Opinion: Why a different voting system might be better
March 16th, 2012
03:45 PM ET

Opinion: Why a different voting system might be better

Editor's Note: Matthew Lane is a Ph.D. candidate in mathematics at UCLA, and is the founder of Math Goes Pop!, a blog focused on the surprisingly rich intersection between mathematics and popular culture.  He is also a contributor to the Center for Election Science.  You can follow him on Twitter at @mmmaaatttttt.

Although Mitt Romney claims to be the mathematically inevitable Republican presidential candidate, voters remain less than excited about him.

According to a recent Gallup poll, only 35% of Republicans would enthusiastically vote for him this fall.  This is below the 47% John McCain had around this time in 2008, and also below the 55% and 53% enjoyed by Barack Obama and Hilary Clinton, respectively, when they duked it out four years ago.  There's still plenty of time until November, but for now it seems Republicans haven't yet completely warmed to their presumptive nominee.

When the results of an election (primary or otherwise) run counter to our desires, it is easy to scapegoat the political process.  The right person didn't win, we may argue, because the system itself is broken.  The two-party system, for example, is sometimes cited as a leading cause of the current dysfunction in Washington.  But perhaps much of what ails the political climate comes from an underlying mathematical dilemma in the way we determine the winners of our elections.  The mathematics of voting highlights many problems with current systems, and also proposes some interesting solutions.

The most common system is the familiar plurality system.  Under plurality voting you may vote for one candidate, and the candidate with the most votes wins.  This system is not perfect: for instance, much to Ralph Nader's chagrin, you are strongly discouraged from voting for your preferred candidate if he or she is unlikely to win.  This has led to the belief that in many cases, a two-party system is a consequence of the plurality voting system, which in general does not seem capable of sustaining many parties (this is known as Duverger's law).

One alternative system used in cities such as San Francisco and Minneapolis is called Instant-Runoff Voting, or IRV.  In this system, you rank, say, your top three candidates.  All first place votes are then counted; if no candidate has a majority, the candidate with the least support is eliminated.  If your first choice is eliminated, your vote now moves to second choice.  This process continues until one candidate has a majority among all remaining candidates.

It's certainly more complicated, but does this system more accurately reflect the will of the people?  Not always.  From a mathematical standpoint, IRV has some weird behavior (here's one example of a particularly strange IRV election).  For example, ranking a candidate higher on your list can actually decrease the candidate's likelihood of winning, and vice versa.  Imagine if, by convincing 100 more people to vote for your favorite candidate, you actually caused your candidate to lose!  Such an outcome is possible under IRV.  Also, like the plurality system, it is not always in your best interest to rank your favorite candidate first.

There are practical considerations as well.  With IRV, it’s not possible to tally the results at individual precincts and then combine the precinct totals (we say that IRV is not additive).  In other words, it's possible for a candidate to win every district, but lose the election overall.  What's more, voter confusion seems to be greater with IRV.  For example, after adopting this system in 2004, San Francisco saw the number of spoiled ballots (the number of ballots filled out incorrectly, and therefore invalidated) increase on average by a factor of seven.

One other system is approval voting.  Approval voting works in nearly the same way as plurality voting, but with one crucial difference: you may vote for as many candidates as you want!  From a practical standpoint, this makes it almost impossible for you to spoil your ballot.  Its similarity to plurality voting also means that the necessary changes to the existing infrastructure used for plurality elections would be minimal.  Furthermore, approval voting is additive, and unlike plurality or IRV, it never hurts to support your favorite candidate.  More information on approval voting can be found here, and more detailed comparisons of approval voting and IRV can be found here and here.

Most importantly, from a mathematical standpoint, is the fact that among these voting systems, approval voting yields the best voter satisfaction on average, regardless of whether voters are honest, or whether they vote strategically.  (Here, voter satisfaction is measured objectively by something called "Bayesian regret.")

By way of comparison, both IRV and plurality voting have the same average voter satisfaction if all voters are strategic, while IRV has much greater average voter satisfaction as the proportion of honest voters increases.  But generally, approval voting takes the cake: in most cases, average voter satisfaction in the presence of strategic voters is still higher for approval voting than it is for IRV in the presence of honest voters.

