# Why does ranked-choice voting give such high preference to the second choice of the least-favored candidate's voters?

Ranked choice voting is in the news lately because of the big mess New York City has made of implementing it in its Democratic primaries for the mayoral race. But in the talk about how it works, one point strikes me as a bit odd.

As I understand it, RCV counts up the first-choice candidate votes. If no one reaches 50%, whoever got the least number is washed out, and their voters' second-place candidates are promoted to first, the numbers are re-counted, and the cycle is repeated until someone reaches a majority.

While this seems like a good system at first glance, the implementation has a strange quirk in it: the people whose second-choice votes get redistributed first -- and are therefore the most likely to influence the final results -- are the ones who voted for the least popular candidate, or in other words, the ones whose preferences are the least representative of the overall will of the electorate.

What's the rationale for giving that group disproportionate power in choosing the winning candidate? That seems a bit counterintuitive.

• I think there is a logic fallacy at work. Just because one voted for the least popular candidate, this does not make one less representative of total voters. 5% of voters is still 5% of voters, no matter whom they voted for in first rank. Jun 30, 2021 at 13:25
• This like saying the only important person in a sporting event is the one that scored the winning point, ignoring that it is only the winning point because of the contributions of all the other actions that happened before it.
– eps
Jul 1, 2021 at 4:37
• I agree that there is a logical fallacy going on here. If three voters are voting between two candidates at a table and voter 1 says he votes for A, voter 2 says he votes for B, and voter 3 says he votes for A, did voter 3 have "disproportionate power in choosing the winning candidate"? What if the vote order was reversed? Jul 1, 2021 at 5:45
• The other way to look at this would be to say that in traditional elections, the votes of people who voted for the least popular candidate(s) had no influence on the result at all -- it was as if they hadn't even voted. That's the source of the common saying that voting third-party is "throwing your vote away". RCV corrects this by allowing a person to vote for an unlikely candidate, and then if that candidate is eliminated, have his vote "fall back" to another choice instead, so that every voter's vote can influence the result of the election, regardless of which candidate(s) they prefer. Jul 1, 2021 at 13:11
• Of all the preference-voting systems that exist, IRV is pretty close to the worst. But its simplicity gives it a kind of "consumer confidence" cachet. Jul 1, 2021 at 13:44

There's three main reasons:

1. It's simple. Voters are giving instructions, "I want this candidate, and if I can't have them, I want this one instead, .... n." Voters understand how their vote will be processed without having to do any maths.
2. It reflects a reasonable approximation+ of strategic voting. In single-vote systems, people often vote against their own preference, because the candidate they prefer doesn't have a realistic chance of winning. (This is, in fact, one of the major problems with single-vote systems.) RCV allows a more accurate picture of their actual preferences, and before their unusual tastes are ruled out of the possibility space, their unearned support for a given strategic-choice candidate is taken out of the picture.

+: This is an oversimplification and applies only to the case of voters whose preferred candidate is dead last (or close thereto). See this link for more detail about the concept of strategic voting. (Credit to @eclipz905 for the link.)

1. Your estimate of their influence is likely too high. Votes are distributed to 2nd choices at the individual vote level. So when candidate #5 is eliminated, the - let's say 1,000 - votes they earned are not awarded to a single other candidate. Instead, they are allocated according to each of those 1,000 voters' preferences. Depending on the texture of the field, it is entirely possible that all four remaining candidates receive a share of that 1,000. It's also possible that some voters did not indicate a 2nd choice, in which case those votes drop out of the electorate that cycle entirely.

In short, this group does not receive disproportionate power. You are correct that they are the main beneficiaries of RCV systems - they're now allowed to rationally vote for the candidate they actually prefer, instead of being forced to make a strategic choice between two candidates they like less (at best).

Under single-vote systems, their preferences are essentially being quashed.

