Another messed-up New Scientist piece on voting

By Warren D. Smith 2008 & incorporating suggestions from others too, especially Chris Benham.

The New Scientist on 12 April 2008 pages 30-33 ran Vote of no confidence; No voting system is perfect, but why do we put up with one of the worst, asks Phil McKenna.

This piece unfortunately was rife with errors and the net effect was quite a mess. (I'd offered to McKenna to proofread his piece while pointing out the numerous errors in New Scientist's previous voting article, but he declined the offer...) We go through them now. Our purpose is not solely to correct/detect the errors in the article, but also to discuss claims and views made by people quoted in the article. Indeed, some of the errors are not really McKenna's fault, but rather due to him too-naively falling for propaganda. (I'd tried to warn him that might happen...)

In 1950, economist Kenneth Arrow, then a PhD student at Columbia University in New York, seemed to prove once and for all that it was impossible to have a method of voting that was entirely fair (Journal of Political Economy , vol 58, p 328).

[McKenna states a different version of Arrow's theorem than is usually stated, which appears to be based on Maskin's lecture.]

But could Arrow have overlooked better options? Warren Smith, a former mathematics professor at Temple University in Philidelphia, and co-founder of, claims to have circumvented Arrow's theorem with a controversial voting system called range voting, which the theorem doesn't cover.

That was a bit misleading because it makes it sound like Smith invented range voting (I did not) or that I am the first to make this "claim" (I am not – in fact we have traced the claim back to a paper published by also-Nobel-prize-winning economist John C. Harsanyi in the 1950s).

According to Smith, range voting consistently yields the most satisfying result for the greatest number of voters.

That was roughly true, but is stated imprecisely by McKenna.

Chances are you are already familiar with range voting. It is used to rate videos on YouTube, or score entrants on Hot or Not, where users subject photos of themselves to public scrutiny. In an election, each voter would score candidates on a scale of 0 to 9, say, or mark them with an X for "no opinion". Unlike plurality voting, where you have only one vote, range voting allows you to express a view about as many candidates as you like. And if you feel equally about two or more candidates, you can give them the same score. When all votes are cast, the candidate with the highest mean score wins. A variant of the system was used in Venice in the Middle Ages to elect the city's leaders. Over the years it fell into obscurity, but in 2000 Smith renamed it and began promoting it again as a fairer alternative to plurality voting.
Range voting satisfies each of Arrow's five requirements, something no other voting system has been able to accomplish. "It's better than plurality in every way except possibly simplicity," Smith says. "It allows voters to express more preference about the candidates, eliminates the problem of vote splitting, and tends to elect winners that are more representative of the majority will."
Smith bases these claims on a series of computer simulations in which he tested 31 voting systems to determine which yielded the least disagreeable result for the greatest number of voters. To gauge this he measured "Bayesian regret", a parameter that attempts to quantify how unhappy groups of people are following a poor outcome. The better the voting system, the less Bayesian regret it causes. He claims the improvement in expected human happiness when switching from plurality to range voting would be about the same as the impact of introducing democracy in a dictatorship.
Smith isn't the first to use Bayesian regret to compare voting systems, but in previous models no one system consistently came out on top. Smith says this is because they didn't include range voting, but his study is controversial because it has not been accepted for publication in a peer-reviewed journal. Smith claims this is because reviewers have an irrational aversion to range voting.

Huh?? Sorry, I do not recall making a claim that "reviewers have an irrational aversion to range voting." Perhaps Hillinger made such a claim. He has a theory of that ilk. Perhaps such a claim is true. All I know is, I did not make that claim.

About the "peer reviewed" business, since you insist, a discussion follows in fine print. I submitted my 1999-2000 paper to SC&W. It was rejected. The referee report rejecting it (I do not have access to my copy right now so I am going on memory) was about 1 paragraph long. It said it was "unprofessional" and such adjectives, and also claimed others were in the process of having similar thoughts to me, hence by rejecting my paper no great harm would be done since those others would soon fill in the gap. It did not, however, point out any specific theorem, proof, technique, or quote that it disagreed with, nor did it point out any specific instance of "unprofessionalism," nor did it explain who those "others" were and what they were doing, nor did studies by others come out since 2000 that do this stuff.

Perhaps my theorems or proofs were wrong, or perhaps I was unprofessional (you can read the paper and judge for yourself) – but I know the review did not point out any specific example. In fact, the only specific suggestion the review made was that I should have cited work of R.Myerson (it did not say what work). So I then contacted Myerson, and he told me the paper by him the reviewer probably had in mind did not yet exist and was not yet written (making it somewhat difficult to cite), but he [Myerson] would be happy to explain it to me if I paid him about $1000, flew to Oregon, and took a summer course from him. (I'm serious. I couldn't make this stuff up.)