As a final remark, one can view approval voting as an example of a slightly more complex voting system called score voting (also known as range voting). If you've ever been to a talent show where the winner is crowned by audience applause, you've seen score voting in action.  Like approval voting, you may vote for as many candidates as you wish; unlike approval voting, you can express the strength of your preference for a given candidate by scoring each one on a fixed scale, say from 0 to 10.  From this perspective, approval voting is just score voting when the range of scores is limited to 0 and 1.  While it's not immune to strategy, average voter satisfaction with strategic voters is about the same for score and approval voting.  With honest voters, however, score voting gives the best average voter satisfaction of all.

Combining the practical with the mathematical, the evidence favors score voting.  If a simpler system is desired, approval voting is the clear front-runner. For more on these voting systems under the influence of strategic voters, see here. if you still can't get enough, you may want to pick up William Poundstone's 2008 book "Gaming the Vote," which touches on all of these topics and more!

The opinions expressed in this commentary are solely those of Matthew Lane.

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    March 31, 2012 at 6:42 pm |

    WELL WELL WELL... It seems that the people have spoken. The american voting system even if not rigged is still flawed!!! Evey single american vote should count. I know the Gov wont aprove any change do the the cost & since we have a budget crisis i doubt any chnges will ever be made.. Its not about who your voting for in this article its about letting EVERYONES VOTE COUNT*** do you feel satisfied that the vote was fair if the polls close without everyones vote in?? I say let them vote every AMERICAN FOR THEMSELVES .. Yes what is one vote to the masses but then again are we not voting for just one man to be president!!! LET THE PEOPLES VOTE BE HEARD & TAKE BACK AMERICA ***

    March 19, 2012 at 10:02 am |
  4. adsf

    Our much larger, more immediate, and more easily fixed problem with elections is electronic voting. No paper trail, easily hacked machines, and shady connections between election officials, politicians, and manufacturers of the machines all coalesce to make our elections a joke. Let's make sure our votes are even being counted before we freak out about how they are counted.

    ...besides, we all know the best method is applause-o-meter.

    March 19, 2012 at 9:35 am |
  5. EJBilot

    Get rid of the Electorial college and let the people decide by popular vote. Times have changed, so must we the people

    March 19, 2012 at 9:20 am |
  6. B

    My question is this:

    If we're all just one short "National Disaster" away from transferring power from the duly elected President of the United States to some guy that, for "national security" reasons no one's ever heard of (Shadow President, Shadow Cabinet, et al), how long will these sham "public" elections keep going?

    Until enough strife can be caused in the country to cause people to lose sight of pesky things like "elections".

    March 19, 2012 at 9:17 am |
  7. humtake

    Here's a great idea...how about you put your vote in for one person and whoever gets the most votes wins? It's amazing no matter how simple something is, you can always count on someone to come in and find a way to make it complex.

    March 19, 2012 at 9:07 am |
  8. Michael Durwin

    They problem with all of these systems is they are based on math, not human behavior.
    The current system, or a slight modification allowing more parties would be fine, because it's not the voting process (though everyone but politicians hates the electoral college) that is the problem.
    The problems with the election process are:
    Big Media – they hype their particular candidate and, in some cases, either support or create outright lies about candidates, seemingly checking their objective journalistic integrity at the studio door.
    Corporations – the idea that multi-million corporations can support a candidate either directly or through super PACs is abhorrent. Why should a small board of directors and executives at a major corporation be able to wield the same influence as an entire state?
    Education – most Americans are simply not educated about the candidates, nor do they want to be. They'd rather follow the rankings of pundits so they can believe the lies they want or ignore the truths they don't want.

    March 19, 2012 at 9:07 am |
  9. Mahhn

    We "need" to get rid of the two party system (Rep & Dem) and make people run on their own merits.

    We "need" to get corrpution out of politics. It's corruption that has ruined this country.

    We should have 5 to 15 people on the ballet. Not this rich boy club whith corperate corruption funding every topic.
    The only donations should be by people and with limits to prevent corruption.

    March 19, 2012 at 9:06 am |
    • Frank Z

      I do not know about the ballot that you see, but when I go to vote, I usually see at least three to six names on my ballot for president. It may seem like a two party system as they are the ones that get most of the air time. If we would like to see this change, then it is up to us to speak to our leaders in a loud way, and have it changed.

      March 19, 2012 at 9:55 am |
  10. Fair and Balanced

    The problem we have with elections is that votes are equally weighted. At every level, weight the vote by the amount of taxes paid.

