between the two finalists - just as many registered voters abstained from voting in the first place. That doesn't change the fact that winner Bob Kiss earned majority support from voters who chose to indicate a preference for either him or Kurt Wright.
Australia avoids this possible outcome by requiring voters to rank all candidates in its IRV races for the House of Representatives. That's certainly an option for those who care about this definition of a majority, and it does ensure the voters take the time to indicate their last choice along with their first choice. But if eligible voters have the right to skip voting altogether, some will argue that they have the right to skip ranking candidates they don't like.
But it's not fair to say that in contrast to IRV, traditional runoff produces a "real" majority while discounting the total number of votes cast in the first round when calculating a majority. By this argument, Vincent Dober won a "real" majority in the March 2009 Burlington's City Council Ward 7 election even though he received considerably fewer votes in the second round of the runoff election than his opponent received in the first:
Ellie Blais 461
Vincent Dober 612
Eli Lesser-Goldsmith 619
Vincent Dober 515
Eli-Lesser Goldsmith 425
Under the standards that IRV opponents apply to IRV, we would use the first round totals to compute a majority, and Dober in the runoff would have secured only 30% of the vote - a considerably worse majority "failure" than in the Mayoral election held at the same time with IRV. IRV opponents can't have it both ways. Either Bob Kiss and Vincent Dober both won majorities or neither of them did. Under normal usage, the candidate with more than 50% of the votes counted in the final round is called a "majority winner."
A more consistent standard to compare IRV and traditional runoffs would be to look at the decline in participation from the first round to the last. In the Mayoral election under IRV, 93% of the voters who cast a ballot in the first round ended up participating in the final round. In the City Council election under a traditional runoff, only 55% of the voters who cast a ballot in the first round ended up participating in the second round.
Another revealing example is the 2008 U.S. Senate election in Georgia. Incumbent Republican Senator Saxby Chambliss won re-election in a December runoff after falling short of a majority in November. Turnout in the second round was only 57% of the first round in spite of the fact that a Democratic filibuster-proof majority was at stake in the Senate.
Saxby Chambliss 1,867,097
Jim Martin 1,757,393
Allen Buckley 127,923
Saxby Chambliss 1,228,033
Jim Martin 909,923
If this election was held under IRV, the number of ballots cast for the final round would have been at least 96.6% of the first round total. It would likely have been higher, as most of Libertarian candidate Allen Buckley's supporters probably would have indicated a second preference. Even if Buckley won a far larger share of the vote and none of his supporters cast votes for their second choice, it would have been mathematically impossible for final round votes to fall to only 57% of the first round total as under a traditional runoff.
To be fair, it is possible for second round turnout to exceed that of the first round under a traditional runoff - and every now and then it happens. However, large declines in turnout seem to be the norm under traditional runoffs - sometimes dramatically so, with turnout falling on the order of ten times in statewide primary runoffs in Texas and North Carolina in 2008. Federal primary runoffs in the several stats that hold them provide particularly strong evidence for large declines in participation from the first to the second rounds of traditional runoffs. From 1994 to 2008, turnout declined in 113 of 116 regularly scheduled federal primary runoffs, and the average decline was about 35% - see FairVote's data on these runoffs.
Bottom line: you can't make a majority of voters like one of the candidates running. But you can enact IRV to make sure you always elect the candidate who has majority support over his or her top opponent in the final round and to ensure the defeat of the candidate whom a majority of voters see as their last choice - a result that plurality voting makes all too possible.