• "... they're now allowed to rationally vote for the candidate they actually prefer ...". This is not accurate. Under RCV (a.k.a. instant runoff voting [IRV]), voting for one's sincere preferences is only safe if the preferred candidate is very strong, or very weak. In competitive scenarios, there is strong incentive to vote strategically. This is specified with the Favorite Betrayal Criterion and visualized here Jul 1, 2021 at 13:57
• What's funny is that approval voting is even simpler to understand and tabulate, and never requires people to cast votes contrary to their true preferences, but for some reason people aren't comfortable with the idea of being able to cast more than one vote despite the fact that at most one of the votes a person casts in a single-winner election could affect the election (votes for anyone other than the final winner have no effect). Someone who prefers A to B but B to C may be stuck in a quandary as to whether to mark the ballot for both A and B, or just A, but neither ballot would be... Jul 1, 2021 at 16:52
• @supercat - I've wondered that myself. I even asked one of the main people from an organization lobbying their state government for RCV why not approval voting instead, and got a kindof non-answer back. Jul 1, 2021 at 21:19
• @Bobson The only possible argument for RCV is "momentum". Unfortunately it's a pretty effective argument Jul 1, 2021 at 23:02
• @supercat: RCV favors the big parties over the small parties. The big parties are perfectly happy to see RCV take votes away from the small parties and reallocate them to the big parties, but they would be very unhappy if e.g. the Schulze method decided that "This centrist is the Condorcet winner, even though 90% of the electorate voted for somebody else as first choice." They don't want a good electoral system as much as they just want to get rid of the spoiler effect from 3rd party candidates. In other words: Approval voting creates the risk of a third party actually winning! Jul 3, 2021 at 7:43

This type of ranked-choice voting is effectively like doing a bunch of run-off elections all at once. In other words, assuming there are five candidates (A, B, C, D, and E), we could do the following:

1. Hold an election
2. If there is no winner, scratch off the worst candidate (E) and hold a run-off
• those who voted for A, B, C, and D will cast the same vote, but E's supporters will have to choose from the remaining four
3. If there's no winner, scratch off the new worst candidate (D) and hold another run-off
• those who voted for A, B, C will cast the same vote, but D's supporters (including those who might have originally voted for E) will have to choose from the remaining three
4. Repeat runoffs until a clear winner emerges

On a ranked-choice ballot, we put who we want to win as the first choice, and who we would vote for if our guy got scratched as the second choice, who we would vote for if both our choices got scratched as the third choice... The only difference from a series of recall elections is that we don't get the opportunity to change our minds if our first-chosen candidate survives into the run-off. But not that many people would change their minds — changing first-preferences reflects either deep apathy or deep strategy — so that doesn't seem to be a great hardship.

It may look as though we are giving excess power to those who support the least popular candidate, but in fact we are just asking them to choose again, as though the candidate they want had never run at all. It's as fair and balanced as any other first-past-the-post ballot; we're just saving time and money on do-overs.

• This is an interesting perspective, but the counterpoint is that the runoff itself can add new and relevant information. I know there have been times I've wished I could change my vote after seeing how a candidate reacted to the results of a narrow election; I can't help but think there are lots of people who would say the same. Is it really a good idea to force the election to be decided on incomplete information? Jun 30, 2021 at 14:33
• Indeed one of the many names of the system (and the one which seems to have been used on Wikipedia) is Instant-runoff en.wikipedia.org/wiki/Instant-runoff_voting. Jun 30, 2021 at 14:39
• @origimbo: A name I very much prefer over “ranked-choice voting”, on the grounds that there are other methods based on ranking choices that are totally unrelated to IRV (e.g., Borda, Condorcet, and their numerous variants). Jun 30, 2021 at 22:01
• The other difference between IRV and traditional run-offs is that in a traditional run-off, not everybody who voted in the first election will vote in the run-offs. Turnout tends to drop off with each subsequent round of run-offs, as not everybody wants to or can wait in line multiple times for the same election. So even the people whose candidate didn't get eliminated in the first rounds might just not show up at all the next time. With IRV, you only need to take time off to vote once, so this isn't an issue. Jul 1, 2021 at 14:36
• @MasonWheeler That way lies madness. When do you know information is no longer incomplete? All elections are decided on incomplete information. Jul 1, 2021 at 16:02

It's mathematically sound. It may seem as if checking the second-place votes of other "losing" candidates besides the last might give different winners, but it won't.

