Duopoly Must Go: An Appeal for Score Voting

by Andrew Jennings, Clay Shentrup, Warren D. Smith

Progressive thinkers on all sides of the political spectrum often wonder why the United States seems incapable of escaping a two-party political system. Is it a result of an extreme demographic situation, an urban and a rural America so large and obstinate that they are incapable of cooperation? Does it somehow come from the unique American spirit, a tradition steeped in individualism and adventure? Are the third parties being silently stifled because of their opposition to our incessant march toward rule by large corporations? The answer, in fact, may be so simple that it is right at our fingertips at least once a year. Every time we vote, in fact.

Fifty years ago, French sociologist Maurice Duverger observed that the plurality voting method tends to favor a two-party system, whereas “the double ballot majority system [a.k.a. 'top-two runoff'] and proportional representation tend to multipartism.” Observations in the social sciences are never absolute, but this tendency for plurality voting to maintain two-party domination is so reliable that it has become known as Duverger’s Law.

Plurality voting (a.k.a. “first past the post”), by far the most common system in the United States, is where each voter votes for one candidate and the candidate with the most votes wins, even if he receives fewer than 50% of the votes. Top-two runoff (a.k.a. “TTR” or “delayed runoff”) is just like plurality voting, except that if no candidate receives a majority of the votes, then a subsequent election is held between the top two finishers.

Few would expect the way we count our votes to be the primary factor determining the layout of our political landscape, but the evidence is overwhelming. Beyond the empirical trends to which Duverger referred, mathematical analysis of these voting methods suggests a causal relationship. For instance, a plurality voter who prefers a Green Party candidate will often take the tactical route, casting an insincere vote for the Democrat in order to prevent the Republican from winning. This costs the voter very little, since a minor party candidate is by definition unlikely to win anyway. It seems clear that such tactics keep us locked in a two-party system.

A top-two runoff system differs considerably. To echo Duverger, most of the approximately 30 countries which use this system have escaped two-party domination, even in single-seat non-proportional elections. And as with plurality voting, analysis of the runoff system strongly suggests that this is not a coincidence, but in fact a result of voter psychology and the different tactical incentives at play. For instance, voters in the runoff have no incentive to cast an insincere vote, as there are only two choices. And once the options are narrowed down to two candidates, voters often have a better chance to get to know an otherwise unknown challenger. These factors may largely explain how Green Party candidate Matt Gonzalez was able to come within striking distance of Democrat Gavin Newsom for mayor of San Francisco in 2003 (the margin was less than 6%) despite being outspent five to one, and despite Newsom’s being endorsed by a host of powerful beltway politicians.

Opinions vary as to the relative merits of TTR versus other systems, and the above is not meant as an endorsement of TTR per se. Rather, it is a testament to the extent to which the voting method determines the party composition of a government. It seems clear that if we want to escape the two-party stranglehold, we must adopt a different voting method; specifically one which is not known to also maintain two-party domination.

Many of the modern efforts for voting reform promote an alternative form of runoff, called instant runoff voting (“IRV”), which allows voters to rank the candidates and appears to offer us a way out of our electoral difficulties. Unfortunately, communities and scholars are discovering that the hope IRV offers us for escaping our two-party system is only illusory.

Like TTR, IRV doesn’t fix the spoiler problem: a bloc of voters may get a worse result by supporting their sincere favorite candidate. For instance, in the 2009 mayoral election in Burlington, Vermont, a group of voters who preferred Republican over Democrat over Progressive could have gotten the Democrat instead of the Progressive by insincerely top-ranking the Democrat instead of the Republican. It may seem strange to think of the GOP candidate as the spoiler, but the ballot data shows that a majority of voters in left-leaning Burlington would have taken the Progressive or the Democrat over the Republican in a runoff election, making the GOP more akin to a third party in this particular circumstance — albeit a strong third party.

And therein lies the rub. See, most voters picture runoffs in the context of weak third parties. The thinking goes that if you prefer, say, Green over Democrat over Republican, then you can safely support the Green. If the Green doesn’t make it to the runoff, then your support will simply go to the Democrat. But that is only the first phase of a third party’s growth. Next imagine that the Green Party, freed from the fear of “wasted votes,” grows to encompass more and more of the electorate until it can outlast the Democrats and make it to the runoff. Finally, imagine a third phase in which the Greens have grown enough to not only defeat the Democrats, but to win against the Republicans in the runoff. This third phase represents the greatest hopes for those who see IRV as a way to end the stifling two-party stranglehold on government.

But this rosy picture starts to darken the moment we take account of two crucial factors. First, it must be noted that each of these three phases is generally a prerequisite for the next. This is explained concisely as follows: as a third party grows, it will become powerful enough to defeat its most similar major party before it will become powerful enough to defeat both major parties. Second, the middle phase is effectively a barrier to the third. It is precisely the scenario experienced in Burlington. In this phase, the Greens defeat their most similar opponent, only to lose in the runoff. For Greens who prefer the Democrat to the Republican, the announced ballot totals will make clear to them that their honesty caused them to get the Republican instead of the Democrat. If even a mere 10% of them decide to cast a tactical vote for the Democrat in the next election, then even a prodigious 10% increase in their popularity by that time will be completely nullified. More realistically, their popularity would increase by less than 10%, in which case the tactical behavior would bring them down faster than they could increase their membership.

Many IRV proponents have argued that such strategy is infeasible and/or inadvisable, since it is likely to “backfire.” We address this theoretical argument in detail elsewhere, but for now let’s put aside contentious theorizing, and turn our attention to empirical reality. Australia uses instant runoff voting to fill each of the 150 seats in its House (has used IRV since 1918). It also uses other methods for other elections, e.g. its Senate is elected with a multiwinner method called PR-STV (proportional single-transferable vote). Australia’s House is two-party dominated; in the elections of 2001, 2004, and 2007 combined, not a single house seat was won by a third-party member. In contrast, quite a few seats in their Senate (e.g. 9 out of 76 in their 2005-2008 Senate and 6 in the 2008-2011 Senate) were/are occupied by third parties, mainly the Greens.

The same trend has been observed with IRV elsewhere, such as the Irish presidency (a near monopoly despite being mostly ceremonial), and in Malta and Fiji (before it was a dictatorship). And it is interesting that San Francisco supervisor Ross Mirkarimi (who helped found the California Green Party) switched from Green to Democrat in early 2010, despite the fact San Francisco now uses IRV, instead of the delayed runoff system it used when Matt Gonzalez made his impressive mayoral bid.

Of all these examples, Australia may be the most pertinent. We noted that their Senate uses STV, while their House uses IRV. STV is a multiwinner proportional system, and it so happens that IRV is actually the single-winner form of STV, so both systems use the same ranked ballot. Thus it is not too surprising that many American election activists see the adoption of IRV as a crucial “stepping stone” to proportional representation via the adoption of STV. IRV gets voters accustomed to ranking the candidates, and puts the basic machinery in place to tabulate those ranked ballots in the specific manner that STV entails. Even IRV proponents who are aware of its tendency for duopoly often support it for this very reason; they want proportional representation. In fact FairVote, the organization most often associated with the push for IRV, was founded in 1992 as “Citizens for Proportional Representation” (and later the “Center for Voting and Democracy”), and it seems that behind the scenes, their pursuit of IRV is a long-term play for proportional representation in America.

The stepping stone strategy might actually make sense were it not for the USA’s rigid impediments to proportional representation, which was made illegal at the federal level via a 1967 law which outlawed multi-member districts. In 1996, congresswoman Cynthia McKinney (who later ran as the Green Party candidate for US President) wrote, but failed to pass, bill HR 2545, which would have overridden that previous 1967 law. She re-introduced a similar bill, HR 1189, in 2001. It failed again. Then she tried again with HR 2690 in 2005. It failed yet again.

This leads us to believe that PR will be federally unobtainable in the USA as long as we are two-party dominated (a Congress dominated by two parties will continue to block anti-duopoly legislation such as McKinney’s). We therefore believe that proponents of PR must find a single-winner voting method which doesn’t maintain duopoly, as a prerequisite to PR. As has been noted, ordinary top-two runoffs fit that description, but they have their own problems, both in terms of voter turnout and the cost and fatigue associated with extra elections. And they can still leave voters justifiably fearful of supporting candidates they sincerely prefer to the apparent frontrunners, in the first round. (As a reminder, voters have no incentive to be insincere in the runoff.)

There are other voting systems that work with a ranked ballot and have several advantages over instant runoff voting (e.g. Condorcet methods), but even more exciting is a simpler class of voting systems discovered in the past few decades, based on an entirely different paradigm: ratings rather than rankings. These systems let each voter consider each candidate separately and assign to each a score or grade.

