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Ranked-Choice Voting: Mathematically Flawed

Thomas Young

Thomas Young is an economics professor and current Treasurer of the Salt Lake County Republican Party.

“The concept of political equality from the Declaration of Independence, to Lincoln’s Gettysburg Address…can mean only one thing—one person, one vote.” (Justice William O. Douglas, Gray v. Sanders, 1963)

The most basic of principles from the founding of our country is the idea of equality, that “all men are created equal…” As such, when creating our government, the democratic process of voting must be fair and equal for all. If my vote can sway an election more than yours can, that is wrong.

Ranked-choice voting (RCV) is a mathematically flawed system of voting. It treats some voters “more equally” than others. It contains paradoxes in vote counting that can give an outsized influence on certain votes. It makes claims like “majority winner” and “consensus winner” that are not guaranteed. But mostly, it violates the concept of one person, one vote.

The advantage that proponents of Ranked-choice voting have is that, like most political topics, there are easy sound-bites and emotionally-appealing aspirations: Better, Faster, Cheaper. All those things sound good. But when you get into the nitty-gritty, the claims don’t turn out quite the way they look on the brochure.

In city council elections that do not use districts, traditional voting would have each voter cast a vote for as many DIFFERENT people as there are seats available. So, if there are three city council seats, you can vote for up to three different people. I emphasized the word different, because in Vineyard and Payson in their 2019 city council races, approximately 25% of the voters only had their vote for ONE candidate counted for all 2 (Vineyard) or all 3 (Payson) seats. In Lehi, in 2021, it was 1,376 people who, while they filled out their ballot like everyone else, because of the RCV algorithm, only their first-choice candidate was tabulated for all the city council seats. The rest of the electorate, however, was able to get 2 or 3 or more different choices tabulated. Why should some voters get more votes counted than others? That’s the entire premise of Ranked-choice voting. In the end, Ranked-choice voting doesn’t end up being fair to all voters.

In Ranked-choice voting elections, there are several paradoxes that occur. I will pick just one to explain. In Moab’s 2021 election, the winner of the first city council seat, Jason Taylor, received 901 votes in the final round of counting for that seat. The next closest competitor was Josie Kovash with 847 votes. In a traditional election, in order to change the outcome of that race, Josie Kovash would need to receive 55 more votes to change the outcome of the election. However, if just 3 specific voters who voted for Jason Taylor as their last choice or second to last choice had voted for him as their first choice, Jason would have lost and Luke Wojciechowski would have won. And Luke wasn’t even in the final round for Seat 1. Giving a candidate more first-choice votes should not make him lose! And being able to change the outcome of an election with just a minimal switch of 3 votes is also problematic. This concept of doing your preferred candidate harm by ranking them high or helping your least-preferred candidate by ranking them last is a concept called non-monotonicity. It is a documented flaw (or feature, depending on your point of view) of Ranked-choice voting. It’s very difficult to have confidence that the will of the voter was carried out when you can make such sweeping changes to the outcome of an election with such small adjustments to ballots. And it’s certainly counterintuitive for a voter to find out they helped their least-preferred candidate WIN by ranking him LAST!


Another problem with Ranked-choice voting is ballot confusion. Ballot confusion in Genola’s 2021 city council race for Seat 1 was 58%. For Seat 2, that number ballooned to 75%. Anything more than a 1% discarded or confused rate should be concerning. In Utah County and Moab in 2021, there were seventeen races that used a Ranked-choice voting ballot. Seven of those seventeen, a full 41%, had discarded/confused ballots in excess of 10% of total ballots cast.