You're thinking we could have candidates A, B, C and D (in order of vote totals) where eliminating D could make A win, but eliminating C could make B win:

``````A <- D (all D's 2nd choice is A) adds to >50%
B <- C (All C's 2nd choice is B) adds to >50%
``````

That would be a possibly unfair situation, except it's impossible. The votes add to more than 100%. Put another way, if the last place being eliminated could make someone else win (be over 50%), then no one else can possibly win (they can't also get over 50%). No matter what order you go in, you'll have to eliminate D and check their 2nd place choices. Similar math works with groups -- say you eliminate candidates Z, then Y, X, W ... and their 2nd choices put C over the top. That's >50%, which means eliminating D through V couldn't have made anyone else win anyway.

There is possible funny business, but with "compromise candidates". Suppose we have votes for A(40%), B(39%) and C(21%) and everyone's 2nd choice is C (C voters have no 2nd choice). So 100% of the voters think C isn't too bad. But our system eliminates C, which removes those votes from the total, making A the winner even though 60% of the voters hate A. But that's a whole different animal, and it's not as if C could win with any system we have now.

• "It's mathematically sound." According to Arrow's theorem, it's not entirely sound. Jul 1, 2021 at 21:49
• That's why the last Para is there. With respect to the Q, the system is sound. But if you step back and say "hey, we have all this extra info we never had before -- can we make up new definitions of fair that weren't possible before and solve for them?" things get complicated. Jul 1, 2021 at 23:35
• I think this is the best answers so far. While other answers are interesting and informative, they talk in general about ranked-choice voting without addressing specifically the OP's question whether it gives too much weight to "the ones who voted for the least popular candidate" (compared to, e.g. the second to last etc). Jul 2, 2021 at 9:59
• @Acccumulation if you put an answer that relates this to Arrow's theorem, I'll upvote it. Jul 2, 2021 at 14:24
• @LucaCiti Most of StackExchange is like that. The first poster wants to answer a slightly different Q than was asked. Reading that influences the next person's understanding of the Q, and pretty soon people are just "answering the answers" without even realizing. Jul 2, 2021 at 14:30

What's the rationale for giving that group disproportionate power in choosing the winning candidate?

There is no rationale, because RCV was never designed to give voters equal power.

Ranked Choice Voting (also known as Instant-Runoff Voting, the Alternative Vote, or preferential voting) is essentially a mistake: a misapplication of the Single Transferable Vote system.

Single Transferable Vote is a multi-winner voting system, designed in the 1850s to elect entire slates of representatives at once. It is primarily associated with Thomas Hare, whose intention was to make parliament more representative of minority viewpoints:

Every detail of this scheme converges to one central point,—that of making the exercise of the suffrage a step in the elevation of the individual character, whether it be found in the majority or the minority. I disclaim for it, therefore, the title of a representation of minorities.

The idea is that after one candidate has been elected, the voters who supported that candidate with their first preferences are now well-represented in parliament, and their further preferences should no longer have weight. The desires of other, unrepresented voters are now given more weight, so that they too have a good representative, and after repeating this process to fill every seat, parliament has good representation of a variety of viewpoints.

The first candidate elected is not intended to be a representative of the entire electorate, but only of the largest faction, and the representativeness of the body is achieved by electing further candidates of different ideologies.

STV does not lead to strict proportional representation of parties, in the way that systems like party list do, but it typically produces a closer approximation than FPTP.

RCV/IRV was then "invented", possibly mistakenly, in 1871 by William Ware, who was introducing Hare's method to Harvard. He describes Hare's method in detail, correctly explaining how it should be used for multi-winner elections, but, while listing the advantages of STV, he says:

It is equally efficient whether one candidate is to be chosen, or a dozen.