In his 2008 book Gaming the Vote, author William Poundstone (an MIT physics grad) suggests a voting method called range voting (a.k.a. score voting), in which voters rate the candidates on a scale such as 0-10 or 1-5. When the scale is reduced to 0-1, we effectively have approval voting, which is identical to plurality voting except that there is no limit on the number of candidates a voter may support. A third method, the Majority Judgement, asks the voters to use a few natural-language terms (Excellent/Good/Acceptable/Unacceptable, for example) to grade the candidates and chooses the winner by finding the candidate who was given the highest grade by a majority of voters (the median grade).

Score voting has historically been overlooked, based on the assumption that it would succumb to pervasive tactical exaggeration. But that view was debunked back in 2000, when a Princeton math Ph.D. named Warren D. Smith performed an extensive set of computer calculations which showed the system working extremely well, even with high rates of tactical voting. This is based on an objective “economic” indicator of voter satisfaction with (or “representativeness of”) election outcomes, called Bayesian regret.

This can be understood if we think for a moment about a voter whose preferences are Nader=10, Gore=6, Bush=0. If this voter is sincere, he casts those very scores. But if he is a tactical voter, like those who voted for Gore instead of Nader under plurality voting, how should he vote under score voting? For starters he wants to give Gore a 10, and Bush a 0, to maintain the tactical advantage he sought under plurality voting. But he can additionally give a 10 to Nader, and any other candidates he prefers to both frontrunners, with no fear of negative consequences. (In election theory parlance, we say that score voting passes the Favorite Betrayal Criterion.) Whereas you will recall that with IRV, tactically placing the Democrat in first place absolutely requires a Green voter to place the Green lower than first place. But with score voting, giving Gore a maximum score in no way prevents a voter from still giving Nader a maximum score too. So third parties face no artificial barrier to growth, as they do with IRV.

A simple way to think of it is that a tactical score voter should support the same candidate as he would with a plurality ballot, and then also support all the candidates he likes better. This means that the appearance of being “unelectable” need not become a self-fulfilling prophecy, like with plurality, IRV, and so many other methods. If it turns out that enough voters prefer a minor party or independent candidate to the presumed frontrunners, then he can actually win, even if the voters are highly tactical! Empirical evidence strongly suggests election outcomes will then be vastly more representative of the actual relative support for the candidates.

We believe this has enormous consequences, beyond the obvious opportunity to escape from two-party domination. For instance, the inordinate importance of cash in elections is largely a product of the need to prove electability. Consider exit polling from 2000 in which 90% of Nader supporters claimed to have voted for someone other than Nader. This shows that the number of votes Nader could have received by convincing voters he could be elected (e.g. by having an enormous campaign “warchest” and/or getting the nomination of a major party) was nine times as large as the number of votes he won by trying his best to convince voters he should be elected. Also consider that in the 2008 US presidential election, Mitt Romney spent large amounts of cash from his personal fortune to bus in voters to straw polls with no legal consequence whatsoever, apparently in order to be seen early on as a frontrunner, so as not to be abandoned by tactical voters, who fear wasting their vote on candidates who can’t win.

These may seem like anecdotes, but their prevalence amounts to something greater. Money matters far too much in today’s political process. And efforts to curb that with typical campaign finance reform are inherently unstable, as cheaters will be more likely to win elections, and then just make their cheating retroactively legal, and/or intimidate government officials who dare to try to prosecute them. We believe it may be more effective to try to reduce the inherent importance of cash, than to wage a potentially futile battle to level the playing field. With score and approval voting, a candidate need not prove his electability in order to earn your vote.

In summary, we would be wise to realize that the lack of alternative choices in American politics is unlikely to be repaired without changing to a better voting system, and that instant runoff voting is probably not the answer. We should give serious consideration to voting systems based on ratings, where voters can evaluate each candidate independently, and never fear giving their full support to the candidates they prefer to the frontrunners. While it’s impossible to predict exactly how these systems will play out in practice, the theory and a great deal of empirical evidence make them seem promising, and it’s clear that the systems we have now are not working and it’s time to look outside the box for a voting system that will truly support smaller parties and encourage alternative ideas in our political discourse.

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33 Responses to Duopoly Must Go: An Appeal for Score Voting

  1. This is an excellent analysis, making a very good case for score voting, or its most simplified form, approval voting.

    Since Instant Runoff (IRV) is receiving a lot of support from people sincerely trying to break the strangle-hold of the two-party system (really one party with two branches differing in style and in a few minor details) it is worth elaborating a bit on why IRV is not really a good idea. One problem is that there are a number of ways, not mentioned in the article, in which IRV can produce bizarre results. For example, it is possible in a multi-candidate race for the IRV winner to be preferred by the voters to only ONE other candidate, while another candidate would have been the IRV winner in 2-candidate races against ALL other candidates. This can’t happen with score or approval voting.

    Another major problem involves vote tabulation. For plurality voting, score voting, and approval voting, ballots can be processed in the precincts where cast and the candidate scores made public and then forwarded to a central point for merging (essentially just addition). This cannot be done for IRV, which, in general, requires detailed information about all ballots to be processed together. So either all ballots for a race must be tabulated in one location, or else there must be transmissions of data back and forth between a tabulation center and the precincts. This is computationally less efficient and, leaves much more room for fraudulent manipulation.

    A more detailed exposition of the above points (and a bit more) can be found at

  2. oklaelliott says:

    This is a great analysis. I still tend to lean toward rank choice voting (picking #1, #2, #3, etc) for its simplicity. The worry with score voting I have is that it will seem too complicated — merely the idea that you can rank two people as equal is so anathema to the voting process in this (and most) countries. A ranking system makes immediate sense and reflects the way we tend to view electoral competition.

    Either way, great analysis, and I hope this gets more people out there thinking about this issue, which I have recently begun thinking of as perhaps the most important in our democracy, since the primary way to fix the other looming issues is to get a different group of people in power.

  3. To oklaelliott’s “worry with score voting… that it will seem too complicated — merely the idea that you can rank two people as equal is so anathema to the voting process in this (and most) countries”… Let me reply:

    * The present system (plain plurality voting) FORCES every voter to rank every candidate equal (except for one). This is thus not “anathema to the voting process in this country” but rather “forced by this country.” I.e. you are forced to provide the least possible amount of info in your vote, not the most, and fored to provide the most possible equalities, not the fewest.

    Also, in many implementations of IRV (such as in San Francisco), voters are forced to rank only at most 3 choices and forced to rank all others equal. Also they often (including in SF) have the option of ranking fewer than 3 in which case even more are ranked equal.

    In contrast, with score voting, no voter is forced to rank any candidates equal.
    So it seems to me, oklaelliott has it backwards in expressing this concern about
    possible equalities.

    To oklaelliott’s desire for “simplicity,” let me respond:

    * there are good reasons to believe voters find scoring EASIER than rank-ordering.

    For example, voters experimentally make a lot fewer ballot-invalidating errors.
    For another example, hotornot.com (one of the most commercially successful websites on the planet) when asking people to rank-order two hotties as hotter/colder, found they got faster responses by asking them to SCORE both hotties on a 10-point hotness scale.

    Thus, counterintuitively, people actually found it easier to score them than rank-order them, even in the maximally-simple rank-ordering case of only two candidates.

    And since hotornot.com got more information via scoring and in less time and easier, they abandoned rank-ordering.

    * The psychological testing literature agrees: scoring is preferred as a question
    format than rank-ordering, for various good reasons supported by many studies
    over the last 50 years.
    * Also from the point of view of the vote COUNTERS rather than the VOTERS,
    range voting is simpler than IRV too.
    * Also, honeybees are known to use score voting to pick new hive locations each year.

    If score voting is simple enough for insects (and IRV isn’t – no nonhuman animal known to use IRV) maybe it is simple enough for us. Score voting has also been used successfully by kindergarteners, (see http://www.scorevoting.net/ShermanPetElection.pdf)
    where again lower error rates occurred with range and approval voting than with plain plurality voting (a result duplicated in other voting studies with adults too…)

    So again, oklaelliott has it backwards: range voting is simpler, not more complicated, than IRV, from the points of view of both voters and counters and error-rate data and timing data and animal data and kindergarten data and according to psychometrics books.

    Finally: I fully agree with oklaelliott that “[voting method reform] is [one of the most important or even] perhaps the most important [issues] in our democracy.”
    This claim seems counterintuitive; a lot of people think it is a minor matter.
    (Or rather, reach that conclusion without thinking.) But it is actually extremely important and voting methods have distorted our so-called democracy hugely.
    For example, the most important 2700 or so USA races are 98% predictable 1 year in advance and zero third-party members have won election to the US congress during the last decade. This means there is only a 2-way choice which is usually only a 1-way choice, i.e. non-choice. Call that democracy? Entire classes of ideas are simply excluded from the debate, essentially do not exist, therefore. E.g. Kerry & Bush both pro-war, US public anti-war but therefore forced to vote pro-war.

