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Why IRV Produces a Majority Winner

by Alec Slatky // Published July 12, 2010

            The Portland (ME) Charter Commission’s consideration of instant runoff voting (IRV) elicited spirited advocacy from supporters and detractors alike.  Under IRV, as described by FairVote, voters can rank all candidates in order of preference.  If no candidate wins with a first-choice majority, the candidate with the least first-place votes is eliminated and their supporters' second choices are distributed to the remaining candidates.  The process of elimination and redistribution continues until one candidate has more than 50% of the votes.

            Ultimately, the commission sided with supporters, voting 10-2 for a unified recommendation of a directly elected major using IRV (or “ranked choice voting”, as they call it), and the Portland Press Herald reported that “Commissioner Nathan Smith, who is leading the subcommittee [examining concerns about IRV], said Monday that the committee has found no reliable evidence that the new voting system would cause widespread confusion or disenfranchise voters. Ranked-choice voting is the best and most cost-effective way to ensure that the mayor is elected with a majority vote, Smith said.”

            As Nathan Smith noted, one criticism of the voting system was that contrary to claims by pro-IRV activists, IRV does not necessarily produce a “majority winner.”  This criticism is misleading, and does not recognize the true meaning of a “majority winner” in any given election.  This post aims to refute the idea that IRV fails to produce a majority winner.

Compulsory voting

            Compulsory voting is not part of United States policy.  Back in the 1770s, Georgia included it in its state constitution, but there are very few other examples.  The United States regards voting as a right – indeed, one of our most cherished and sacred rights – but not an obligation.  Voting is something people are encouraged to do, as they should be, but is not, nor should it be, an act that citizens are required to perform.

            Compulsory voting restricts the freedom to not vote, which citizens do for a variety of reasons.  Some citizens are not registered, and thus do not have access to the ballot box, a problem that should be remedied.  But plenty of other respectable citizens do not vote for a number of perfectly valid reasons: they may believe the system is illegitimate and fraudulent, and thus want no part of it; they may be religiously compelled to avoid politics in all its forms, like Jehovah’s witnesses; they may believe that since the probability of their vote changing the election is very low, the trip to the polls is not worth their time.  Feel free to disagree with all of these rationales, as most people do, but nothing gives the government the right to force people to act against them.

            The most obvious reason to abstain from voting is the lack of a favorite candidate, or more importantly, the lack of any candidates deemed even acceptable.  The phrase “the lesser of two evils” has become common parlance in American electoral discourse.  Some people do indeed cast their ballots for the lesser of two evils, which is fine.  Others prefer to avoid helping candidates whom they despise, even if one is despised slightly less than the other.  Some might even consider the two candidates equally bad.  The point is, if a voter doesn’t like McCain and doesn’t like Obama, who is to say that they should be forced to make a decision to support one of them?

            In instant runoff voting, the idea behind allowing voters to “bullet vote” – cast a ballot for only one candidate rather than ranking all candidates behind him – is the same.  If a voter has a clear first choice, even a clear second and third choice, but none of those preferred candidates make it to the final runoff, he or she does not have to express a preference for either of the final two candidates.  Voters can decide to do so, like those who choose the lesser of two evils in a plurality election, but they also have the freedom not to.

            Consider a slightly ridiculous example, and bear with me on a rewriting of history.  World War II, before the USA entered it, had 3 parties: the Axis, the Allies, and the U.S.S.R.  The USA is eager to support the Allies, with whom they align on general political views, and they do so.  Unfortunately, the Allies are wiped out, leaving only the Axis powers and the Soviet Union fighting it out.  The following question is soon raised in Congress: should we support the Soviets, the Axis, or neither?  My personal answer would be neither, but someone else might say the Soviets, or even, shockingly, the Axis.  Reasonable people can disagree on this point.  No matter what, the war will be decided – either the Soviets or Axis will emerge victorious – but the USA doesn’t have to take a side with a group it sees as morally bankrupt, and would prefer to see the rest of the world determine the outcome rather than being active participants.  They can take a side, but they are not required to, ethically or politically.  Now consider the same scenario, but where the League of Nations thinks that this war is so important to the fate of the world, that everybody must take a side.  Even with the debate about which faction to side with, if any, legislators in the USA would universally condemn this declaration as an infringement upon the country’s sovereignty.  People might disagree on whether the USA should pick a side, but few would claim that they should be forced to do so.

            Now, I grant that the preceding example was somewhat absurd, and that deciding to fight a war is obviously different than electing a representative, but the principle holds true.  The Allies are akin to a first choice that is eliminated in the runoff, leaving the Axis and the U.S.S.R. as the final two candidates.  Some will express a preference, and some will not, and both decisions must be regarded as equally acceptable.

Was Barack Obama a “majority winner” in the 2008 Presidential election?

            The obvious answer to this question is yes, Barack Obama was a majority winner in the 2008 Presidential election.  It would be nearly impossible to find anyone who says otherwise.  Forgetting about the Electoral College, Obama received 69,456,897 votes out of the 131,257,328 cast, equaling 52.92% of the votes.  Since that percentage is greater than 50%, Obama is considered to be a majority winner; put simply, he won a majority of the votes.