So. What was I to do?

  1. I asked SC&W for clarification. What was "unprofessional" exactly? But no clarification ever came.
  2. I could argue with the referee, saying my work really was good. Trouble with that was, the referee, as I said, gave no specifics. So there was nothing specific for me to argue about.
  3. I could guess about what was "unprofessional" etc and try to redo the paper in light of that guess, but it would be only a guess. I would then perhaps get back a new referee report saying the new paper also was unprofessional, again without explaining how or why (?) and then we could continue iterating, each time with me getting 1 bit of information, and each iteration taking about 1 year. A low-bandwidth process.

I decided not to go with routes 2 and 3. I instead just placed it on the world wide web.

Now what has happened over the years as a result of readers on the web corresponding, etc, is a quality and quantity of feedback which exceeded that referee report by a factor of around 100 to 1000. So, in light of that, I do not think "peer reviewing" actually accomplished much or should be accorded much respect. Also, Bill Poundstone based a fair fraction of his book on my "unprofessional" paper – apparently he somehow did not notice its unprofessionality. It's apparently difficult to notice. I guess Poundstone was not professional enough. (Except wait, he is a professional.)

Others say his methods are unclear. "One would have to study the computer program to know whether the comparison is valid," says Eric Maskin at the Institute for Advanced Study in Princeton, New Jersey,...

My computer programs are publicly downloadable. They have been examined and used and modified by several people I know of. As has their raw output (also publicly downloadable). Now because my work is based on a computer program, which is publicly downloadable, that is a greater amount of precision and clarity about exactly what it is that I did, than is obtainable in almost all published scientific articles. Note, computer programs specify exactly what is done in full detail. Nothing missing. Nothing unclear. So the claim that my methods are "unclear" is exactly wrong. In fact, e.g, they are "more clear" or at least "more precise" than all or almost all articles Maskin ever wrote.

Also, even without examining my computer programs, since what they do is mathematically defined (and stated in my paper) Maskin also could independently write his own computer program to perform the same computation and thus verify or deny the same result. That (to some approximation) has also happened (although it was not Maskin writing the new program).

There have been other Bayesian Regret studies by others (which by the way were published in peer-reviewed journals and/or as books) but none of them made their computer programs public.

...who won the 2007 Nobel prize in economics for work he did on the rules that govern voting systems.

Wrong: Maskin did not "win the 2007 Nobel prize in economics for work he did on the rules that govern voting systems." Maskin in fact knows quite little about voting systems and has done little work on them.

The Nobel prize committee said Maskin got his third of the 2007 Nobel "for having laid the foundations of mechanism design theory." The Nobel committee continues to say "[mechanism design theory] has helped economists identify efficient trading mechanisms, regulation schemes and voting procedures" which is the only mention they make of the word "voting." Now that part may sound nice at first – and I presume was what misled McKenna – but if you look in books about voting procedures, you will see few if any references to either Eric Maskin or mechanism design theory. Maskin for example is not cited in Brams' 2008 book Mathematics and Democracy nor in Nurmi's voting methods book. I actually do not know of any way in which Maskin's work has managed to have a significant impact on voting theory, and indeed I have criticized what little there was of it (see also more criticism) which Maskin work, by the way, also has not appeared in a peer-reviewed journal as of 2008. I found it rather annoying that McKenna dwelled on my BR paper not appearing in a peer-reviewed journal, while neglecting to mention that, as of early 2008, zero papers by Maskin with the word "voting" or "vote" in their title have ever appeared in any peer-reviewed scientific journal, and indeed only two such articles by Maskin have appeared, both in magazines which seem not to count as scientific journals, namely Scientific American and The National Tax Journal. By mentioning this about me but not Maskin, and mentioning Maskin's Nobel and falsely claiming it concerned voting, the net effect was to make Maskin appear to be a great expert and me a novice. In fact, on this topic, I believe I know more than Maskin, I own a greater publication record (small though it may be) than Maskin, and I certainly have made more and larger contributions than Maskin to the field. All of the voting systems discussed in this article, including the one Maskin recommends, were invented when Maskin was a child (or before), and by others. Therefore Maskin's work did not influence their "design," although the reverse direction of influence might have happened.

Critics also point out that the system requires voters to assign values to candidates, something Arrow ruled out on the grounds that the values assigned have no real meaning.

What does "real meaning" mean? Arrow and the New Scientist do not here say.

Claude Hillinger, an economist at Ludwig Maximilian University in Munich, Germany, who has devised a similar value-based method that he calls evaluative voting, says Arrow's exclusion is groundless. "Systems that give a range of values have more meaning than ranking systems because you have the freedom to assign any number to any candidate that you wish."

The use of the word "more" by Hillinger seems justified.