    E.g. “public option” in health care reform was “off the table” before the debate even started, despite support by a large fraction of US public and US medical pros.

    Weird political bundlings occur, such as anti-abortion implies being for tax-cuts for the wealthy and vice versa (which makes no logical sense; it is a side
    effect of our crazy voting system) — thus again excluding vast classes of people
    from political office (e.g. those who hold only one of these two views) or forcing them to be massively dishonest like secret-gay public anti-gay IA senator Larry Craig.

  4. brokenladder says:


    First I would like to reiterate that, while IRV may seem to allow for a good degree of expressiveness by allowing you to vote e.g. Third>Democrat>GOP, you will often get a better result by insincerely ranking Democrat in first place (so it becomes strategically advisable to do it always, just in case). While approval voting seems superficially less expressive, some would consider an approval for Third and Dem to be more expressive than an insincere ranking for Democrat>Third>GOP. That may not matter much to you if you always vote your conscience, but the vast majority of voters apparently cannot bring themselves to do that very often. With approval voting, they never have a reason to do so, so in a way their approval voting ballots will be more expressive than their IRV ballots would be.

    Further, IRV ignores (literally discards) a significant amount of the ballot data you give it, so a lot of that expression goes for naught. That doesn’t happen with score or approval voting.

    Score voting appears to be simpler than IRV in the following ways:

    A. Voters experimentally make fewer ballot-invalidating errors when using score voting than when using IRV. For instance, here in San Francisco we experienced about seven times as many spoiled ballots with IRV as with plurality voting. We see this as an indication that voters empirically find IRV ballots to be more complicated. Simply put, they mess up more often with IRV, and less often with score voting (and even less with approval voting).

    B. Score voting (and by extension, approval voting) is additive, or “precinct summable”, so the counting process is relatively simple and transparent. We can obtain the final result by simply summing the totals from each precinct. Whereas IRV cannot be counted in precincts, which is why if you went to the San Francisco government website to seek results of their 2006 November 6th ranked-choice voting elections, you still got this message for many months:

    Due to the requirement that all ballots must be centrally tallied in City Hall and not at the polling places, the Department of Elections has not set a date for releasing any preliminary results using the ranked-choice voting method.

    C. Score/approval voting runs on all of today’s voting machines without any modification (including non-computerized machines). IRV does not. While either method can certainly be counted by hand, that makes no difference if government officials decide to use machines. And in fact, IRV may incentivize the adoption of voting machines particularly of the electronic variety.

    Computer scientist and election integrity expert Dr. Rebecca Mercuri warns:

    IRV and other proportional balloting methods have been proven to incentivize the introduction of electronic ballot tabulation in places where none previously was needed or has existed, and they further complicate what has become an increasingly closed process for the determination of election results.

    The complexity of counting STV (remember, IRV is the single-winner form of STV) apparently catalyzed the adoption of electronic voting in Scotland. According to a report by the UK government,

    Experience of counting STV elections elsewhere led the Scottish Executive to examine the feasibility of counting the ballot papers electronically.

    D. Write a score voting computer program and an IRV computer program (preferably with error-checking of the inputted votes). The score voting program will be shorter and will run faster, assuming essentially any reasonable programmer does it. (This, called “Kolmogorov Complexity” is the standard objective metric used by scientists to assess “simplicity.”)

    A human may not be a computer, but the task of rank-ordering a list of candidates is still bounded by the mathematical rules of sorting algorithms. The fastest general case sorting algorithm known is the quicksort, whose average case complexity is n*log(n) (where “n” is the number of candidates in this case). Since few (if any) humans have the mathematical acumen to perform a quicksort algorithm in their heads, that will more realistically become a bubble sort, with an (even greater) order of complexity n^2. Whereas the computational complexity of rating is simply 2n. You make a first pass through the list in order to establish reference points for a second-pass normalization. That goes down to a mere 1n if you normalize relative to spectrum of candidates with which you are already familiar (which I suspect is approximately what many voters would do). Thus with a crowded field of candidates, such as the 9 we were asked to consider in the last SF mayoral race, IRV plausibly took roughly six times as much mental work as score voting would have (using (2^9)/(1.5*9)).

    Actually, it was less than that, since voters could only rank three choices in the SF system. But that is presumably a result of trying to limit the increased complexity and ballot size associated with IRV (that we believe would not come with SV or AV).

    Admittedly, this analysis is probably a little unpalatable if you’re not a mathematician or a software engineer, so here’s a simpler way to see the effect clearly, by exaggerating it. Pick 10 to 20 movies or books off a friend’s shelf, and ask that friend to rank them in order, and then to rate them (or vice versa). I believe your typical experience will be that the rating takes less time. And even if it doesn’t, I still see this as a small issue in comparison with representativeness, which according to our best Bayesian regret estimates, is significantly better with score and approval voting than with IRV.

    A ranking system makes immediate sense and reflects the way we tend to view electoral competition.

    That may be, but ranking does not reflect the nuance that people feel when they say something like, “I like Nader a lot more than Gore, and I like Gore vastly more than Bush.” Rankings cannot convey intensity of preference. One might intuitively think that approval voting also cannot convey intensity, but when a voter uses a reasonable preference intensity threshold, then approval voting inherently does benefit from being able to incorporate “revealed preference” which exposes preference intensity.

  5. icr says:

    Are US voters really in love with the two-party system? :
    When pollsters ask the American people whether they are likely to vote Republican or Democrat in the next presidential election, Republicans win growing pluralities. But whenever pollsters add the preferences “undecided,” “none of the above,” or “tea party,” these win handily, the Democrats come in second, and the Republicans trail far behind. That is because while most of the voters who call themselves Democrats say that Democratic officials represent them well, only a fourth of the voters who identify themselves as Republicans tell pollsters that Republican officeholders represent them well. Hence officeholders, Democrats and Republicans, gladden the hearts of some one-third of the electorate — most Democratic voters, plus a few Republicans.
    With this much discontent it’s possible that anti-duopoly reform could be enacted in some states with initiative and referendum. My idea of reform would be range or approval for single seats and electing one house of the state legislature by party-list (open or closed) PR. Why not even elect the PR house via a single statewide constituency (like Israel and Netherlands do for their national parliaments) ? We’ve been pointlessly electing state legislatures with mirror-image houses since the SCOTUS “one man, one vote” decisions of the early ’60′s.

  6. brokenladder says:

    FairVote’s Rob Richie recently submitted this letter to the editor at the New York Times web site, proposing that New York City switch from traditional delayed runoff elections to Instant Runoff Voting. I’d like to respond to a few of his points.

    IRV is used to elect mayors in cities like San Francisco, Minneapolis and Oakland

    To my knowledge, Oakland has never held an IRV election.

    Turnout tends to be sharply lower in runoffs, as was the case in last year’s expensive runoffs for city comptroller and public advocate.

    Actually, turnout seems to be higher in runoffs in important races. For example Los Angeles is the biggest US city to elect its mayor via a two-round runoff system, and turnout went up in all three of the most recent occasions a runoff happened in LA.

    Louisiana was only state to elect governor via this system and in all four of its elections with a runoff, turnout went up.

    So turnout went up in the last seven most important runoff elections in the USA. Also in the last Mayor and DA races held in San Francisco before it switched to IRV (a switch engineered in large part by FairVote) the turnout went up in the runoff round. Richie is correct that in more minor races, turnout in runoff elections tends to decrease, such as San Francisco district supervisors.

    As for turnout improving with IRV, it is noteworthy that in Minneapolis, a city Richie mentioned, the turnout after IRV was adopted was the lowest since 1902.

    IRV would likely save New York City $15 million in 2013

    Actually, IRV seems to have increased costs in San Francisco and Minneapolis. A study conducted by the Vermont Secretary of State’s office, in partnership with the University of Vermont, projects the same for a possible use of IRV in some statewide races.

    Finally the claim that IRV “upholds majority rule” seems to be contradicted by the last IRV mayoral race in Burlington, Vermont, in which Democrat Andy Montroll was preferred to Progressive victor Bob Kiss by a majority of voters.

    * Several of these points are paraphrased from a discussion list conversation by Warren Smith, of ScoreVoting.net.

  7. brokenladder says:

    This comment is by Okla and was moved from a different post, which was then converted into the previous comment.

    I understand Oakland is using IRV in the current election, right?

    Also, you seem to use single exceptions to make universal claims about IRV which don’t seem to apply to the overall trends. For example, while a few elections may show increased turnout in run-off elections, that certainly is not the overall statistical trend. Every analysis I have ever seen — as well as a simple news search for run-off elections — shows that run-offs tend to get much lower turnouts. A recent Alabama run-off, for example got 30% and that was considered quite high and people were surprised.

