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From a website called Fair Vote -- http://www.fairvote....
Paragraph breaks added for readability.
How Instant Runoff Voting Works: IRV allows voters to rank candidates in order of preference (i.e. first, second, third, fourth and so on). Voters have the option to rank as many or as few candidates as they wish, but can vote without fear that ranking less favored candidates will harm the chances of their most preferred candidates. First choices are then tabulated, and if a candidate receives a majority of first choices, he or she is elected.
If nobody has a clear majority of votes on the first count, a series of runoffs are simulated, using each voter's preferences indicated on the ballot. The candidate who received the fewest first place choices is eliminated. All ballots are then retabulated, with each ballot counting as one vote for each voter's highest ranked candidate who has not been eliminated.
Specifically, voters who chose the now-eliminated candidate will now have their ballots counted for their second ranked candidate -- just as if they were voting in a traditional two-round runoff election -- but all other voters get to continue supporting their top candidate.
The weakest candidates are successively eliminated and their voters' ballots are redistributed to next choices until a candidate crosses a majority of votes.
Instant runoff voting allows for better voter choice and wider voter participation by accommodating multiple candidates in single seat races and assuring that a "spoiler effect" will not result in undemocratic outcomes. IRV allows all voters to vote for their favorite candidate without fear of helping elect their least favorite candidate, and it ensures that the winner enjoys true support from a majority of the voters.
Plurality voting, as used in most American elections, does not meet these basic requirements for a fair election system that promotes cost-saving elections with wider participation.