It's not clear whether he fully understood the implications of using a multi-winner system to elect a single candidate, but this is cited as the first description of what we now call IRV or RCV.

So RCV applies exactly the same process as STV, but stops after a single candidate has been elected, meaning that they are not a good representative of the electorate as a whole, but only of a large faction.

Other voting systems were designed from the beginning with single-winner elections in mind, and do a better job of representing the electorate as a whole.

For example, Condorcet's "ranked choice" system considers all voters' preferences simultaneously when deciding the winner, not discarding some and keeping others like RCV does. It is able to elect a candidate who is preferred by the voters over all other candidates, even if not the first choice of many. Other "Condorcet-compliant systems" try to achieve the same goal while reducing incentives for strategy, etc.

Likewise, the more recently-invented cardinal voting systems like STAR, Score, or Approval voting try to find the candidate who has the highest overall approval/consent/utility, meaning they are the best representative of the electorate overall, or would make the voters happiest as a whole.

• Love your answer endolith. If people want to read about how Hare RCV messed up in Burlington Vermont in 2009 by failing to elect the majority candidate and failing to protect from the spoiler effect, please read this paper. Jul 17, 2021 at 1:35
• @robertbristow-johnson Cardinal methods collect more information than ordinal methods and are better at finding the candidate who is the best representative of the will of the voters. Human desires are inherently cardinal, but ordinal methods quantize this into equally-spaced steps, arbitrarily assigning equal weights to preferences that are not equal, distorting the outcome. Gibbard showed that all voting systems are subject to strategy, but cardinal systems typically don't have as much of a problem with it. Jul 17, 2021 at 18:12
• @robertbristow-johnson All voting systems place a burden of tactical voting on the voter, but cardinal systems allow us to express our true preferences. If you enthusiastically prefer A > B, and I am indifferent between them, forcing me to choose A>B or B>A at random is undemocratic, and my weak (actually nonexistent) preference should not be given the same weight as yours. The goal is to find the candidate that best represents the voters. Rejecting indifference and discarding strength of preference information makes that less likely. Jul 17, 2021 at 19:56
• @robertbristow-johnson That it's immediate and obvious is a strength, not a weakness. The effects of strategy under ordinal systems is not obvious, leading to pathologies like the Dark Horse candidate winning because everyone thought they had no chance and ranked them second. But regardless of strategy, ordinal systems are just inherently less democratic and more likely to lead to dysfunctional government. Jul 18, 2021 at 17:04
• @robert bristow-johnson "One person, one vote" suggests that each voter should submit 1 ballot and that all ballots should be weighted equally. In the context of the US supreme court, it was invoked to correct an imbalance resulting from state congressional districts varying wildly in size, giving less proportional weight to voters from large districts. The principle has to do with how ballots are weighted, not how they are marked (e.g. ordinal vs cardinal). It certainly is not intended to mean that ballots must prohibit voters from differentiating between strong and weak preferences. Jul 20, 2022 at 18:26

Suppose people are voting on what topping they want on a pizza. Alice ranks the toppings [pepperoni, pineapple, olives, onions, anchovies]. Bob ranks them [anchovies, pepperoni, onions, olives, pineapple]. The first topping to be eliminated is anchovies, so in the second round of voting, Alice and Bob counted as voting for pepperoni. Neither of their votes count any more than the other. They are both one vote for pepperoni. And not only do they both get one full vote, but Alice's one full vote is going towards her first choice, while Bob's is going to his second choice, so in a way Bob is worse off than Alice.

There are situations where RCV leads to counter-intuitive results, but those situations are more complicated than just "the lowest ranked choice has their votes redistributed first".