More than half a century after publishing his landmark theorem, Arrow, now 86 and professor emeritus at Stanford University, maintains that voting systems based on scores rather than rankings don't measure up. "I don't think [range voting] is a true voting system," he says. Before publishing his theorem, Arrow and his colleagues considered value-based systems but dismissed them. "We felt there was no meaning to compare values between people," says Arrow. Maskin, a former student of Arrow's, agrees. "If I say that I prefer Clinton to Obama, the statement has meaning - I would put Clinton in office rather than Obama. But what does it mean to assign Clinton 7 points and Obama 4?"

The "meaning" of a range vote is entirely determined by its effect on the election-winner, which in turn is determined by the rules of the voting system. This is definable with mathematical precision. It is as well defined and as valid as the real numbers.

If you give Clinton 7, Obama 4, that has the same Clinton vs Obama election-altering effect (with sum-based range voting) as two voters each giving difference=1.5, or three each with difference=1. An example "statement" this voter is making, then, is "I would like my vote to have the same Obama vs Clinton election-altering effect, as three Clinton=3, Obama=2 voters." Does that statement have meaning? Yes, I think so.

In short: If Maskin disputes range votes have meaning, he must also dispute that "1+1=2" has meaning.

I presume Maskin does not dispute that 1+1=2 has meaning. Therefore, his real objection is not that range votes lack meaning – they have mathematically precise meaning – Maskin's real objection is they don't "feel good" to his (limited) mind, in a non-mathematical, but rather more psychological or fuzzy, sense.

Should we care whether Maskin's mind feels good in a fuzzy sense? Well, far outweighing that in importance is the Bayesian Regret a voting system causes society. Maskin could take a Valium and feel good in a fuzzy sense, curing his personal problem. But if we adopt a voting system with larger Bayesian Regret, that causes quantifiable, objectively mathematically defined, damage to society which will certainly be in the millions-of-deaths ballpark. So, which matters more – millions of deaths, or Maskin's mind feeling good in a fuzzy sense?

Arrow's quote is slightly more defensible than Maskin's. There actually has been this religious notion in some economist circles, that utility is not interpersonally comparable, and utilities are trapped inside people's minds and not externally measurable. I do not agree with that religion. But whether you agree or not with it does not matter for two reasons:

  1. We are not comparing utilities. We are comparing range votes. Those are both measurable and mathematically well defined.
  2. My "Bayesian Regret" methodology, although based on utilities, never needs to measure any utility for any human.

To make an analogy, any critic of Bayesian Regret methodology who criticizes it based on the belief that utilities are unmeasurable, is making the same error as a critic who says the statement "If Mary likes apples and bananas, then Mary likes some fruit" is meaningless because whether Mary "likes" something is unmeasurable or non-meaningful. The truth: It does not matter whether Mary liking something is measurable. That sentence is still 100% valid.

One final point. Suppose you (a voter) are asked to choose between these three choices:

  1. You get one dollar.
  2. You get one dollar, and are tortured to death.
  3. You're tortured to death and do not get any money.

Do you feel it is "meaningless" for you to express a large preference for A over B, as opposed to a small preference for B over C? (Only the bare fact you prefer A>B>C is meaningful and intensity is not?)

I do not believe you feel that way. Also, I do not believe Maskin feels that way either. If Maskin really had acted in the way that stance would imply throughout his life, not only would he not have won a Nobel prize, he probably would have been confined to a mental institution.

Not only are the numbers meaningless, Maskin says, but such attempts to quantify preference give voters a strong incentive to exaggerate. "Say I slightly prefer Clinton over Obama, but I am concerned that Obama is surging ahead, I have every incentive to overstate my liking of Clinton and my dislike of Obama," Maskin says.

True... But read the article's next sentence:

No system is entirely safe from such manipulation,

And to be more precise, this sentence refers to the Gibbard-Satterthwaite theorem. Gibbard identified two probabilistic voting systems which are strategyproof, therefore the quoted sentence is false. But it effectively is true since Gibbard's two systems "leave too much to chance" (in his words) to be acceptable in most uses. Range voting satisfies weakened forms of G&S's "impossible" strategyproofness conditions:

  1. In 3-or-fewer-candidate elections (and even with imperfect info), it is always strategic to submit a vote which does not misorder ("misordering" means saying X>Y when you honestly feel Y≥X).
  2. if N-candidate elections with perfect information, it is never strategically-forced to misorder.
  3. It is never strategically forced to score your true-favorite below top.

Properties A, B, and C are enjoyed by range voting. But by the G&S theorem, every deterministic rank-order voting system (obeying unanimity) fails to obey A and fails to obey B. (There are rank-order-based systems that obey C, but they are rare. IRV and all Condorcet systems fail C.)