    I have to say, my choice is still IRV, as it makes the most sense, seems the simplest and surest method, and (according again to nearly every analysis I’ve seen) will in the aggregate reduce costs where traditional run-off elections occur. Here again, the few examples you cite do not counteract the statistical trends.

    That said, I think we can agree that election reform is absolutely necessary.

  8. brokenladder says:

    This comment is by Rob Richie and was moved from a different post, which was then converted into a comment on this post.

    Too had this is the kind of blogpost you all want to post here. For the record:

    1) Oakland is using instant runoff voting for its mayoral election this year. it was passed by Oakland voters 69% to 31% in 2006. It’s generally called “ranked choice voting” there now.

    2) As to turnout, IRV puts all the focus on a single election. When you spread an election over two rounds, you typically will have lower turnout in one or the other. In primary runoff elections, it is usually the runoff — indeed, fully 113 of the 117 fededarl primary runoffs in 1994-2008 had a drop in turnout, by an average of well over 30%. See: http://archive.fairvote.org/?page=1489

    But IRV won’t always lead to competitive elections. Minnapolis’ election in 2009 would have been noneventful under any winner-take-all system. Its neighboring city of St. Paul had an even bigger drop in turnout with a similar situation, using traditional runoffs.

    3) San Francisco has saved money with IRV — see Geard Gleason’s discusson of it here. http://archive.fairvote.org/victoryfund/?page=2555

    Minneapolis decided to spend a lot on voter education and did a detailed handcount procedure. Once it has equipment ready to run IRV elections, which it will have in 2013, it will save money by having one election rather than two. Cary (NC) saved money with its IRV election in its very first year in 2007.

    • brokenladder says:

      This comment is by Dale Sheldon-Hess and was moved from a different post, which was then converted into a comment on this post.

      Except that the “few examples” are ALL the examples in the entire US.

      I don’t know what other “trends” you could possibly be referring to when literally every example is of the opposite. Costs have always gone up. Attendances have not; when they have, they haven’t exceeded normal yearly fluctuations.

      IRV is no magic bullet. If there are any improvements at all, they are minor. The much-hyped cost savings and attendance numbers have not occurred.

      (And the (non-instant) runoffs with lower turnout were ALWAYS ones where another, more important race on the same ballot didn’t go to runoff. I haven’t looked to closely at Alabama, but I believe the races for Democratic governorship & senate nominees might qualify.)

  9. brokenladder says:


    As I understand it, Oakland should be using IRV for this first time this fall, after approving it in 2006. I point this out because I think Richie’s comment might give some the idea that Oakland has already used IRV to elect a mayor.

    I did point out that Richie is correct about the overall trend of lower turnout in runoff elections. My point was that the exceptions tend to be larger elections with a greater net impact. Richie does not mention that, and I think many readers would find that important. I think it is also significant that IRV does not necessarily increase turnout, as was the case in Minneapolis.

    As for costs, IRV appears to have slightly increased costs in various places where it’s been adopted. I linked to the official election costs from San Francicso and Minneapolis for instance. It could be that a lot of those costs would diminish over time (for instance, every year the voters are more familiar with IRV, education costs presumably go down), but that’s hard to see given IRV’s tendency to be repealed. For instance, Burlington VT and Pierce County WA (and probably Aspen CO this November) have discontinued IRV after a very limited experience with it.

    I want to be clear that this post was not meant an indictment of IRV per se, but rather an attempt to address some of Richie’s specific points that I feel could be misleading.

    That being said, I do feel the need to address your point about complexity. IRV is one of the more complex voting methods. Score Voting, Approval Voting, Borda voting, and several Condorcet methods are all simpler according to every objective measure I know:

    1. Kolmogorov Complexity
    Write a computer program to compute the results of each of these methods (preferably with error-checking of the inputted votes). The programs for Approval, Score, Borda, and some Condorcet methods will be shorter and will run faster, assuming essentially any reasonable programmer does it. (This, called “Kolmogorov Complexity” is the standard objective metric used by scientists to assess “simplicity.”)

    2. Voters experimentally make fewer ballot-invalidating errors when using Score and Approval Voting than when using IRV. (Voters themselves apparently find IRV more complex, whether or not they are consciously aware of it, because they empirically mess up more often with IRV.)

    3. Almost every voting method, except for IRV, can be sub-totaled at the precincts, so that the precincts can simply report their subtotals, and the final result can be computed as the sum of those subtotals. This explains why I once got this message for many months after one of our IRV elections:

    “Due to the requirement that all ballots must be centrally tallied in City Hall and not at the polling places, the Department of Elections has not set a date for releasing any preliminary results using the ranked-choice voting method.”

    4. Score/Approval Voting run on all today’s voting machines without any modification (including non-computerized machines). IRV does not. Thus some have a reasonable fear that IRV may catalyze the adoption of (expensive and fraud-prone) electronic voting machines. This relevant excerpt from a Minneapolis report is concerning to me:

    Future Elections Costs without a Hand Count Though certified voting equipment capable of running an RCV election is not currently available, if it were to become available the City could conduct future RCV elections without a hand count.

    I absolutely agree with you that reform is necessary. Regardless of the relative merits of different voting methods, I would like to see the utmost accuracy and transparency in the rhetoric used by their respective proponents. That was the central aim of my post, aside from my going on a bit of a tangent in this response.

  10. brokenladder says:

    This comment is by Warren Smith and was moved from a different post, which was then converted into a comment on this post.

    To respond to Rob Richie,

    1) Oakland enacted IRV but has not yet used it as of the current date.

    2) That FairVote page RR refers to is highly interesting:
    Assuming it can be trusted (a bad assumption to make about whatever Richie & FairVote say, in my experience… they have a very poor record and often are deceptive) it tends to confirm the view I’ve developed independently by looking at my own considerable data, which is, in MAJOR elections (e.g.Mayor, Governor) turnout tends to increase in the 2nd, runoff, round; in MINOR elections (e.g. Texas Railroad Commissioner, which FairVote’s S.Hill once used as his sole example in an op-ed he published) turnout tends to decrease in 2nd round. Hill used that example to argue that Texas should change its Railroad Commissioner election to be IRV. A better lesson would have been for Texas to change that seat to become appointed, not elected (I would say; Hill apparently felt differently). I cited the 7 most important USA runoff elections (Los Ang. mayors and Louisi. Governors, all most recent) and in all 7 cases turnout increased. Richie’s page cited 117 runoffs in PRIMARIES (hence by definition more “minor” races — primaries generally get below 1/3 the turnout) and in 113 he says turnout went down. Also Richie in his original letter to the NY mentioned the “city comptroller” and “public advocate” as his sole examples, again intentionally selecting MINOR races so he could have turnout go down. Richie forgot to mention that
    there WAS NO runoff for either city comptroller or public advocate — he really must have meant the Dem.party PRIMARY for city comptroller & p.a. (?), making it even more minor still.
    So the combined data all supports my view: major race==>turnout up, minor==>down. In the particular case R.Richie had been addressing in his letter to the NY Times — NY City Dem Party primaries — the most recent 3 mayoral Dem Party primaries involving runoffs were
    1973: 773K in primary, 903K in runoff.
    1977: 893K in primary, 780K in runoff.
    2001: 785K in primary, 790K in runoff.
    Note turnout went up in 2 out of 3 cases, contradicting the false impression a reader would have received from Richie’s letter that “turnout tends to be sharply lower in runoffs.”

    3) The actual San Fran election budget numbers are here:
    and it appears costs increased after SF adopted IRV. I stand by this pending any superior analysis (which, as I explained there, might be possible). The “analysis” Richie cites (a FairVote page) does not actually give the budget numbers, so it clearly cannot be taken seriously.

    It does naively make sense that IRV costs ought to be lower once we get along in years so that the startup costs of buying new machines & training etc become relatively small. However, when you look at the numbers you realize that (a) with plain (non-instant) runoffs, often they are not needed, (b) the lifetime of these machines is finite and hence the “one time” expense can
    easily fail to pay for itself in savings even over the whole life of the machines, (c) SF also had problems like uncertified and uncertifiable and breaking machines. Univ. of Vermont’s cost study indicated IRV would increase costs. My own calculations suggest costs will go up with IRV sometimes and down other times, depends on the situation, and it is not
    at all legitimate to claim it clearly will save money. All in all the evidence I
    am aware of tends to argue replacing real runoffs with IRV tends to be a cost increase. FairVote has systematically tried to replace real runoffs with IRV
    using as its main argument cost savings. This campaign, to the extent it has succeeded, probably both raised costs and made our elections worse.

    As I said, in SF and Minneapolis, costs appear to have risen with IRV. Those were 2 out of the 3 cities R.Richie cited in his NY Times letter which said
    “IRV would likely save New York City $15 million in 2013.”
    The third city Richie cited, Oakland, has not yet held an IRV election.

