Thursday, August 23, 2012

What are Instant Runoff Voting and Approval Voting?

Voting is actually a very complex topic within political science and applied mathematics, but let me introduce you to the simplest form of two of the most popular alternative voting systems in the world: Instant-Runoff Voting (IRV) and Approval Voting (AV).

Both systems seek to solve a simple problem with the system that the United States (and most nations) currently use, which is called Plurality Voting (PV). That problem is that PV forces voters into two opposed camps, each camp taking one candidate as their "champion". This results in what often turns out to be a maximum of unhappy voters. For example, if you place people's views on a scale from 1 to 10 with 1 being the most liberal and 10 being the most conservative, PV tends to foster candidates that fall around the 2-4 and 7-9 range However, if your goal is to elect someone who represents the majority of Americans, it would certainly make much more sense to elect someone that falls into the 4-7 range and let the end-points tug that center-line back and forth. The problem is that centrists are essentially blocked out of PV systems because they are seen as "spoilers" for the extremes.

In AV and IRV, this problem is solved by allowing people to vote for as many candidates as they wish. In IRV, you rank your choices. So in a race between candidates A, B and C, you might put a "1" next to B and a "2" next to C. This says two things: that you prefer B to C and that, in no circumstances, would you vote for A.

In AV, you simply select every candidate that you like (or, to look at it the opposite way, you vote for everyone except the candidates that you will not accept).

The tallying methods for the two are very different. In approval voting, the person with the most total votes wins. In IRV, you hold "runoff" votes until someone has a true majority.

To explain that last one, let's imagine that you're not using IRV, but rather a simple PV system like we use today. Everyone votes for one candidate. If no one gets above 50% of the votes, then you throw out all of the votes, disqualify whoever got the least number of votes and hold a new election with the remaining candidates. You do this until you either end in a multi-way tie between all remaining candidates, or someone has more than 50% of the vote. That's a basic runoff vote, and it's what IRV does. But the "instant" part of IRV means that, instead of holding a new election, you take everyone whose #1 candidate is disqualified because they got the least votes, and shift all of their votes up one, so they have a new #1. By doing this, you get a new result and you can repeat the process again.

There's a little bit of complexity in this sort of instant runoff, but it doesn't affect the voting. For example, what do you do when you get down to 3 candidates with the bottom two tied at 30% of the vote and the remaining candidate at 40%? One definition says that you disqualify the two at 30% and re-run the election with just one candidate. The result of that depends on how many people didn't rank every candidate. For example, if you remove the bottom two who are tied and end up with 49% of people voting for the remaining candidate and 51% with no vote, then the vote could be considered "failed" because no one got a true majority. On the other hand, you can disqualify all voters who have no remaining votes and then the remaining candidate would be considered to have 100% of the votes.

Either way, you figure these things out ahead of time and therefore just have to apply the rules to the votes you get. No one has to worry about what happens in such a case as long as they do vote.

In terms of outcome, each system has some pros and cons. AV gives you the mathematically best result in the sense that the distance between a person's desire for a candidate and the winner will be lowest on average with AV. It will be slightly greater with IRV and largest with PV (which we use now), so both systems are an improvement over what we have, but AV is the largest improvement.

AV has one large problem, however. It's not only possible, but fairly common that the winner of the election will not be the person who is most people's first choice. Since this is also the strength of the system, it's considered acceptable by most people who study voting systems. However, when you have a Gallup Poll that shows that 60% of the population wants candidate A to win and candidate B wins, it's hard to explain that that really was the will of the people...

IRV doesn't have this problem, since any candidate who has a simple majority of #1 votes going in, just wins in the first round. It's only when no one has 50% of the vote going in that they can lose, even though they are the "favorite" according to a PV, but then you go back to the confusion over why.

Both IRV and AV are more resistant than PV to false voting. That is, if you vote because you want to "spoil" someone's chances, rather than just favor your own choice, then PV is where you will have the most success. In IRV it's harder to spoil the result, but there are strategies for false voting that have some impact. In AV, you have essentially no way to skew the vote other than to support the candidates that you want to see win.

There are also other ways to tally both IRV and AV type systems, but that's beyond the scope of this article.

So, what's the best system?

It really depends on what your goals are. If you want to polarize the field down to a small number of choices that sort of "summarize" the various positions, IRV works well. This is handy in pre-elections like party primaries. If you just want to choose the candidate that will best represent all of the voters, then AV is the better system (as long as you can tolerate the consequences of a popular candidate losing the vote).

Either way, the U.S.'s current election voting system is a terrible way to run anything more complex than audience participation in a comedy routine.


  1. Hi Aaron,

    That was a thoughtful article. I have to say, however, that the choice between IRV and AV is really no contest. AV wins in both simplicity and performance.