            Under any denominator other than votes cast, though, Obama does not emerge as the majority winner.  According to Census estimates, 30.8% of the total voting-age population voted for him; 33.7% of the total citizen voting-age population voted for him; even among just the registered voters, that number only increases to 47.5%, less than a majority.

            But if someone claimed that Obama was not a majority winner and cited these statistics, who would take him seriously?  It is clearly true that Obama did not receive the support – meaning votes – of a majority of the country, but this is not the metric on which we base calling someone a majority winner; if this is the case, then very few Presidents, including the ones who received greater than 50% of the vote, can be called majority winners.  This proposition is foolish.  The nonvoters did exactly that: chose not to vote.  If you choose not to express your preference, you are not counted – in fact, you are choosing not to be counted.  The reason for not voting is irrelevant, because we grant people the right to not vote, with a price: forfeiting your right to be counted.  So if nonvoters voluntarily give up their right to be included in the electoral results, then utilizing them to say that a majority has not been achieved is unfair.

Majorities in IRV

            Joyce McCloy has a new blog post describing the “Instant Runoff Voting Lie” that “IRV…provid[es] a 50% + 1 majority win,” and cites statistics from Cary, North Carolina, which she claims prove that IRV does not always elect a majority winner.  Her statistics are absolutely correct.  The District B City Council race featured three candidates.  In the first round of the instant runoff, Don Frantz received 1151 votes, Vickie Maxwell had 1075, and Nels Roseland finished with 793, in addition to 3 write-in ballots.  Since no candidate achieved a majority, the runoff was conducted using the ranked ballots.  The write-in candidates and Roseland were eliminated, and their 796 votes were distributed to the higher ranked of Frantz and Maxwell, according to the ballots.  After the runoff, Frantz won the election with 1401 votes, which is 50.9% of the runoff vote, but only 46.4% of the initial votes cast.  What happened?

            There were 3022 votes initially cast, and 2754 tabulated in the runoff.  That means that 268 ballots were not included in the runoff, for a very simple reason: they chose to rank neither Frantz nor Maxwell, but instead bullet voted for Roseland (if the write-in voters made up part of those 268, they may have ranked Roseland second but still ranked neither of the other two candidates).  This essentially amounts to not voting in an election between the top two candidates.  In fact, these voters were in the voting booth, so there was no reason for nonvoting like a general opposition to the system.

            There are two conceivable rationales for not ranking Frantz or Maxwell on the ballot.  First, a voter might have been completely indifferent between the two, and in an election would be equally pleased or upset if either of them were victorious.  This voter would not have voted in a plurality election between the top two candidates, because he would not want to express a preference he does not truly have; this applies to IRV as well.  The other possible reason is that both candidates were so abhorrent to the voter that even choosing between the lesser of two evils was unacceptable.  It is not a large assumption to guess that those voters would be nonvoters in a separate election between the top two candidates.

            The argument boils down to this: some number of voters, 268 in Cary, did not care to choose between the top two candidates, even when given the opportunity to do so.  They voluntarily opted out of the election at that point, and thus are not counted, just like nonvoters are not counted, because neither expressed their preference.

            A possible response might be that if those 268 voters knew that the election would come down to Frantz and Maxwell, they would have expressed a preference.  But they knew beforehand that there were three possibilities: Frantz and Roseland are in the runoff, and their votes help Roseland; Maxwell and Roseland are in the runoff, and their votes help Roseland; Frantz and Maxwell are in the runoff, and their votes help nobody.  They knew that ranking either Frantz or Maxwell second could never hurt their first choice candidate, Roseland, and yet they declined to do so.

            IRV voters should not have to rank all candidates, for the same reasons as we permit registered voters to sit out an election.  As long as we do not have compulsory voting as part of our electoral system, voters are allowed to not express a preference.  When that happens, they become part of a pool that is not counted in the election, and thus should not be under consideration when determining a majority winner.

What we mean by a “majority winner”

            A majority winner is based on, essentially, a majority of the willing, a majority of the voters who expressed their preferences.

            If a majority winner means a candidate who won a majority of the electorate, then no, IRV does not always produce a majority winner.  But this has never been the definition used in political discussion.

            If a majority winner means a candidate who won a majority of voters who displayed any preference, including those who did not rank either of the final two candidates on the ballot despite given an opportunity to do so, then no, IRV does not always produce a majority winner.  But this is not the definition when it comes to nonvoters, so it should not be the definition when it comes to the voters who, when given the opportunity to do so, declined to include either of the final two candidates on the ballot.

            If a majority winner means a candidate who won a majority of voters who expressed a preference between the final two candidates, which is the only description logically consistent with the modern connotation, then yes, IRV always produces a majority winner.

Why IRV Produces a Majority Winner, in 4 sentences

            All registered voters can vote; some choose not to.  All voters in IRV can rank all of the candidates; some choose not to.  Since we don’t consider nonvoters when describing the winner of a plurality election as a “majority winner,” there is no reason to consider voters who choose not to rank all of the candidates in IRV when describing the victor as a “majority winner.”  Under all reasonable definitions of the phrase, the mathematics of IRV requires it to produce a majority winner.