    Richie now in his response here cited Cary, a small Carolina town, as having reduced costs by using IRV. I do not know if this claim is correct, but I will note that Cary repealed IRV, regarding the experiment as a failure.

    Richie/FairVote are not doing too well on the truth, as usual.

  11. Rob Richie says:

    Warren Smith is a man of great certainty in his opinions, but one final note on this exchange:

    1) He claims FairVote is deceptive. We interpret information differently than he does (for instance, the definition of a majority voting system), but we are widely and rightly accepted as an objective source of facts. So those indeed are all the regularly scheduled federal primary runoffs in 1994 to 2008, for example, and turnout dropped in 113 of 117 of them, as will also be the pattern this year – -if Warren callS US House and US Seante primaries as “non-major” elections so be it.

    2) Part of the reason that turnout will rise in a runoff in a city like Los Angeles, is it’s clear that there will need to be a runoff. People care most about elections theyh know will be decisive — it’s why more people watch the Super Bowl than the playoffs.

    3) The context of the discussion in NYC about IRV has been in the context of replacing the citywide primary runoffs with IRV. It’s a non-controversial position in the city to believe those runoffs are problematic for a number of reasons.

    4) Cary is a city of well over 100,000 people, not a “small town.” It didn’t repeal IRV. It used it for a one-time pilot. It may well use it again.


    4) San Francisco’s differences in overall spending are tied to the fact that in many years, it does many other elections. IRV has allowed the city to not hold a citywide runoff in 2005, which would have cost $3 million or more, and has allowed it to not hold numbers Board of Supervisor runoffs. With open seats coming up for citywide offices next year, IRV will save millions more.

    • brokenladder says:


      This is not just an issue of interpretation. You and FairVote have made numerous false and misleading claims.

      For instance, claiming that the Burlington election did not suffer from non-monotonicity, even though it is an irrefutable objective fact that it did (according to FairVote’s own definition of monotonicity).

      We don’t have a different definition of “majority voting system”. The only way in which IRV is a majority system is that it guarantees the winner will be preferred by a majority to at least one other candidate. So it is entirely possible to have a 10-candidate IRV election in which 8 of the winner’s 9 opponents were preferred to that winner by a majority of voters. This is an objective mathematical fact, not a difference in interpretations.

      You co-authored a piece in Science Magazine which claim that with IRV, “a voter’s best strategy is to sincerely rank the candidates.” This is simply mathematically/statistically false, as explained here. A concrete example is the bloc of voters preferring Republican over Democrat over Progressive in the last mayoral race in Burlington VT. Had some of them insincerely ranked the Democrat in first place, they could have had the Democrat instead of the Progressive. And that move makes perfect sense given that Burlington is quite liberal, and the Republican would be highly unlikely to defeat either the Progressive or Democrat in a runoff.

      You and other FairVote activists have also repeatedly claimed that Score and Approval Voting would degenerate into ordinary Plurality Voting, since voters would almost all just vote for their favorite candidate and no one else. That argument is utterly refuted by the fact that, in Plurality Voting elections, something like 90% of voters will vote for their favorite among the frontrunners, even if that is not their true favorite.

      For instance, around 90% of Nader supporters in the 2000 US presidential election claimed in exit polls to have voted for someone other than Nader. The reasonable assumption is that a Nader supporter who voted for Gore would have also voted for Nader if he could have used Approval Voting. In order for your “degenerate-to-plurality” argument to be true, that switch from Plurality to Approval Voting would somehow cause such a voter to switch from Gore to Nader. As implausible as that seems, it would at least be an improvement from tactical Plurality Voting to sincere Plurality Voting, in the worst case scenario.

      More realistically, people would vote for the same person they would have under Plurality Voting, plus everyone they liked better. And in fact that is exactly what seems to be the case in all Approval Voting elections for which we have a good picture of voting trends.

      Yet despite the overwhelming theoretical and empirical evidence to the contrary, you and other FairVote members and allies make bizarre claims like this:

      because “approving” a second choice may help defeat the voter’s first choice, most experts agree that it [Approval Voting] is likely to devolve to typical vote-for-one pluarlity [sic] voting.

      I do not know of any “voting experts” who believe a switch from Plurality to to Approval would make an insincere voter switch to a sincere Plurality-style “bullet vote”. I even created a poll and invited IRV advocates to express their opinion. So far 100% of them have agreed with me.

      Because you cannot win on the substantive issues, you delve into semantics.

      Cary voted to stop using IRV, whether you want to call that “repeal” or some other word. According to Wikipedia, “in 2009.. the Cary Town Council voted to use a traditional runoff method.”

      Then you want to quibble over whether Cary is a “small town”. I recently visited Lawrence KS where I attended the University of Kansas in the late 90′s. Its population is around 92,000, yet I describe it to people here in San Francisco as a “small town”. It’s relative, but the fact that you want to distract from the real issues by bringing up such minor points is telling.

  12. Some information pointed out by Warren Smith and Joyce McCloy:

    To correct Rob Richie some more [his quote was "Cary (NC) saved money with its IRV election in its very first year in 2007."]

    Cary repealed IRV after the first (and apparently still the only?) person to be elected in NC by IRV, Don Frantz, criticized it based on his experience:

    They went back to traditional 50%+1 majority elections with traditional runoffs if needed.

    The claim Cary saved money is somewhat dubious because many IRV-related expenses were off the town’s books (e.g. conducted by IRV advocacy organizations, not the town) and that would not have been possible if we instead were talking about someplace large. But I do not dispute that IRV is capable of saving money in some cases. I (along with the University of Vermont…) just dispute that that is a clear expectation.

  13. Rob Richie says:


    You analysis of “false claims” is not convincing, and you are wrong on other points. Please look on our site for false information (as opposed to analysis with which you disagree). If you find it, we’ll try to change it (the old template is largely beyond reach, though, so focus on the new template if you’re interested).

    1. My point about the best strategy with IRV is to vote sincerely is based on the practical realities of what it means in real elections. Afterwards, if you have all the rankings, you can try to show what different strategies would have done, but you just don’t see those in real elections — and there have been thousands of them. Leading Australian analyst Antony Green just made this same point in an analysis for their national television station.

    So what you see as a “lie” is simply a fact that I’m talking about IRV in practice, and you’re talking about IRV in theory.

    2. Cary’s default was to use runoffs in 2009, so it simply is false to say IRV was repealed. To use IRV, the council had to vote to enter the pilot program again. It didn’t, but that’s not a repeal. (Note: the other NC city to try IRV in 2007 did so again in 2009 and has voted since to say it wants to keep using it.) It also is true that Cary voters preferred IRV — by overwhelmingly percentages both in a 2007 exit poll and a 2008 survey by the city that found voters were fully ten times more likely to rate IRV highly than poorly.

    Note that there were other IRV elections, some won by IRV backers. The fact that only one race went to a second count doesn’t mean the others didn’t experience an IRV election. Frantz wasn’t a fan of IRV before the election, either.

    3 I dispute that the Burlington 2009 election was a nonmononotic election – this t is an example of seeing facts differently. The fact is, Progressive Bob Kiss did NOT lose by getting enough of Republican Kurt Wright’s votes so that Wright dropped from first to third behind Democrat Andy Montroll. If he had, it would have been a nonmonotonic election, but no one lost in Burlington in 2009 by getting additional votes.

    I also reject any assumption that approval voting, range voting or Bucklin voting would have elected Montroll. The fact of later no harm” and the fact that most voters in Burlington want their first choice to win. Not everyone will bullet vote, but the most tactical voters will. And in Burlington, most voters were more interested in electing their party’s nominee than making sure their least favorite candidate was defeated. Approval/range/Bucklin work better when you’re more interested in defeating someone than electing someone.

    So you can go on about Burlington, but I’m confident that your proposals quite possibly would have elected Wright, the Condorcet loser (among the top three) who led in first choices. Of course you can dispute that with simulations ,but you can’t dispute it with actual elections because even the few election held with approval voting suggest that bullet voting becomes a key tactic that advantages the more tactical voters. (The Dartmouth Alumni trustee elections being a good example, contributing to its 82% to 18% repeal last year.)

    • brokenladder says:


      The fact of later no harm” and the fact that most voters in Burlington want their first choice to win. Not everyone will bullet vote, but the most tactical voters will.

      All theoretical and empirical evidence says that bullet voting is a myth. For instance, if you prefer Nader but vote for Gore with Plurality Voting, then with Approval Voting you obviously want to vote for Gore and Nader. It would make no sense to switch your vote from Gore to Nader just because you have been given the right to vote for an unlimited number of candidates.

      I mentioned this in my previous post. And 100% of IRV proponents I polled agreed with me.