This brings me to my final set of concerns: false majorities and lack of consensus. Winning with a majority is a “benefit” that RCV proponents tout. I bring it up only to show that it doesn’t always turn out that way. Knowing that a candidate won with a plurality, say 40% of the vote, is beneficial and completely transparent. If you can get enough votes to win, but not enough votes for a majority, then you know the level of support from your electorate. You may not be able to make major changes because your message didn’t resonate with a lot of the people. But if you were able to garner 5th, 6th, and 7th place votes, via RCV, in enough numbers to give you a “majority”, is that truly transparent and does it reflect the true consent of the governed? I would argue, it does not. Additionally, the “majority” is often only a majority of the final round of counting. Ballots that are confused or discarded, as mentioned above, do not count toward that “majority”. And ballots that did not rank the final two candidates (known as exhausted ballots) are also excluded from that calculation of majority. In San Francisco in 2010, there were 21 candidates in a Board of Supervisors race. The winner received 4,321 votes after 20 rounds. However, there were 9,608 exhausted ballots—more than TWICE the number of votes received by the “majority” winner. Ranked-choice voting is also touted as electing the consensus winner: the person who is supported by the greatest number of people. However, often, when you compare the rankings of candidates two-by-two, you will find that the consensus winner was someone other than the final victor. In Moab’s 2021 election, the “consensus winner” for seat 1 was Luke Wojciechowski. However, as was previously mentioned, Jason Taylor won that first seat.

Ranked-choice voting has many paradoxes and unintended consequences. Some voters are treated more equally than others. The mathematical flaws are well-documented and concerning. Voter confusion and discarded ballots are much higher than in a traditional election, which leads to voter disenfranchisement.

In short, our system of government is only legitimate if we, the people, give our consent to those who represent us. If a voting system does not treat voters equally and provide a transparent, fair method of counting, do we really have consent of the governed? Traditional elections provide us with a simple, transparent and fair process that treats all equally: one person, one vote!

9 thoughts on “Ranked-Choice Voting – Mathematically Flawed”

  1. Professor Young, thank you so much for your in-depth explanation why RCV is flawed. I am look forward to meeting you in person. I Can be reached at 801-793-0800.

  2. I interpret “one person, one vote” to mean all people vote and those votes are added up. It should not be set aside because of a group of people, whom we don’t vote into power, get to vote for the actual outcome. It seems that one person’ vote doesn’t always count.

    1. Great observation. Any city with ranked choice voting or which is in imminent threat of having it must follow the voters themselves. Place it on the ballots as a permanent referendum. Voting is our fundamental stake in government as citizens and the left thinks little of anyone as citizens except on election day. No committee must decide this, WE THE PEOPLE are the only ones who should classify our own votes. Ranked choice voting must STOP!

  3. How can we get RCV abolished? As you have noted, RCV is NOT fair, does not make sense, and should be forever banned from our elections. As Democrats are a perfect reverse barometer, it should tell us something when they love RCV.

  4. I am a strong opponent of RCV, but Steven is exactly right: there is no perfect system. “One man, one vote” is not an electoral system. It is a slogan. It is language found nowhere in our founding documents for the very good reason that many of the institutions created by the Constitution do not follow it. The Senate is one example, and we see RCV proponents already taking aim at it. They have been after the Electoral College for years, and for the same reason: it does not conform to the slogan.

    Young’s quote of William O. Douglas at the beginning , however, is extremely problematic. If I recall the case, it was one of a series that included Wesberry v. Sanders and Baker v. Carr, in which the Court struck down electoral systems that overweighted rural voters and/or required that all State senates be composed of the same number of voters, instead of representing counties (the analogy to the U.S. Senate should be clear). Douglas then (and RCV today) wanted a nationalized electoral system that would feature popular election of the president and proportional representation in the House and Senate.

    RCV is a Siren call. Let’s resist it before we crash on the rocks.

  5. Interesting that we use a form of RCV in our own County and State conventions. When we have 3 or more candidates and none receives >50%, we eliminate the lowest candidate and vote again until someone gets a majority of the vote. The only real difference is that we see the outcome of Round 1 before we cast our Round 2 vote. I see a disconnect when we lash out at RCV.

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