    March 19, 2012 at 9:03 am |
  11. aurelius

    The Republican voters have skewed the system so badly that nothing can change it. If it wasn't for the fact GOP supporters vote, not for a Republican candidate but strictly to cast an anti-President Obama vote for three basic reasons: bigotry, prejudices and racism, the GOP nominee would get less than 30% in the general election.

    March 19, 2012 at 8:59 am |
    • Frank Z

      I just knew this would come up.

      So one hand we have people that will not vote for Romney because he is Mormon, and we have people that will not vote vote Obama because they are racist, that is very hypocritical. I for one will not vote for Obama because of things that he has failed to do. He has failed to bring this economy to a good place for all to live in. (Oh sure the economy appears to be heading in the right direction, especially if you want to believe all the hype.)

      Why would it take three to four years to see the light? This man is obviously playing the politics card very good. Once re-elected he will go back to his old ways of conducting business.

      There is one thing that people have forgotten about, and that would be his birth certificate. What would it take so long for someone to produce a birth certificate, I tell you, it is forged.

      All this has nothing to with the color of his skin, which is another card that he is playing well, bytheway.

      March 19, 2012 at 9:51 am |
  12. Steve

    I think the author is missing the point. Most of our voting districts are so gerrymandered that the election is already decided at the primary. That isn't true representation of the people. We need to have voting districts in all states that are simple squares or rectangles, and then you get a random sampling of each party in each district. Many of the gerry mandered districts are bizarre works of art, that "throw" the election to one party or the other from the beginning, and the 20% – 25% of voters who show up for the primaries, decide the election for all the rest of us!

    March 19, 2012 at 8:58 am |
  13. BruceB

    The problem is not HOW we elect candidates, it's WHO we elect. The best and brightest minds in America have no desire or reason to put themselves to a vote when all they have to do is buy a malleable candidate who will do their bidding and spend enough money to elect him/her. The typical voter in the US gets their information from TV ads and media that supports what they already believe, so there's actually no informed choice being made at all, other than to vote or not. That said, the electoral college was a short-sighted solution back then and is just plain dumb now.

    March 19, 2012 at 8:57 am |
    • T i m


      March 19, 2012 at 9:12 am |
  14. Q

    yes i know typo errors. sorry.

    March 19, 2012 at 8:57 am |
  15. Q

    Doesnt matter who wins. They're still puppets to the oil corp machine and Jews. Which makes me ask why doesnt someone that is Jewish run for president if they have so much influence? Why do they hide in the shadows? I know the answerbut do you. I dont expect this comment will be approved but what the hell.

    March 19, 2012 at 8:55 am |
  16. DYBO

    Get rid of the electoral system. Let everyone's one vote count. Get rid of nerd mathematicians.

    March 19, 2012 at 8:55 am |
  17. totheleft78

    Considering 1/3 of Americans don't know what a colon is I can't see them being able to understand a new way of voting.

    March 19, 2012 at 8:54 am |
  18. Sam

    I wonder – if the votes from Hawaii and Alaska are ever counted – because more often than not – the winner of the general election is declared well before those polling booths close...I wonder how people of those states feel about that!

    March 19, 2012 at 8:51 am |
    • Frank Z

      I have often wondered about that myself. I feel that there are only two ways to correct this, and one would be to ask the citizens of these states to start voting at like three or four in the morning their local time. A second way to correct this would be to have online voting as it was suggested earlier.

      March 19, 2012 at 9:00 am |
      • T i m

        You are wrong about on line voting . That is part of the problem with voter fraud now . Electronic process is so easy to change .

        March 19, 2012 at 9:07 am |
  19. William

    Why don't we have an option for a vote of no confidence. Otherwise we really have no voting power in that someone gets in to office. So what if we dont like anyone on the ballot especially those in Congress who keep running for Office Like John Mica of Florida. What happens is collectively the write in ballot wont work because we are so divided as a Nation. The reason John Mica and others need to go is that they have been there too long and have colluded with one another to get their way or nothing at all done in Congress. We do not have Representives of the people! With a way to have a no vote then all of the money in the world will have less power over our Candidates. As it is right now it's a joke! We have no real vote because we can't say No!

    March 19, 2012 at 8:49 am |
  20. CommonSense

    The problems in the voting system are secondary in comparison to the major issue of the two party system. It serves no purpose, absolutely no benefit. I challenge anyone to cite one valid benefit of having the party system, there are none. It creates division, presumptions and completely stagnants our entire political process.

