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Scoring the Candidates

Range voting would prevent third-party spoilers--and give voters more say.

By Alan T. Sherman '87, Warren D. Smith '84, and Richard T. Carback III

September/October 2008

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In the 1995 women's figure-skating world championship, Chen Lu, Nicole Bobek, and Surya Bonaly were in first, second, and third place after they finished skating. Then 14-year-old Michelle Kwan surged into fourth with a strong showing in the free skate. In a bizarre twist attributed to an unusual new judging system, Kwan's strong performance caused Bonaly and Bobek to switch places. Bonaly got the silver, Bobek got the bronze, and Nobel Prize-winning economist Kenneth Arrow got even more vindication for his work on the drawbacks of rank-order voting.

Credit: Jason Schneider
Additional Information:
"How We Think Range Voting Would Have Affected the 2008 U.S. Presidential Race"

In the 1950s, Arrow had argued that there is no "good" election method. His research focused on methods in which each voter lists some or all of the candidates in a strict linear order (first choice, second choice, etc.). Arrow proved that any such method must display at least one of the following unreasonable characteristics: (1) a "dictator" always decides who wins, regardless of how everybody else votes; (2) outcomes sometimes conflict with even unanimous electoral preferences; or (3) a seemingly irrelevant candidate changes the relative standing of two others.

The 1995 championship illustrated the third problem. Previously, judges scored skaters from 0 to 6, and the one with the highest average won. But that year, scores were used only to produce rank orders. Final standings were determined by a complex algorithm based largely on the number of times each skater was ranked first, second, third, and so forth. When some judges gave Kwan a higher score than Bobek, some of Bobek's rankings slipped. So even though her numeric scores didn't change, she was demoted to bronze.

Arrow's theorem could have predicted this oddity. But when he concluded that all election methods are inherently flawed, he had neglected an important fact: election methods do not have to be based on rank ordering.

Honeybees hold "elections" each year to choose a new location for their hive; bad decisions could lead to the colony's annihilation. Over 50 million years, natural selection produced a system in which scout bees "score" each candidate site with dances describing the site's direction and distance. The more intense the dance, the greater the chance that other scouts will investigate the site. When a site attracts a sufficiently large majority of followers, it wins.

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Sparta, the longest-lasting substantially democratic government in history, voted in a similar way from about 700 b.c.e. until at least 220 b.c.e. Spartans elected Gerontes and Ephors (council members who had the power to dethrone kings) by means of a shouting system. The candidate with the loudest support won.

Both the bees' system and the Spartans' are examples of range voting: each voter scores each candidate within a given range (say, 0 to 99); the one with the highest total wins. As John Harsanyi (also a Nobelist) observed when Arrow's research was published, range voting accomplishes what Arrow deemed impossible. But since his point went against 1950s economic gospel, it was ignored.

Comments

  • IRV Promotes More Sincere Voting
    What Mr. Smith, Mr. Sherman, and Mr. Carback III fail to not about the inherent flaw in Range voting is that it is seriously susceptible to insincere or tactical voting.  For instance, If i like Ralph Nader or Bob Barr as my choice for president, and I want my candidate to win, then in the Range Voting system, i can further their interests by rating every other candidate a 0 out of 9, or whatever the arbitrary top end number is determined to be in this entirely theoretical system.  So i would vote the following:  Nader 9, Barr 9, Obama 0, McCain 0, McKinney 9.  (These are not my personal preferences, just an example of the application of this system on REAL PEOPLE that is missing from all this mathematical theory.)

    The authors of this article seem to imagine people won't work to game the system and will vote entirely honestly.  On that account, they are mistaken.  If i can change my vote, as in the example above, to increase the likelihood that a candidate that matches my values will win, I and 99% of the other people in America will do so.  In gaming a range voting election as described, the outcome would hardly be different from plurality elections.

    Unlike Range Voting--and even worse Approval Voting--Instant Runoff Voting provides very insignificant incentives to rank candidates different than a voter's sincere preferences.  There are highly improbable (never happened thusfar in a real world election in over 90 years of use in Australia, 50 years plus in Ireland, and quite a few other places in recent times) mathematical possibilities which if a voter changed the order of their rankings, the outcome would change.  Since this never manifests in the real world, and since you would be required to have extensive and very precise poll data to determine the possibility manifesting, Instant Runoff Voting is largely immune to the psychologies that would inspire a voter to modify their vote in an insincere manner.  In other words, Instant Runoff Voting doesn't promote insincere voting to the extent that Range Voting or Approval Voting do.

