Ranked choice voting and approval voting

There are many problems with the most common voting system in the US which is the plurality system where each voters picks just one candidate and the person who gets the most votes wins, even if they do not reach a 50%+1 majority. The problem with this method is obvious, that if there are three or more candidates, it forces a voter to sometimes have to choose between voting for the person they really like or voting for someone they like less because that person has a better chance of beating the third person whom they really dislike. This voting for the ‘lesser of two evils’ means that an ‘evil’ person or party will always win.

One alternative that is gaining some popularity is Ranked Choice Voting (RCV), also called Instant Run-off Voting (IRV). In such an election, voters rank each candidate in order of preference. The candidate who gets the least first-choice votes is eliminated and their second choice votes are then distributed to the other candidates. That process is repeated until one candidate reaches the 50%+1 bar.

The recent primary election to select the Democratic party’s candidate for mayor of New York City in November used this system and voters could rank up to five people in a crowded field. So how did it turn out?

New York City’s grand experiment with ranked-choice voting ended in a bit of an anticlimax on Tuesday when a newly released count showed Eric Adams — the frontrunner on Election Day in the Democratic primary — hanging on for a narrow victory.

The new system did not end up propelling an underdog candidate past the first-round leader. But it almost did: In first-choice votes, Adams led by 9.5 percentage points over Maya Wiley. Yet by the time the reallocation rounds had worked their magic, Wiley was gone, and Adams led the remaining candidate, Kathryn Garcia, by just 1 percentage point. Garcia had been in third place in the initial round, but ultimately nearly won.

Ranked-choice voting was the dream system of many progressive election reformers, and New York’s mayoral contest was its biggest spotlight yet in the United States. There were many questions about how voters would adjust to this new system during a pandemic and whether it could live up to its promises.

Ultimately, the results are mixed. It wasn’t the utter disaster some feared, but whether the advantages of ranked choice justify its drawbacks is certainly debatable.

One question that has arisen is whether the new system of voting confused some people who had become accustomed to just putting a check mark against one person.

For instance, there are questions about whether some voters were confused by the new system. Fifteen percent of ballots in the mayoral contest ended up ranking neither Adams nor Garcia, so they played no role in the final tally. It’s hard to say whether that’s because those voters preferred other candidates or because they didn’t understand the system, but in any case, the outcome was so close that their ballots could have made a difference.

One number analysts tend to look to here is the number of “exhausted ballots.” Those are ballots that end up playing no role in the final round because all the candidates they list have been eliminated.

Overall, about 15 percent of ballots in the Democratic mayoral contest ended up exhausted by the final round, meaning those voters ranked neither Adams nor Garcia. So another way to view the final result is that 43 percent of voters ultimately chose Adams, 42 percent ultimately chose Garcia, and 15 percent ultimately chose neither.

Exhausted ballots may have been more consequential in the final elimination round, when Maya Wiley was eliminated. Nearly 74,000 of her voters’ ballots ended up exhausted because they ranked neither Adams nor Garcia.

The remaining Wiley voters broke strongly to Garcia over Adams: Garcia picked up about 129,000 votes from them, while Adams gained about 49,000. This was almost enough for Garcia to pass Adams, but not quite — she fell about 8,400 votes short. So if fewer Wiley voters had exhausted their ballots, it’s entirely plausible that Garcia could have overtaken Adams.

So it looks like if there are four or more candidates, the problem of voters having to make complicated strategic choices remains.

Another voting option that I only learned about recently is what is called Approval Voting.

Studied since the 1970s and often cited as one of the best alternative voting methods, approval voting simply asks voters to select all the candidates they approve of and the candidate with the most votes wins. It’s been shown to easily elect a “good” candidate and encourage competition. However, this simplicity comes at a cost that frustrates some, as voters can’t differentiate between how much they like or dislike candidates.

This system has many advantages, one of which is that ballots will look the same as they do now and voters will still put check a mark next to a favored candidate. Voters will simply be able to put more than one check mark. The counting is also easier.

Our extensive analysis over the years overwhelmingly supports the view that Approval Voting is a much simpler and more democratic system than IRV (also referred to as ranked-choice voting, or RCV). The results of approval voting elections are also much easier to understand than the numerous rounds of vote transfers that IRV utilizes. In an approval voting election, you would only see approval percentages and total votes for each candidate — much simpler than IRV.

But there are criticisms about this system too.

No voting system is going to be perfect and solve all the problems. But my own preferences are for Approval Voting with Ranked Choice Voting next.


  1. mnb0 says

    My preference is the German voting system.


    or rather the entire political system of that country. Its worst side is that the amount of seats of the parliament is not constant. I can very well live with this.
    I’ve never understood the advantage of directly voting for a president. Exactly the USA has shown that members of parliament that belong to the same party as the president hardly act as political independents. What you American voters have is the choice between one huge PoS and a huger one. A feast of democracy, really.
    But if you Americans are too addicted to it to get rid of it, at least adopt the French system.