    It forces any potential candidate to align with one of 2 major parties because running 3rd party is a losing ticket. Not only that but it forces their issues to align with that party. It's ridiculous to think that all candidates are one of two ideals and it's just that cut and dry.

    In government it just creates more division, more bickering and representatives holding to the party line. It does absolutely nothing to encourage unity and compromise. People throw labels at it because it's comfortable to label something. It's just ridiculous.

    March 19, 2012 at 8:47 am |
  21. Stan

    Until a positive ID procedure is put into place voter fraud in America will continue. What is so hard about issueing and requiring a positive photo ID to voters. Most states issue personal IDs for no drivers so they can be identified by banks, to cash checks and for medical reasons in case of emergency. I will not go into who is crying the loudest about this but if you are not a legal voter you should not vote and if you do vote you should only be able to vote once. If you do legally vote, you should vote for the candidate you want not the party lines. Lastly, who you vote for may not really matter because it is the electorial college that determins who wins anyway. Presidential voting is a sham.

    March 19, 2012 at 8:41 am |
  22. Bob Hobbs

    Let's have ONLINE VOTING, and eliminate the Electoral College.

    One Person, ONE Vote!

    March 19, 2012 at 8:39 am |
    • Frank Z

      Now I think you have something. When you do online voting you would have to put in all your information. Once your information has been accepted then you get a ballot for your location, and once submitted you could not go to a poling place to vote as the machine would reject you.

      I can see one adverse remark, and that would be that someone could "sway" your vote. Could that still happen while you are line? There could be someone that states, please vote for candidate X as he/she is the best one for this position.

      March 19, 2012 at 8:48 am |
      • T i m

        NNOO , that is the whole problem now !!!!! HOW EASY IS IT TO CHANGE A VOTE , IN THE MIDDLE OF THE PROCESS . How many times does your computer NOT ALLOW YOU TO DO SOMETHING , even when you follow instructions perfectly ........KEEP THE PAPER BALLOT .....T im

        March 19, 2012 at 8:56 am |
    • rlowens1

      I'm all for online voting, as long as we can, at any time, go back and review how our vote was cast, and as long as election monitoring is done by a neutral third party.

      March 19, 2012 at 8:54 am |
      • T i m

        NNNNOOOO , ONLINE VOTING ....................GIVE ME A PEICE OF PAPER .

        March 19, 2012 at 9:17 am |
  23. Hobbits

    YES, WE NEED A NEW VOTING SYSTEM! However, the powers in Washington and the money behind them will never allow it to change because they have the control they want to affect outcomes.

    1. All State Driver License or IDs must be in the same format as directed by the federal government
    2. To vote, you must present your ID that will be scanned. You can vote anywhere in your state, your address will bring up the correct ballot. Your ID is scanned into the system so you cannot vote twice.
    3. The Federal government regulates the voting process for all states, i.e. The type of machine used, its security, maintenance, etc. Every voting place has the exact same device everywhere in the country.
    4. Voting is open once full week beginning on midnight Sunday and closing midnight Saturday. Voting can be conducting online just like SEC Proxy voting for stock holders.
    5. Winners are based on popular vote, there are no electoral colleges.
    6. Parties are powerless to strip any state of its voting during primaries
    7. All primaries are held in the same fashion, with total popular vote determining the parties official nominee.
    8. Absentee voting is regulated by the federal government so all ballots are the same format / design. They are direct and simple to understand. A push to have voters use the Internet for voting is preferred over mailing the Absentee ballot.
    9. Any vote disputed is counted as valid unless obvious proof exist of fraud or electronic malfunction. A federal monitoring board reviews all votes in question and has the final say. The board is made up of non-partisan members of the federal government whose FT job is to regulate and monitor all voting across the nation for national, state, and local elections.

    None of the suggestions will ever happen.

    March 19, 2012 at 8:38 am |
  24. Tom

    I would like to see a variation on what they have here. Once again you cast a vote for each; Yes, Maybe or No. The weighting is simple; +1 for Yes, 0 for Maybe and -1 for No. Top score wins.

    March 19, 2012 at 8:37 am |
  25. SPW

    Our elected officials are scared to put in any system which could jeopardize their longevity in office.

    For the people? Don't make me laugh, we continue to patch the leaking water bed that is our government when we could easily refine it into a simple system ran by the very people of this country, instead of relying on people who should be restricted to term limits.

    How wet do you want to get people? Going to wait until all the water is gone until we finally change the mattress?