    Arrow didn't consider non-ranked systems in his theorem because he never took these systems seriously.  There is more to voting than just imagined mathematical outcomes, as we are talking about groups of people and how they think and behave. It is too bad Arrow didn't include non-ranked systems in his analysis, as perhaps people wouldn't attempt to use this as evidence that they are somehow without flaw.

    I am a little disturbed at the attempt to imply Fidel Castro (a totalitarian communist) or Adolf Hitler (a totalitarian fascist) would win in an IRV election in America when they are not on the ballot, nor have they ever been candidates in America.  And as this article points out:  these inferences, while grossly alarmist at the core, are the IMAGININGS of the authors and all their own ideas, not based on real world elections, but computer simulations.  I can imagine Range Voting failing as well, and I don't have to create numbers from thin air to demonstrate it--i merely have to refer to principles of sociology and psychology, and how people will try to maximize their representation and winning in any system.  This apparently doesn't show up in their computer simulations with numbers pulled from imaginationland.

    Either way, to categorize Fairvote's mission as purely Instant Runoff Voting, when in fact they also promote Single Transferrable Voting and proportional representation systems for legislative, multi-member bodies, is just completely innacurate.  Fairvote also promotes DC voting rights (in congress), a national popular vote for President, and many other issues you can read for yourself on their Web Site:  www.fairvote.org . Fairvote is far from a single-issue advocacy group as they are painted in this article.

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    anthonyviva
    08/19/2008
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  • Spartan system fails one person, one vote criterion
    In Sparta, the person with the loudest voice would have a greater voice than others.  As would be the case if i voted insincerely in a range voting election, rating candidates 0 who were the opponents of my chosen candidate. In our representative republic, the people are all supposed to have an equal voice, and our ability to make noise is not created equal.  Not sure why this is cited as an example here, considering those details, but I am glad I don't live in Sparta, as i certainly don't have the loudest voice in my community, just the most persistent and often rational.
    Rate this comment: 12345

    anthonyviva
    08/19/2008
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    • Re: Spartan system fails one person, one vote criterion
      Good observation, it is definitely an unfair range voting system in the sense that some people will be louder than others. Hopefully this difference in ability isn't/wasn't significant between various factions of the population. It did seem to work for them for a fairly long time!

      Obviously we're not in support of giving different ranges to different voters, and unfortunately we were under space constraints, so this factual bit slipped out of the article as "obvious."
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      rcarback
      08/19/2008
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    • One person, one ballot
      Smith's Bayesian regret calculations factored in the insincere exaggeration you speak of, and Score Voting still dominated.

      And all deterministic voting methods are susceptible to that strategic behavior. With IRV, for instance, voters have an incentive to insincerely rank their favorite front-runner first place, even if he's not their favorite overall candidate.
      Rate this comment: 12345

      brokenladder
      10/03/2008
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  • Anthony Lorenzo is confused
    It's amazing that Anthony Lorenzo has persisted in making these erroneous arguments against Score Voting (aka Range Voting) after being corrected so often by people like Warren Smith, the Princeton math Ph.D. who co-founded the Center for Range Voting.

    Smith's extensive Bayesian regret calculations show that Score Voting performs about as well with 100% strategic voters as IRV does with 100% honest voters, so that ought to be the nail in the coffin as far as Lorenzo's strategic voting issue.
    See http://rangevoting.org/StratHonMix.html

    But many voters prefer to be expressive, and for every voter who votes expressively, Score Voting becomes that much better than IRV for the average voter. Even with a mere 10% or so expressive voters, Score Voting begins to handily thump IRV - and we think it's plausible that a lot more people than that will choose expressiveness over strategy.

    But the contrast between Score Voting and IRV becomes even more stark when considering the real vulnerability of IRV to strategic voting. Lorenzo and other IRV advocates try to argue that strategic voting opportunities have never occurred in historical IRV elections, and that they are too hard to predict to be exploited. But this reasoning is confused and highly misleading.

    For one thing, very few elections have had their full ballot data released to the public, so most elections restrict analysis to mere inference of plausible scenarios. In other cases we have to look at traditional runoff elections, or other types of elections to make estimates of how they would have behaved under IRV. What data we do have suggests that the problems mentioned by IRV's critics are indeed real. (For instance this page About the 2007 Federal IRV elections in Australia.) Furthermore, statistical analysis and computer modeling of elections strongly suggest that opportunities for strategy are quite real with IRV.

    But even if such examples are rare, that in no way prevents a savvy voter from wanting to strategically downgrade weak candidates with IRV. It demonstrates lack of expertise on Lorenzo's part that he does not grasp that. Here's why.