  2. garnetstar says

    I’d like to get, here in the US, another system of voting besides just who wins the most votes.

    Sadly, though I have read a lot about ranked-choice voting, from several sources, I cannot understand it. I’m a professor, I’m supposed to be good at book-learning and explaining things to people, but I just can’t understand it.

    And, I think that’s the main challenge to its being adopted. Changing to it was on the ballot in my state last fall, and I voted for it although I could not make head nor tail of the explanation of what I was voting for that was printed on the ballot. And, the measure didn’t pass.

    So, I suppose I’d like to try Approval Voting, or the German system, or whatever else I can understand.

  3. consciousness razor says

    It always makes my skin crawl a bit when people say “50%+1 majority.” I know it’s common, but it’s simply wrong.

    There can be an odd number of votes — certainly not a rare occurrence — meaning that 1/2 or 50% of that total can’t be a natural number. (Instead, it’s a half-integer.) Taking this value and adding one to it will also not give a natural number, so this can’t be the actual number of votes cast by a group of people.

    And perhaps then, some very confused people will ask themselves whether they should be rounding up or rounding down to come up with the right answer. Maybe they don’t even know that you’re allowed to round down, because that’s not normally what kids are taught…. But hopefully, they’ll start to wonder why they got started doing any rounding at all, if they realize this is supposed to be a direct and exact count of the number of votes for a candidate, which doesn’t need to be derived somehow from anything else, and then give up on the bad formula which led them down that dark path.

    Anyway, what’s really needed for a majority is “greater than 50%” of the total, or “more than half” or something equivalent which is just as easy to say.

  4. anat says

    Ketil Tveiten @4, as an Israeli, really really not! Once you have multiple small parties it can be a total disaster of corruption and political blackmail.

  5. prl says

    Australia uses ranked choice/instant runoff/single transferable vote for all state and federal elections. And of course, we name it something different, either preferential voting or Hare-Clarke (the latter especially in its multi-member variety), after the inventors of the variety used in Australia.

    The single-member variety is used for most lower chambers of parliament (except in the ACT and Tasmania, where the ACT has only one chamber, and both use multi-member electorates). The multi-member variety is used in all upper house elections where the state or territory has an upper house.

    The Australian single-member variety is is just the degenerate case of its multi-member variety, where there is no redistribution of over-quota votes, because once a winner is declared, counting stops.

    The multi-member version is quasi-proportional, where to be elected, floor(N/(M+1)) + 1 votes form a quota (N is the number of votes cast and M is the number of members to be elected). In a normal Australian senate election, there are 6 senators elected for each state, which votes as a single electorate, so the quota is ~14.3%. That can be made up of first preference votes for the candidate, votes transferred from failed candidates and votes transferred from candidates who reached more than their quota.

    The mechanism for dealing with the transfer of over-quota votes results in fractional votes in the count, but final votes are always reported as whole numbers.

  6. prl says


    Sadly, though I have read a lot about ranked-choice voting, from several sources, I cannot understand it.

    In its simplest form, single member ranked choice is quite easy to use and to count. In an Australian lower-house seat, the ballot paper lists the candidates with boxes beside them. You number the boxes for the candidates in the order of your preference for the candidate. Something like:
    2 Andrew (Party 1)
    1 Beatrice (Party 2)
    3 Charles (Party 3)

    The counting is simply:
    1. Group the votes by their first preference.
    2. If any candidate has a majority, declare that candidate elected and stop counting.
    3. Find the candidate with the lowest current count, and eliminate that candidate from the count. Transfer all that candidate’s votes, individually, to the voters’ most-preferred remaining candidates.
    4. Go to 2.

    The counting of the lower house seats in Australia using this system is fast enough that it is clear who will form government by about 9-10pm in the eastern states on election day, though some close seats may still be undecided for a few days after that, especially when recounts are required.

  7. garnetstar says

    Thanks for trying, prl@8! I will study your post carefully.

    I can’t understand how stocks and bonds work either. I think I just have a broken spot on the internal drive where some subjects cannot be written or retrieved.

  8. says

    There are many problems around voter reform, most importantly fairness. Parties rarely achieve a proportion of power that matches their popularity. During the last federal election in Canada, the Bloc Quebecois (7.6%) got enough seats (22 out of 338) to control a minority Liberal government, while the Green party (6.5%) have only 3 and the NDP (16%) have only 24.

    Another major problem is simplicity. If people don’t understand a new system, they’ll reject it and stick with “first past the post” even when it’s the worse option.

  9. prl says

    That happens with the National Party vs Greens in Australia, too. In Australia (and I suspect with Greens vs Bloc Quebecois in Canada, too), it’s more a matter of regional concentration of the vote in single-member constituencies than the voting system within the constituencies. In the 2019 Australian Federal election, the National party got 4.5% of the first preference vote, and 10 seats; the Greens got 10.4% of the vote and 1 seat (that’s out of a total of 151 seats).