• One such situation where Hare RCV led to a bad result is Burlington 2009. Jul 17, 2021 at 1:42
• Jul 23, 2022 at 2:23

Those voting for the least popular first-choice candidate don't have more power than anyone else. After that candidate gets eliminated, it's exactly as if that candidate wasn't in the election at all (not considering any psychological effects their presence in the election might have on voters or voters having fewer ranked choices than there are candidates). It's equivalent of no-one having voted for that candidate and moving subsequent candidates up one place in the ranking of anyone who voted for that candidate. If you do that, it should be clear that everyone is still on equal footing.

If voters have fewer ranked choices than there are candidates, this arguably means they now have strictly less power (not more), since they now have 1 fewer remaining choice than everyone else. The extreme result is that all their choices are eliminated early on and they don't get to influence the decision between the final two (or more) candidates. The less extreme result is that they need to compromise more in their choices to make it more likely to affect the final result (e.g. in a US election they'd probably always want one of their choices to include the Democratic or Republican candidate, as those are the most likely to be the final two candidates).

If anything, the voters whose first choice is popular (especially if it's one of the two most popular candidates) have more power.

They get to eliminate the least popular first-choice candidate even if that candidate is the most popular when you take the second or third choice of voters into account. Similarly for the least popular second-choice, third-choice, etc. candidates. They may also then get to influence the decision between the final two candidates, all just with a vote for one single candidate.

Although this is still less power than they'd have in single-choice/"regular" voting, since in that case the other voters who'd prefer a less popular candidate would actually get a voice in deciding between the two most popular candidates without having to vote strategically by not voting for the candidate they'd actually prefer.

• //"After that candidate gets eliminated, it's just as if that candidate wasn't in the election at all."// That is simply false, as Burlington 2009 has shown. Jul 17, 2021 at 1:40
• @robertbristow-johnson It seems quite optimistic to assume anyone would read a 9-page document linked to in a comment. But, based on one or two paragraphs (correct me if I'm wrong) their point seems to be that the candidate who was eliminated first (Montroll) should've been elected. If so, then that would have no effect on the "it's just as if that candidate (Montroll) wasn't in the election at all" statement, which appears to still be 100% true in that election. Jul 17, 2021 at 7:24
• if you read the document, the Spoiler was Kurt Wright. If Hare RCV fails to elect the Condorcet Winner, that election must be spoiled and whoever loses in the Hare RCV final round is the spoiler. But you're right, Andy Montroll, the Condorcet Winner, should have been elected because he was the only consistent majority candidate. To claim that Hare RCV "guarantees" a majority winner is a falsehood. It did not elect the majority candidate in Burlington 2009. Jul 17, 2021 at 14:20
• @robertbristow-johnson I was only comparing ranked-choice voting with ranked-choice voting which excludes the least popular candidate. I wasn't making any claims about how that would compare to any other voting system nor whether it always elects the majority candidate. Jul 17, 2021 at 15:00
• the question is who is the least-popular candidate? that can be a subtle question. Jul 17, 2021 at 15:25

By cutting the most losing candidate's votes out of the final results and redistributing them among their second choice candidates, it empowers the first choice votes of closer runner-ups.

The main benefit of redistributing the votes is to be able to check if Candidate A with a small minority advantage of votes over Candidate B isn't overriding the most preferred election results of the voters in the election.

If Candidates C and D are also in a close race, starting with Candidate E, if E is the lowest case voter, allows for a priority of consideration in determining who of Candidates B, C, and D would be most likely to be the next popular choice, if Candidate E's second choice votes don't confirm Candidate A's small lead into a larger lead. It's not actually empowering the lowest candidate's voting choice in influence, but instead empowering votes who didn`t make the threshold to be given enough influence to effect the results beyond the amounts they already, in cases where no candidate reached 50%, have yet to achieve.

By focusing on the votes that appear to have the lowest collection of effect on the election, their votes are allowed to avoid spoiling the election for another candidate because they weren't able to get full support of candidates that they aren't usually voting for.

The reason is that those who support the least-favoured candidate are effectively disenfranchised under single-vote system, unless they vote strategically. It's not that they are suddenly given influence that they don't deserve; it's that they get back the influence they were previously missing.

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