    March 19, 2012 at 8:34 am |
  26. David M

    The voting system is fine. What we need are viable candidates.

    March 19, 2012 at 8:28 am |
    • Clay Shentrup

      No, the voting system is certainly NOT fine, as many of Matt's links attest.


      Even with absolutely no change in the quality of candidates, better voting systems radically increase average voter satisfaction with election outcomes. Plus, you can easily change the voting system (aside from the political difficulty of passing enabling legislation). Whereas there's no clear system that can keep out "bad candidates". Who would decide which candidates are "viable" aside from voters themselves in the voting booth?

      You might spend some time pondering why we don't see more quality candidates running for office, who haven't been politically entangled with all sorts of corrupting influences like big banks and insurance companies. It's largely BECAUSE of the current bad voting system. A candidate can run who would be preferred by a majority to both the Republican and Democrat nominee, and will almost assuredly lose merely due to the ASSUMPTION that he or she "cannot possibly win versus the two major party candidates." So you get Approval Voting, and that completely disappears. People can vote for their favorite of the major party nominees (to be on the safe side) and also vote for candidates they think are even better, regardless of what a long shot it seems to be. Then, if there's a candidate whom enough voters sincerely prefer to the two presumed frontrunners, voters can end up being pleasantly surprised, when some candidate they thought had no chance ends up winning.

      Most of this stuff is very counterintuitive, which is why there's so much emphasis on solving the wrong problems. The main problem that we need to focus on is upgrading the voting method.

      March 19, 2012 at 9:05 pm |
  27. watash60

    1. If you are on any type of welfare (housing, food, ...) you cannot vote

    2. Only 18 years old in the military (or have a draft card) can vote – else you need to be 21

    March 19, 2012 at 8:22 am |
    • rlowens1

      So, some group of clowns comes in and ruins the economy, like GWB and the Republicans, but the people damaged by their recklessness who end up on public assistance don't have any say in who gets to replace the clowns who made the mess? You're a fascist and a fool.

      March 19, 2012 at 8:28 am |
    • B

      Another elitist post, but this time from a member of our military.


      March 19, 2012 at 9:19 am |
  28. bubba9

    You have to remember that the founding fathers of the US (yes – George Washington, Thomas Jefferson, etc.) were all rich aristocrats. They set up the Electoral College system because they did not believe that the "common people" had any inteligence whatsoever...they NEVER intended to let the president be elected by the ignorant masses. This is actual history – look it up. The EC should have been eliminated a LONG time ago!

    March 19, 2012 at 8:20 am |
  29. Rozelle

    1) Cap the amount of money that can be spent on any election – not how much contributors can contribute but the size of the pool of $$$ that each candidate can draw on to finance their campaign. Abolish super pacs but allow smaller pacs. This allows the less wealthy to compete on a level playing field while at the same time giving voice to organizations which wish to band together to support a candidate.
    2) Primary elections should be open and held on the same day with both Democrats and Republicans voting and line-crossing allowed.
    3) Winner take all. Our votes actually count more under the electoral college rather than the popular vote. One vote gets lost in the millions, however one vote can make a difference at the local level.

    March 19, 2012 at 8:17 am |
  30. Jim

    Yup, Maybe one where we actually vote for our candidates, rather than the illusion of it. The rigged part of elections, including the media and their endless slanted articles towards certain candidates and away from others, is what makes all this possible. The electronic machines and endless attempts to hide vote counts, is more evidence of the fraud.

    March 19, 2012 at 8:17 am |
  31. rtbrno65

    Are yew sher yew know what yer talkin' aboot?

    March 19, 2012 at 8:16 am |
  32. Tyler


    Just yesterday I read that 2 out of 3 adults have trouble understanding the instructions on how to take aspirin. Good luck with a new political system. What this country really needs is an emperor

    March 19, 2012 at 8:07 am |
  33. rlowens1

    Of course, I'm jaded, but I don't think it matters who we vote for. The corporations who fund the elections are the ones controlling the outcome. They prop up a few candidates, all of whom meet THEIR approval, and then, they don't care which of those candidates we choose, so long as it is one of the ones they own. Until we do something about that, I don't think it matters how we tally the votes.

    March 19, 2012 at 8:05 am |
  34. Anti Sarah

    Every four years we hear this.
    The electoral college works.
    A party that isn't enthusiastic about its choices needs to figure out why it is getting those choices. What doesn't work is whining about it.

    March 19, 2012 at 8:01 am |
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