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The problem with the plurality voting method (limit of a single choice) is that it only ever allows for two viable candidates. The point of reform isn't necessarily to provide a majority winner, but to use a method that allows for multiple viable candidates to compete on a level playing field.

IRV is one option that allows voters more expression on the ballot, but there are others that both perform better in terms of reflecting the will of the electorate and are less cumbersome to implement. IRV's multi-round nature is opaque to voters in terms of how it actually chooses the winner, and because it requires all the rankings to be centrally located before the count can proceed, it is not summable by precinct.

A system that embodies all of IRV's advantages without its weaknesses is R-IRV - you can check out here: http://equalvote.co/r_irv . Basically, instead of rank ordering candidates, all the voters score the candidates on a scale (0 - 5, for example). The two highest rated candidates advance to an instant runoff where the voters' scoring differences are used to determine which candidate gets which voter's vote. It's always two simple stages, and it shows much more clearly each candidate's approval from the electorate. Plus it can be summed by precinct and avoids some of the weird math problems that IRV has.