    The National Party (formerly Country Party) has a strong rural constituency. It runs in few seats, but wins in most of the seats it contests. The Greens are a largely urban party, and run in a large number of seats where they have little chance of winning.

    I don’t think that this situation would change much if Australia went back to first past the post (plurality). Even the single Greens seat would probably be safe in FPTP: the first preference votes for their seat were: Greens 49.3%, Liberal 24.5%, Labor 19.7%. I’d expect that voting in FPTP would closely follow first preferences.

  10. prl says

    Another major problem is simplicity. If people don’t understand a new system, they’ll reject it and stick with “first past the post” even when it’s the worse option.

    It got changed in Australia. Preferential voting got started off in some states in the first decade of the 20th century, and was first used federally for the lower house in a general election in 1919. The Australian upper house changed to its current multi-member, per-state preferential voting in 1948.

    There doesn’t seem to be much of a movement to change it from its current form, though there’s always some messing about at the edges, especially for the Senate, where a normal Senate election ballot can easily have 50-60 candidates.

    The Australian Capital Territory changed from D’Hondt proportional to multi-member electorate preferential in 1992.

    New Zealand changed from first past the post to a mixed-member proportional in 1993.

  11. lanir says

    I actually suspect this has something in common with Mano’s previous work as a teacher. What all of these different voting systems are trying to accomplish is having people give multiple choice answers you can read as much into as the answer to an essay question. The difference is that no one benefits from having a muddled question appear on a test while by contrast some politicians seem quite intent on having everyone who takes the test give a very specific answer whether it’s right or not. And a badly firmed question on a test becomes obvious and can be ignored. With elections generally your only recourse is “try again next time.”

  12. friedfish2718 says

    Neither Mr Singham, nor the commentators mentioned the “Arrow Impossibility Theorem”.
    No matter the forum or platform, whenever I see people debating voting systems, I check if the “Arrow Impossibility Theorem” is ever mentioned. The theorem is very rarely mentioned. The theorem was proven in the early 1970’s. Professor Arrow won a Nobel Prize for the theorem.
    A few years ago, on the Scientific American website there was an area called “Ask the Experts.” Someone asked: “Is there a universally fair voting system?”. Twelve experts answered. 6 got it wrong (these are the pseudo-experts; at least 2 of the pseudo-experts are marxists). The other 6 got it correct (answer is NO.), all citing the “Arrow Impossibility Theorem”.
    I am amused by the silly arguments and the circuitous rabbits holes clueless pundits run into.

  13. John Morales says

    friedfishe, your plaint is akin to complaining about Gödel’s incompleteness theorems. We can still use math just like we can still use voting systems.

  14. sarawolk says

    Great article! You should definitely also look into STAR Voting too. It’s got the advantages of Approval and RCV and addresses the shortcomings of both.

    Score candidates from 0-5 stars. The two highest scoring candidates are finalists. The finalist preferred by more voters wins.

  15. GerrardOfTitanServer says

    Note that Arrow Impossibility Theorem only applies to election systems where there is a single winner. For example, it doesn’t apply to proportional party-list election systems.

  16. khms says

    Let me just offer a drastically simplified version of the German (federal) voting system mentioned above, reduced to the most important parts:

    1. Every voter has TWO votes. One is for a local representative, pretty much exactly as in the US. One is for a list of candidates (a party). The representatives are associated with parties or independent.

    2. Every elected representative gets a seat.

    3. People from the lists, in the order they are on the lists, get assigned seats until the percentage of seats for that party corresponds to the percentage of votes the lists have gotten. (A complication here is when they have gotten more direct representatives than the list votes suggest, which is when the number of total seats rises, and that party will get NOBODY from their lists. This has sometimes eliminated prominent politicians.)

    4. If a party got less than 5% of the total list votes, they get NO seats from their list votes.

    Result: everybody gets a local representative, every party that manages 5% or more gets proportional seats. New parties can grow over time (right now, the German Christian Union (“the” conservatives since WW II) are fighting for most votes with the Greens (which were brand-new in 1980)).

    Oh, and you can obviously vote for a representative of party A and for the list of party B. This is fairly common; there’s a long tradition of smaller parties campaigning for the list vote (“Zweitstimme”).
    Oh, and governments are almost always coalitions, for which a contract is negotiated before they vote for their candidate for chancellor -- no direct vote for that position.

  17. GerrardOfTitanServer says

    If a party got less than 5% of the total list votes, they get NO seats from their list votes.

    I never understood how this is a thing. This seems like a nakedly transparent attempt for the oligarchs to maintain power by squeezing out grass-roots competitors.

  18. prl says

    a drastically simplified version of the German (federal) voting system

    I can’t see garnetstar liking that more than ranked choice 🙂

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