    Say a voter prefers..

    m1 > m2 > .. > M1 > m3 > m4 > .. M2 > ..

    where the lowercase m's represent minor candidates and the uppercase M's represent major candidates. If m1 and m2 are people like Dennis Kucinich and Mike Gravel, a savvy voter knows they very likely won't win - but that they may spread the first-place votes enough that M1 -- "Obama" -- is eliminated early on, only to have one of the m's lose to M2 ("Clinton") in a later round. Such a voter would later feel the wasted vote syndrome, that he could have helped to at least get the "lesser evil" between the major candidates by raising that candidate to the top.

    This same feeling was observed by some large polls earlier in this year's primary process, when many people reported that they honestly preferred Clinton > Obama > Republicans, but would support Obama because they felt he had a better chance of beating the Republican. That same logic would compel them to insincerely vote Obama > Clinton > GOP (ignoring the others for simplicity) if it were an IRV race.

    The naive mistake people like Lorenzo always make is to assume that IRV strategy is only justifiable if voters know that, to use this case as an example, Clinton will lose to the Republican opponent. But on the contrary, they don't have to know that at all. All they have to have is evidence (e.g. polling data) that says which event is more likely. So in one final example, in an IRV election, you might prefer this..

    Kucinich > .. > Gravel > Obama > Clinton,

    but if Obama and Clinton are clearly the front-runners (which they were), then you'd want to vote

    Obama > Kucinich > .. > Gravel > Clinton

    Because you know that this almost certainly cannot hurt you, but may help you by preventing Obama from being knocked out.

    That these IRV advocates either do not understand this basic exercise is illustrative of their understanding of the subject of voting methods.

    Finally, Anthony Lorenzo is kidding himself if he thinks Score Voting advocates haven't thought about the subject of strategic voting already. Here are some pages he apparently forgot to mention.

    http://rangevoting.org/StratHonMix.html
    http://rangevoting.org/PleasantSurprise.html
    http://rangevoting.org/TarrIrv.html
    http://rangevoting.org/DH3.html
    http://rangevoting.org/Honesty.html
    http://rangevoting.org/HonStrat.html
    http://rangevoting.org/ShExpRes.html
    http://rangevoting.org/RVstrat1.html
    http://rangevoting.org/RVstrat2.html
    http://rangevoting.org/RVstrat3.html
    http://rangevoting.org/RVstrat4.html
    http://rangevoting.org/RVstrat5.html
    http://rangevoting.org/RVstrat6.html

    Clay Shentrup
    San Francisco, CA
    Rate this comment: 12345

    brokenladder
    08/20/2008
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    • Re: Anthony Lorenzo is confused
      Yes, the Web Site quoted where i am "corrected" quotes me largely out of context and refuses to incorporate my full responses.  It is owned by the folks who are responding to my comments, i might add, and is highly biased in favor of their viewpoint.  One should certainly mention that as a disclaimer when quoting it.

      As such, I am sure Range Voting is better than what is used in my elections. I am just disagreeing on the point that IRV is inferior to range voting, or somehow seriously flawed.  That is all i disagree with here.  I would also love to see some of the advocates for range voting actually organize an organization that can put forward range voting for real world elections involving people, not mathematical simulations only.  I would look forward to seeing some data based on actual use, rather than purely mathematical theory.
      Rate this comment: 12345

      anthonyviva
      08/24/2008
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      • Re: Anthony Lorenzo is confused
        Saying that ScoreVoting.net is biased is an ad hominem. Creationists can say that a site like TalkOrigins.org is "biased" in favor of evolution, but that does not refute the scientific evidence presented therein. If you have any evidence to present, feel free to present it. But we've presented an enormous amount of evidence that Score Voting (aka Range Voting) is vastly superior to IRV.

        Also I am a little tired of hearing this confused comment about looking at real elections instead of "mathematical theory". You cannot measure Bayesian regret with real elections, because they are rare and, more importantly, because we cannot read human minds.

        The bottom line is that the results of Warren Smith's Bayesian regret calculations show Score Voting to be better than IRV by a very large margin, and criticisms that they are not sufficiently realistic are countered by the consistency of those results among all 720 different combinations of election parameters. For instance, you can turn the strategy knob all the way from 0% (all voters are expressive) to 100% (all voters are strategic, even if it means misrepresenting their preferences), and the results are consistent among that whole range.

        So you can't say that wasn't realistic. We use the whole range of values that possibly could exist in reality.

        Despite the best of intentions, Anthony's pattern of behavior is to simply disregard these complex aspects of voting theory and repeat the same talking points, like the "use reality, not theory" argument I just addressed.
        Rate this comment: 12345

        brokenladder
        10/03/2008
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Scoring the Candidates
Range voting would prevent third-party spoilers--and give voters more say.
By Alan T. Sherman '87, Warren D. Smith '84, and Richard T. Carback III
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