      The Later No Harm criterion is a similar red herring. It means that if I prefer Nader over Gore, and I rank Nader in first place, then I don’t have to fear also ranking Gore after Nader. That won’t cause Gore to defeat Nader. But that’s only relevant if I sincerely rank Nader in first place. If I’m a tactical voter, I won’t. I’ll rank Gore in first place.

      This is why you should focus on the Favorite Betrayal Criterion (which Score and Approval Voting pass, and IRV fails) instead of the Later No Harm Criterion. The LNH is a practically meaningless criterion, which appears to be totally contrived to make IRV look good. Whereas the FBC actually has practical relevance to tactical incentives placed on voters.

      So you can go on about Burlington, but I’m confident that your proposals quite possibly would have elected Wright, the Condorcet loser (among the top three) who led in first choices. Of course you can dispute that with simulations ,but you can’t dispute it with actual elections because even the few election held with approval voting suggest that bullet voting becomes a key tactic that advantages the more tactical voters. (The Dartmouth Alumni trustee elections being a good example, contributing to its 82% to 18% repeal last year.)

      Robert Z. Norman, a Dartmouth math professor with a penchant for voting theory responds:

      “the claims about bullet voting in the Dartmouth Alumni election [by Rob Richie and other IRV proponents] remind me that with a per voter average of voting for 1.8 candidates, the proportion of bullet votes has to be fairly small. The alternative..is that nearly everyone voted for one or three candidates but not two. Unlikely as that might be, it would suggest that most of those who voted followed a strategy of either voting for the petition candidate or voting for all [3 opposing] nominated candidates, in which case [FairVote's Rob] Richie’s claim that the opposition was disorganized falls apart, as does the claim by some of the Alumni Council people that in a 1 on 1 situation the petition candidate would been defeated.”

      I told you about this via email in the fall of 2007.

      And in Burlington, most voters were more interested in electing their party’s nominee than making sure their least favorite candidate was defeated.

      What’s your evidence for that statement? In my experience you have a habit of just making things up like this.

      Consider that around 90% of Nader-favoring voters voted for someone other than Nader in 2000. Do you expect me to believe that Burlington voters are just so much more honest that they’d support their party’s nominee even if he wasn’t one of the two frontrunners in the polls? And if that’s the case, how do you account for your bullet voting argument, which says precisely the opposite — that Burlington voters would primarily be tactical?

      I’m talking about IRV in practice, and you’re talking about IRV in theory.

      Here is the practical, inescapable reality of IRV. Your support for a third party candidate can have three basic effects, depending on the strength of the third-party candidate:

      1) Weak third-party candidate
      The third-party candidate is eliminated, and then your vote goes to your favorite major party candidate. Insincerely supporting your favorite major party candidate neither helped nor hurt you.

      2) Medium-strength third-party candidate
      The third-party candidate defeats your favorite major party candidate, but loses to your least favorite major party candidate. Insincerely supporting your favorite major party candidate in this situation either has a neutral effect, or it helps you (by preventing your true favorite from being a spoiler) — it cannot hurt you.

      3) Strong third-party candidate
      The third party candidate defeats your favorite major party candidate, and then goes on to defeat the other major party candidate as well, winning the election. In this case, insincerely top-ranking your favorite major party candidate either has a neutral effect or it hurts you — it cannot help you.

      Most of the time, a third party or independent candidate will be weak, by definition. But on the rare occasion that this isn’t the case, it is much more probable for scenario 2 to occur than scenario 3. Thus the tactical insincerity is more likely to help a voter than to backfire.

      You can dismiss that as “theoretical”, but it is really quite obvious and empirically verifable. It is easier for a party to move from third to second than from third to first.

      Afterwards, if you have all the rankings, you can try to show what different strategies would have done, but you just don’t see those in real elections — and there have been thousands of them.

      Well, you’re changing the subject. My point is that an IRV voter’s best strategy is to top-rank his favorite of the major party candidates, even if that’s not his sincere overall favorite. This refutes your claim in Science Magazine that an IRV voter’s best tactic is to vote sincerely.

      Apparently your point here is that this tactic is beneficial in only a handful of IRV elections, since most of them feature weak third party candidates. Well, so what? If I prefer Green over Democrat over Republican, I still might as well rank Democrat in first place, just in case the Green Party candidate does surprisingly well and becomes a medium-strength candidate like in scenario 2, above.

      Leading Australian analyst Antony Green just made this same point in an analysis for their national television station.

      Well, he is mistaken. He says:

      The best strategic vote is to number the candidates in the order you would like to see them elected. If you had perfect knowledge of how everyone else was going to vote, you could try and convince blocks of voters to shift around and engineer a particular outcome. But in electorate of more than 90,000 voters, and without perfect knowledge, such a strategy is not possible. Anyway, you only have one vote, so what are the odds of your one vote deciding the outcome? Simply number the the ballot paper in the order you would like to see candidates elected.

      His assertion that honesty is the best strategy is not supported by any empirical or mathematical evidence. Moreover, his argument about your odds of deciding the outcome demonstrate mathematical incompetence. The same logic says that you shouldn’t vote in countries where it’s not compulsory, since it’s so incredibly unlikely that your vote will make a difference anyway. (Yes, I know that voting is compulsory in Australia, but that makes no difference to this particular point.)

      As for Cary, you are still stuck on semantics. The council voted to use an ordinary runoff instead of IRV. They could have voted to use IRV, but they did not.

      I also reject any assumption that approval voting, range voting or Bucklin voting would have elected Montroll.

      Warren Smith provides a very strong argument that Montroll would have won with Approval Voting. Feel free to critique it if you wish.

      Approval/range/Bucklin work better when you’re more interested in defeating someone than electing someone.

      That is just wrong. If you want to get X elected, you vote only for X. If you want to prevent X from being elected, you vote for everyone except for X.

      The rational strategy would be to do neither of these two things, but to instead try to maximize your expected value. The basic strategy in that case is to vote for your favorite between the two strongest candidates, plus everyone you like more. If you don’t have pre-election polling, you can just vote for every candidate you like better than the average.

  14. brokenladder says:


    Let’s look at FairVote’s cited example of a non-monotonic pair of elections.

    Election 1 | Andrea wins
    39 Andrea > Belinda
    25 Belinda > Cynthia
    26 Cynthia > Andrea
    10 Belinda > Cynthia > Andrea

    Election 2 | Cynthia wins
    39 Andrea > Belinda
    25 Belinda > Cynthia
    26 Cynthia > Andrea
    10 Andrea > Belinda > Cynthia

    The second election is just like the first, except that the 10 voters in the 4th row increased their preference for Andrea from least to most preferred, counter-intuitively causing Cynthia to win instead of Andrea.

    The problem of non-monotonicity is that you have a mathematical certainty that the wrong winner has been picked in at least one of the two scenarios — although you don’t know which one.

    For instance, if Andrea really was is right winner in the first election, then she necessarily must still be the right winner in the second election, since support for her has increased relative to the first election. Yet IRV does not elect her in the second election.

    Conversely, if Cynthia really is the right winner in the second election, then she must also be the right winner in the first election, since her support has increased relative to the second election. Yet IRV does not elect her in the first election.

    When an election suffers from either of these two kinds of non-monotonicity, you can’t be sure whether it was the real election that picked the wrong winner, or its hypothetical opposite. But a 50/50 chance of having the wrong winner is a pretty disconcerting thing.

    The Burlington election was like Election 2, where Bob Kiss was “Cynthia”.

    The “mono-raise” definition of monotonicity, which you cite from Douglas R. Woodall, can be equivalently/oppositely stated as a “mono-lower” as follows:

    A candidate x should not be helped [i.e., change from being a loser to a winner] if x is lowered on some ballots without changing the orders of the other candidates.

    That is, both elections in the non-monotonic pair are non-monotonic. You can’t have one without the other. You seem to be using clever rhetoric to confuse the lay reader.

  15. dlw says:

    You guys are arguing over small fries, like “non-monotonicity”…

    The much more important points in the OP are that IRV, as advocated by FairVote (and Richie),
    (1) doesn’t seem to help end effective two-party rule in the US
    (2) nor does it seem to pave the way for the use of Proportional Representation.
    (3) It also would be much harder to use in less local than municipal elections, due to our inability to summarize vote-tallies at the precinct level.
    (4) Plus, the higher vote-spoilage rates with ranked choice systems might be regressive if less educated voters are more likely to get confused by the ranking systems.

    These are the contentions about IRV3 that are most important. However, they merely point to the need to continue to debate about election reform, rather than crowning AV or SV as the obvious replacement to IRV3.

    What if a limited form of AV was used in an open primary where all primary voters would have to approve of two or three of the candidates? Might that not redress the practical problem of more strategic voters wielding an undue influence in AV elections???

  16. brokenladder says:

    IRV’s non-monotonicity may be small potatoes, but FairVote’s repeated false statements about it (and lots of other voting issues) are a big deal, to me.