    It looks like you've got your eyes on the 1st-choice votes. But don't get too fixated there. Most 1st choice votes isn't indicative of really anything because of vote splitting. And you might think to yourself that IRV solves vote splitting, but it doesn't.

    Like PV splits votes, so does IRV split 1st-choice preferences. Imagine three people running with two of them being clones. Even if either of those clones is better than the third candidate, their vote splitting can easily allow that third candidate to win. So vote splitting really destroys any value 1st-choice votes might represent.

    I think you said it best here: "If you just want to choose the candidate that will best represent all of the voters, then AV is the better system ..."

    You should also check out the article

    And, I think you'll find great benefit in joining this group:

    I'm also a co-founder there.

    1. Thanks for responding, Aaron. I agree that IRV has many problems, and that AV is superior, but IRV resolves the first-past-the-post problems in part, and certainly is an improvement over such systems (FPTP and PV not being exactly equivalent ideas, but rather PV is a superset of FPTP).

      As for your Facebook group, I'd join, but I just don't use Facebook. Let me know if you come up with a Google Plus Page for the group!

  2. Thoughtful piece, Aaron S -- thanks for writing it. Some thoughts:

    1) Both methods of winner-take-all systems designed to elect one person. They can open up campaigns, but are unlikely to affect representation in many instances. For that we need proportional representation, something that Aaron Hamlin and I both support. Forms of PR can be adopted for Congress and state legislatures, and ideally we'd all get behind efforts to do that. See some fun new simulations of what even modest forms of PR could mean for Congress at http:/

    2) The biggest single problem with approval voting is that you can't indicate support for your compromise choice without that indication of support counting against your favorite choice. So if you think your favorite might win (and people tend to be hopeful of that possibility even when polls suggest otherwise), then you likely won't want to give support to your "lesser of two evils" choice at the same time.

    As a result, you easily end up with plurality voting-type results -- and much talk of strategic voting as people play a kind of game of chicken about whether to vote for more than one candidate. For more on this, see the analysis at

    3) Legality is another important consideration. IRV is legally tested, as it's so widely used both inside and outside of the USA -- for national elections in several countries and for major city elections in several US states. Approval voting is not legally tested because it's never been used for any governmental election. I would hope it would be upheld legally, but courts may have other ideas, as suggested by court decisions striking down the similar system of Bucklin voting. See this discussion:

    4. Ideally advocates of single winner reform would get along. But they don't because they tend to focus mostly on their preferred system -- which in turn is instructive for why approval voting would have problems in candidate races. IRV objectively is clearly better than plurality voting, but Hamlin and is electogy group bitterly fight IRV in a highly sectarian manner -- suggesting that backing both a favorite choice and a compromise choice at the same time isn't easy for people to do.

    - Rob Richie, FairVote (

  3. Well, Aaron, it's your lucky day. You get to hear all the good arguments on this one.


    Legality isn't really an issue here. FairVote's report references state case law from the early 1900's. Moreover, the method tested isn't Approval Voting. On top of that, even IRV wouldn't be used in the US for at least half a century. And Approval Voting wasn't officially developed until the 70's with Guy Ottewell and later Steven Brams with Peter Fishburn. So there's an order problem here.

    Further, the "one person, one vote" idea wasn't clearly established until the 60's US Supreme Court cases of Baker v. Carr and Reynolds v. Sims. And that just states that the weight of ballots must be the same, which they are in Approval Voting.

    So it makes no sense that Approval Voting would be unconstitutional according to the U.S. Supreme Court. And the US Supreme Court supersedes any out-of-date state decision because of the Constitution's Supremacy Clause. I should note that I have a law degree and am more qualified to speak on this point.


    The Center for Election Science has been eroding this FairVote myth for awhile now. The argument goes that because Approval treats all votes equally, you can help a lesser preferred candidate beat your preferred candidate. And so no one will want to support anyone but their favorite candidate. Thus, we have Plurality Voting outcomes.

    Already this logic has serious contradictions. For one, voting your favorite can hurt you in Plurality Voting (and IRV). But it NEVER hurts to vote your favorite in Approval Voting. So how can Approval and Plurality give the same outcome if voters under Plurality are frequently dissuaded from voting their favorite? Easy, they don't.

    It makes a lot of sense for voters to pick their favorite and hedge their bets against candidates they don't like. It's much better for a compromise candidate to win than a really crappy candidate. And voters recognize this.

    Several Approval Voting studies have been done on this. And what you find is that not only can the results differ, but third parties and independents get much more representative support. And the Approval results are simple unlike the complex tables showing the numerous rounds often needed with IRV.

    You can get a nice summary of how Approval treats third parties here:

    We also interviewed an OWS organizer who did a voting methods experiment showing similar results here:

    So that's a lot of evidence against Approval devolving to Plurality. Since we started doing this, FairVote has moved the goal posts saying that these were just experiments and not competitive elections.

    So we got more evidence.