    I do not see how your forcing voters to vote for some minimum number of candidates makes the situation better. It could very likely make it worse. For instance, I have to vote for 2 candidates and there are 3. I prefer the Democrat over the Republican over “Hitler”. But the evidence says Hitler has no chance of winning, so to help the Democrat defeat the Republican, I give my second vote to Hitler.

    But then it turns out that LOTS of Democrats AND Republicans did this, and Hitler wins.


  17. Sean says:

    I have a question about approval voting…

    What if you have 3 candidates, Fringer, Lefty and Righty – and 100 voters.

    70 voters love Fringer, but hate Righty and would accept Lefty. In a normal election they might vote Lefty just to be safe because Fringer doesn’t have a perceived chance. In AV they would vote for Fringer and Lefty (Lefty being their backup).

    10 voters like Lefty best and would vote that way in either election style because there is no perceived tactical danger in doing so..

    20 voters like Righty but hate Fringer to the point that they would even accept Lefty since Lefty is basically a watered down Righty. In a normal election they would vote Righty but under AV, they vote Righty AND Lefty because they understand that the new AV voting method could actually give Fringer a chance in this riding.

    70% of voters prefer Fringer in this case, but 90% put lefty as a backup and 10% actually like Lefty, so Lefty was on every ballot.

    Does the way AV is enumerated result in a Lefty win?

    And even if all of Righty’s supporters have enough faith to only back Righty, Lefty is still on 80 ballots and Fringer only on 70.

    Does AV result in a win by the candidate who was first choice of the majority, or does it toss the win to whomever is “least offensive” to the majority?

  18. Sean,

    For the sake of a fair comparison, let’s start by estimating how this election would turn out under some alternative voting methods.

    With Plurality voting, that 70% bloc of Fringer supporters would virtually all cast a strategic vote for Lefty. That is also the best general strategy with IRV — that is, to insincerely rank Lefty in first place. And voters empirically do tend to exaggerate like that when using ranked ballots. So Lefty wins under pretty much any ranked voting method, as well as our status quo.

    But the real problem here is that you’re focusing on a single hypothetical election, whose real-world probability/frequency we do not know. (The favorite candidate of 70% of the voters doesn’t register as viable in the polls?) We do not even know the voters’ actual utilities, so we don’t by how much worse off the average voter was by having Lefty instead of Fringer. Election theory has been severely hampered by this kind of analysis, which degrades into a competition over who can create the worst worst-case scenario for a rival voting method.

    The solution is to instead use Bayesian regret calculations. Instead of looking at purposely constructed election scenarios, of unknown real-world frequency and severity, Bayesian regret calculations rely on the aggregate performance of millions of hypothetical election scenarios, chosen randomly from a realistic distribution model.

    Although, if you really want to talk about counter-intuitive election outcomes, I would encourage you to look at a few of these links. I think you’ll find that alternatives to Score and Approval Voting fare far worse.

  19. Both score voting and its simplified version, approval voting, get my approval vote. I would rank either system about equal as well. Keep in mind, however, that for any change to the current voting system to take place and to be effective, a couple of other changes are necessary. These changes are completely orthogonal to the type of voting and are in no way contradictory to approval or score voting.

    We desperately need, in addition to a change in our type of voting, verified voting to prevent scamming whatever system is in place with such extreme cases of obvious fraud as the Volusia Error.

    Further, we must also ensure that politicians are not beholden to anyone other than the voters. This will require public finance of all elections. Candidates must not even be allowed to spend their own money on a campaign. Any candidate who gets the required number of signatures would then get a predetermined amount of money with which to run the campaign. Spend too quickly and run out? Sorry. Perhaps this might even have the side effect of supporting candidates who are good at managing limited funds. Imagine that.

    Lastly, I do not want to support additional parties. The correct number of parties in my mind is zero. We should vote for candidates, not parties. This may be a relatively minor point compared with the others. Perhaps I feel this way because my own preferred party has been actively killed by the party I now find myself voting for, but seriously. If the repugnicans have shown us anything, it’s that a block of candidates all coerced into toeing the line and voting a particular way is not a democratic system.

    • brokenladder says:


      I agree with you that fraud reduction is important. The general view we hold at The Center for Election Science is that an upgrade to Score or Approval Voting has about 50% more benefit than the elimination of fraud. That’s a ballpark figure, but here’s some justification.

      So I want to tackle both issues, but I see the voting upgrade as being a higher priority. It’s important to note that the inherent properties of Score and Approval Voting make them more fraud-resistant, compared to alternatives like IRV. Precinct-summability is one major factor there.

      Warren Smith actually partnered with Ron Rivest (the “R” in RSA encryption) on a fraud-resistant “verifiable” voting scheme called “3Ballot” which you might find interesting.

      As for the effect of money on elections, I’m not sure about the efficacy of public financing. We believe that an upgrade to Score/Approval Voting actually would have a greater anti-cash-importance effect than the adoption of public financing. Of course, these are not mutually exclusive reforms. My fear with public financing is, as described in that link, that it will cripple the candidates’ ability to compete with reality TV and numerous other things vying for the attention of the electorate.

      Lastly, a point about parties. I do not so much think that parties are all that harmful. I think two-party domination is a symptom of having a harmful voting method. The idea is to have a voting method in which party affiliation does not carry much of an effect, and primarily matters from an organizational standpoint. I think that Score Voting and Approval Voting do that, because they satisfy the Favorite Betrayal Criterion. Even if your favorite candidate is not one of the “major parties”, you can fearlessly support that candidate.

      Regarding multi-winner (proportional) voting methods, there are some which are inherently tied to party. The party list system is one, of course. With Reweighted Range Voting and Asset Voting, voters vote for candidates, not parties. They also support the FBC. The STV method also is based on candidate rankings, without regard to party; but because it fails the FBC, party affiliation definitely makes a difference, insofar as it’s a sign of “electability”.

      • brokenladder,

        You may be right about the relative merits of score or approval voting over verified voting. However, the -16000 vote problem in Volusia leaves me unconvinced.

        As for money in politics, we’ll definitely have to agree to disagree. First, who said that public funding would start with a much lower number than candidates have been spending? If, for each position, we start the public finance of the campaign at the 10 year median amount spent for each position adjusted for today’s dollars, the money would effectively be the same as it is today.

        But, more importantly, if a candidate must raise money to have any hope of being elected, that candidate will have to get the money from somewhere, whether it be the pharmaceutical companies, the fossil fuel companies, Wall St., or some other major source of funding, the candidate is then beholden to whoever funded the campaign.

        Two very serious examples of this are the financial sector and the fossil fuels industry. In the case of the former, you may or may not be familiar with the Graham-Leach-Bliley Act. This was signed into law under Clinton with huge bipartisan support, overturning decades of success with the Glass-Steagal act that prevented banks and casinos brokerage houses from merging. There were also many other cases of deregulation of the financial industry leading up to the global financial collapse caused by the subprime mortgage crisis. This was a direct result of Wall St. backed politicians from both parties. This would not have been prevented by a better voting system alone.

        Similarly, recent science states rather clearly that the Permian/Triassic extinction, the worst in the planet’s history, was caused by global warming of about 5C warmer than today’s temps and 6C warmer than pre-industrial temps. This is well within the range of most estimates for “business as usual” scenarios where we take no action to prevent global warming and remain on the path we’re still clinging to.

        So, what action are our politicians taking? Mostly none. Obama’s campaign was largely paid by Ole King Coal. W and Cheney were both themselves oilmen. So, we (and the rest of the world) are continuing to do less than nothing. Not only are our emissions not declining, they are still increasing year over year.

        How can we po$$ibly change our political $tance on any i$$ue$ if politician$ are $till relying on corporate dollar$ to have any hope of getting elected?

        Further, even if a politician were actually not beholden to those who gave him/her money during the election, how can s/he ever do his/her job while always looking for the money for reelection? It totally shifts their focus away from what people believe their jobs to be, i.e. legislating, and toward raising campaign money as a full time job.

        So, IMHO, regardless of the voting system, we will remain in a country with a government of the corporation, by the corporation, and for the corporation for as long as we choose to have corporate funded elections. And, with the last supreme court ruling, that will be a long time indeed. The only way out now is to legislate for publicly funded elections.

        • brokenladder says:

          Volusia County is a great example. It appears that significant fraud there played a role in causing Bush to win instead of Gore. But so too did the presence of third party “spoilers” like Ralph Nader. If that election had used Approval Voting, then it appears Gore would have won even with no change whatsoever in the amount of fraud. The argument we make at the page I previously linked to, is that the frequency times severity of wrong-way elections as a result of fraud is smaller than as a result of having a bad voting method. I agree that fraud is a gravely important issue, and we have to work to address both problems.

          As for public funding of elections, remember that the Supreme Court recently ended corporate campaign spending limits (in the name of “free speech”). So all you’re really doing then is adding an equal amount of money on top of what the candidates already had. If candidate X started out with 5 million dollars more to spend than candidate Y, he still does.

          This was a direct result of Wall St. backed politicians from both parties. This would not have been prevented by a better voting system alone.

          I believe Score Voting would have had an enormous mitigating effect on this problem, as my link explained. A major reason cash currently matters so much in elections is that you have to not only prove to voters that you should win, but that you can win. Maybe raising a million dollars is enough to convince a majority of voters that you should win, but if your opponents all have 5 million dollars, you are likely going to be written off as unelectable, and then many of those voters who support you cast a strategic vote for their favorite of the “frontrunners”.

          With any voting method which satisfies the Favorite Betrayal Criterion, voters can safely support their sincere favorite, even if he seems “unelectable”, due to a lack of money or whatever else.

          How can we po$$ibly change our political $tance on any i$$ue$ if politician$ are $till relying on corporate dollar$ to have any hope of getting elected?

          Exactly my point. All your points about money are true. But I think they point to the solution of upgrading the voting method, more so than to public funding of elections. Although I have no explicit resistance to public funding.

          I think your concerns, particularly on climate change, are very much the right ones.

          • brokenladder,

            A significant point you missed about my post is that I am NOT suggesting public financing ON TOP of existing campaign bribery. I am suggesting that the public funds are to be THE ONLY FUNDS used in any campaign. My suggestion would be to not even allow candidates to spend their own money on their campaigns.

            In this way, I would also be overturning the supreme court’s misruling by making it completely irrelevant.

            I do not agree that score voting will reduce the problems inherent in any system that allows and encourages corporations to buy candidates. Those with the highest campaign contributions will still get the word out far better than those who are not corporate whores. There’s just no way around that. A significant percentage of the population is voting almost purely based on either party or name recognition, especially in non-presidential elections. This will not change.

            As for the supreme court ruling, I see no other way around it. It is a truly unconscionable ruling on the part of the SCOTUS. Corporations have no rights. They are neither human nor animal nor sentient. A corporation is a tool created by humans for human purposes, in this case limitation of personal liability.

            Just as a hammer has no rights, so too does a corporation have no rights. For some reason the court has chosen to endow a hammer with rights. These rights are at odds with and in direct competition with the real rights of real live human beings. I cannot imagine what this group was thinking when they did this.

            • brokenladder says:

              Misanthropic Scott,

              There is overwhelming evidence that Score Voting would significantly decrease the effect of cash in elections.

              Money helps candidates win in two primary ways. First, it helps them “get the word out”, as you note. Second, it helps some of them prove that they are front-runners (i.e. “electable”).

              The amount of money needed to garner name recognition and support (i.e. “get the word out”) is smaller than the amount needed to prove electability. So, say that the amount of money needed to effectively saturate the electorate with your message is 1 million dollars. And say there are 8 candidates for some office. The first two raise 100,000. The next four raise 1 million. The last two raise 5 million.

              No matter how great they may have been, the first two are eliminated because not enough voters know how great they are.

              Of the other six candidates, the two with 5 million are nearly guaranteed to be seen as the “frontrunners”. People assume that because they have all that money, one of them will be the victor, and so there’s no point wasting their vote on anyone else. So the vast majority of them strategically vote for one of those two candidates. And then one of those two candidates wins — even if the electorate universally thought them to be the two worst candidates.

              A great example of this kind of thinking is the fact that 90% of voters who claimed to prefer Nader claimed to have voted for someone else, primarily because they didn’t think Nader had a chance. He had enough money to get the word out to that 90%, and convince them he was the best candidate. But he would have needed vastly more money to convince them he was a frontrunner and thus could win, in order to get their votes.

              With Score Voting or Approval Voting, that wouldn’t happen. Yes, it can’t help with the initial problem of getting the word out. But that eliminates far fewer potential “right winners” than does the strategic favorite betrayal problem.

              So it is seems clear to me, based on numerous real world examples, that Score Voting would indeed vastly decrease the effect of cash on elections.

              Whereas your proposed solution does not seem viable to me. You cannot really police all campaign spending. If some rich candidate’s wealth donors decide to buy a blimp with his name on it, and fly it around, how are you going to stop that? If they pay people to mention that candidate’s name on Twitter, how are you going to police that? It is really infeasible to limit campaign spending. You can mitigate it, but it’s only a very partial solution. And overturning that Supreme Court decision seems politically very difficult.

              Also, candidates who cheat the law will be more likely to get elected, and then just make whatever they did retroactively illegal and/or non-prosecuted.

              Score Voting makes money inherently less consequential, at a game theoretical level. Which to me means it’s a real solution.

              • We’ll have to agree to disagree on this point. Money speaks very very loudly regardless of the voting system.

                Personally, I would not have voted for Nader regardless. He did get the word out. His word was stupid. He claimed there was no difference between Gore and Bush. Therefore, he is an idiot.

                As for your take on score voting, I think you have become way too single minded. There is no one silver bullet to fix our government. You believe you have found one. I believe you have hit on something that would be a big help, but not a cure-all.


  20. brokenladder says:

    Misanthropic Scott,

    Regardless of what you think of Nader, there were millions of voters who preferred him. He “got the word out” to those voters, by definition. We can’t “agree to disagree” about that. It’s an empirical fact.

    But of those voters, only about 10% actually voted for him. But nine times that amount would have voted for him if he had convinced them that he could win, e.g. by coming in first or second in fundraising.

    You make a vague, unquantifiable assertion that “money speaks very loudly regardless of the voting system.” I’m not discounting that point. But here is a ridiculously simple thought experiment which demonstrates that it does not refute my point.

    Say that E = “amount of money required to saturate the electorate with knowledge of a candidate’s views, personality, etc.”

    Say that fundraising numbers for 3 candidates are:
    X = E
    Y = 10E
    Z = 11E

    Now say the true preferences of the voters are as follows:

    % of voters — their ranking
    51% X>Y>Z
    49% X>Z>Y

    X is the universally agreed “best candidate”, and has the money required to convince 100% of voters of that. But Y and Z have the money to convince most voters they are the “frontrunners”, and so if voters are strategic, the results are Y=51%, Z=49%. That is, even though voters unanimously prefer X, they see that Y and Z blow X out of the water on fundraising, and thus they assume X cannot win, and so they vote for their favorite “electable” candidate, between Y and Z. Even if the typical 10% of voters (or more) are sincere, X still gets a negligible fraction of the vote, and Y or Z wins.

    But say the voters use Score Voting, or just Approval Voting for simplicity’s sake. Then, even if 100% of the voters are strategic, you get:


    Now all that extra money couldn’t buy Y or Z the election.

    As for your take on score voting, I think you have become way too single minded. There is no one silver bullet to fix our government.

    You’re putting words in my mouth. I never said anything remotely like that. In fact I linked to a page which describes our take on the relative importance of various democratic reforms. My point is simply that Score Voting is the most beneficial single reform, especially when weighed against the cost of implementing it. Compared to lots of other reforms, it is actually extremely feasible. In fact it would be much cheaper and simpler than the “ranked choice voting” currently in use in San Francisco, for instance.

  21. Oaklander says:

    In the elections last November in Oakland, San Leandro, and Berkeley, California, the IRV method was used for the first time. I served as a precinct IRV specialist to answer any questions and deal with any problems related to the “new” method of voting. We had only one person who truly did not understand how to cast her vote, and there was one other question about how the votes were to be tabulated. The only ballot problems we had were a couple of over-votes for non-IRV offices, which the machine caught and the voters recast their ballots. All in all, it went very smoothly.

    However, after wading through this very comprehensive but interesting discussion, here is my vote on the the different methods:

    Score Voting: 99 (assuming that 99 is the maximum score)
    Approval Voting: 70
    Instant Runoff Voting: 50
    Top-Two Voting: 10
    Plurality Voting: 0

    • brokenladder says:


      Thanks for reading the (rather lengthy) piece, and providing a very polite response.

      What do you think explains the difference in spoiled ballots between there and San Francisco, where there are typically 7 times as many spoiled ballots?

      Another issue is that, even people who understand how to rank the ballot properly don’t actually understand how that affects the race, due to not understanding the tabulation algorithm of IRV. I included a kind of humorous instant message conversation about this, with a fellow software engineer at my day job, in this response to a recent LWV response to the San Leandro election.

      Interesting fact: The current Secretary of State of Colorado is tepidly supportive of Score Voting and Approval Voting, so hopefully this will be at least given a trial in the next few years.

      Thanks again for your feedback.

  22. Pingback: The Two-Party System « The Impasse of Americanism

  23. Blanca says:

    This is a good tip especially to those new to the blogosphere.
    Simppe but very precise info… Many thanks for sharing
    this one. A must read article!

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