    Some third parties have begun to wise up and abandon IRV in favor of Approval Voting. The Texas Libertarian Party used Approval to elect their US Senator nominee. With six candidates, there were an average 1.43 votes per ballot (not 1, as FairVote's logic would suggest).

    The German Pirate Party elected a local chair with Approval. Seven candidates, average of 2.41 votes per candidate.

    And the Reform Party became the first US party to use Approval Voting for their US Presidential nomination. Over 70% approved more than one candidate (as opposed to the 0% predicted by FairVote).

    So I wouldn't fret over the legality of Approval. And the myth that Approval Voting tactically leads everyone to choose just one candidate (bullet vote) is just that--a myth. It's awesome that you're considering these questions. Unfortunately, many people mistakenly overlook the voting method itself. With time, however, we hope to change that. And we'll be there with good alternatives.

    1. Well... thanks for replying, Aaron (boy, there are a lot of Aaron's around today...) but I'm not sure what points from my article you are responding to. You seem to be responding to some group called FairVote, with which I'm not associated and also to a suite of concerns that I didn't raise (e.g. approval voting devolving to plurality voting, which doesn't actually happen in any reasonably robust simulation or real-world implementation that I'm aware of).

      One point about IRV: results seem to often be over-complicated. While you CAN display every round of voting, it's really not necessary, any more than it's necessary to see the individual turnout numbers from every district to understand a plurality vote. You need to retain all of that information for auditing, of course, but the final result is the important one: who was disqualified due to insufficient votes; who were the final candidates; and what number of voters voted for them as their final choice. Beyond that, I applaud anyone who wants to go look up how the sausage is made, but that's not a requirement.

    2. I meant to have this one as a reply to Rob and didn't click the reply link. Sorry about that.

      I still think there's value in easily seeing all the candidates' support. We should keep in mind that pre-election polling also plays a role. And with Approval Voting will come Approval polling.

      Under pre-election Plurality polling you get distorted support for third parties (which often don't make the top two). If we didn't care about anyone but those in the final round, then we wouldn't see those challengers' support. And their inclusion is important for a healthy, competitive democracy.

      So that's why it's beneficial to have a method that easily displays everyone's support, not just the top two. Otherwise, we risk excluding good ideas from the discussion (as is the case now). And challengers have less opportunity to grow.

  4. Aaron Sherman misrepresents both IRV and approval voting in this article.

    With IRV, a candidate with the most votes, after the votes are fully counted, is the winner. Always. Just like plurality voting and approval voting.

    Aaron should list for us all the implementations of IRV for government elections that handle a 30% vs 30% tie the way he describes: throw them both out and let the interim 40% leader win, don't bother finishing the vote counting. Besides, significant ties are rare, even in an election with just a few thousand voters and ten candidates. In practice, the rare significant ties and near ties get resolved the same way for IRV, plurality voting, and, if it were ever trusted with important elections, approval voting: challenge the vote counting, recount the votes and get different vote counts.

    The existence of a objectively identifiable, "best" candidate is a nonsensical myth. Pigs can fly in computer simulations. But that doesn't mean we should run our democracy expecting flying pigs in real life.

    But anyone who believes in such fairy tales also learns that that nearly always, sincere approval voting can elect the worst candidate. The claim that “on average” approval voting elects better candidates is just mumbo jumbo served with a patina of mathematical rhetoric to impress those who don't know better or don't bother looking at the details.

    That's because sincere approval voting is not just indeterminant, it can elect just about any candidate. That means strategic voting is almost a given with approval voting. It makes voting more complicated for many voters. IRV, and not even plurality voting, behaves that crazily.

    -- David Cary

    1. I referenced a ton of data to support my arguments, David. All I see on your end is conjecture.

    2. David, "Instant Runoff" is so-called because it seeks a simple majority vote for a single candidate in a number of runoff elections that are performed without the need for a second round of polling the electorate. IRV without the runoff wouldn't be IRV, but rather an overly complex form of approval voting (the only time you would perform a runoff is when you had a true tie, which is usually extremely rare, bordering on functionally impossible, in a large population).

    3. As for the "objectively ideal candidate" this refers to the distance between the elected candidate and the voter on a particular political axis. For example, if I'm in favor of preventing all abortions and a candidate is in favor of preventing abortion in all cases except incest, then that candidate objectively differs from my stance, but is closer to my stance than one who favors open access to government-funded abortions under all circumstances. By taking many of these linear positions and plotting out an N-axis space, we can actually measure how closely aligned a candidate is with any given position.

      An ideal candidate (which does NOT measure an ideal result... that's got more to do with what they can get done and who they can play ball with) will be the one who is closest to me in that n-space. However, in many voting systems, strategies for electing a candidate can involve selecting someone who is further away from me because of strategic voting concerns. Approval voting minimizes THAT phenomenon, but to be clear it neither eliminates it nor addresses the general-case problem of resolving political deadlock.