So we conclude from this that range voting actually comes closer to being strategyproof than any rank-order voting system – including Maskin's and including IRV. That fact is contrary to the claim Range Voting is "ripe for manipulation," and had the article actually investigated the basis for that sentence, then it would have recognized that.

but Maskin says range voting is particularly prone to strategic voting because voters can safely inflate and deflate scores without compromising their support for their preferred candidate.

What does "safely" and "compromising their support" mean? I do not know. Perhaps Maskin knows, but it is not explained.

When and if this is explained, then we could try to analyse the claim.

Political campaigner turned voting reform advocate Rob Richie is also dismissive of range voting. "I think what Smith and the other range voting supporters haven't grasped is campaign psychology," says Richie, who is executive director of voting reform advocacy group FairVote. "It's one thing to use range voting on Hot or Not or for other internet voting when you don't have a big stake in the outcome. But when you really care who wins, you are really trying to help your side."

Range voting has been tried in poll studies which you might naively say "do not matter" but in which, actually, the voter has comparable incentive to lie as in a "real" election that "matters." (If you work out the numbers quantifying their incentives.) [And, by the way, there has been a large amount of clear evidence people lie to pollsters.] So far, every such study has found, apparently, less voter strategy with range voting than with plurality and IRV voting. This is true also in studies in which the voters are instructed to vote "as they would if this poll were the real election."

So to thus-dispute the latter kind of study, you'd have to postulate that its voters strategically decided to lie in their vote about their strategies by strategically not being strategic(!) and you'd have to postulate that the reason they did that was because they cared enough to so-lie, even though the argument was supposedly that these voters did not care, because it was a poll.

(My mind somewhat boggles that anybody could be assuming all that... but the fact is, the studies so far of real voters unanimously disagree with this worry, finding that, whether rationally or not, real human range voters act comparatively unstrategically. This experimental-psychological fact is not to be sneered at, especially by those such as Richie, Arrow, and Maskin who to my knowledge have never run such a study.)

Range voting has also been tried for hundreds of years in very real very consequential elections in Venice and Sparta – but I find it hard to draw a clear conclusion on this precise question from that. Assuming we had all the Venice data for example (I do not, but it might be obtainable so suppose we had it) then how exactly would we deduce from that data how strategic the voters were and how much that mattered? Not so clear! Indeed these concepts are not even defined, as yet.

Range voting has also been used to e.g. pick Olympic medalists and best-movie awards. Some of those votes are publicly available and do "really matter." Again, in the cases where the votes were made public, there was plainly little strategic distortion. I.e. name one Olympic judge ever, who range-voted in strategic style "all 10s and 0s only." Never existed. Almost always the Olympic judges provide similar honest-looking scores.

Mind you, probably Olympic judging has involved strategic voting. But very little, as a percentage.

In other words, the big problem Richie foresees is that candidates would have a strong incentive to persuade their supporters to vote strategically. "Strategic voters will beat non-strategic voters, and when that occurs there is a real problem with our democracy," Richie says.

But (a) neither Richie nor Maskin advocate a voting system which avoids that problem; (b) it does not actually matter per se if "strategic voters beat nonstrategic voters," what matters is the Bayesian Regret that causes; which leads us into the theme that (c) missing from this whole assessment (as usual) is anything quantitative saying how often this occurs and how serious its effects are in which voting systems. All they give is an anecdote or intuition, not a measurement. When you actually do the measurements, you find out – both from polls and simulations – that this effect is a lot less serious than it might naively seem. I'll return to this theme at the end of this page.

Incidentally, the Richie/Maskin view is supported by the fact that with range voting, strategic exaggeration is useful even in the "zero-info" case when the voter has zero knowledge about what the other voters are doing and thus assumes all their range voting scores are independent uniform random numbers. Meanwhile, with IRV and Condorcet it is a plausible conjecture (although nobody has ever proven it) that best strategy for voters with zero info is to vote honestly. However: the zero-info model usually is unrealistic because usually anybody with enough knowledge about the candidates to be voting at all, automatically also has knowledge about how others feel about them. In particular just the sole knowledge that candidate X is "a Republican" or with "the Socialist Party" in the USA immediately tells you a great deal about his or her likely election chances.

Smith says these effects would cancel out between the different candidates because a similar share of each candidate's constituency would vote strategically.

That is one reason. There also are simulations indicating that random strategic imbalances, while they do hurt range voting's BR, do not hurt it enough compared to how much it hurts the BR of other systems... so that range voting still comes out with better BR.

If the one voting system that apparently satisfies Arrow's criteria for single-winner elections is destined to be confounded by political manoevrings, what's the alternative? Many electoral reformers argue that instead of getting hung up on devising a perfect voting system, we should adopt the system that works most of the time. So which among the dozens of alternatives would that be?
For Maskin, the answer is the Condorcet method, named after 18th- century French mathematician the Marquis de Condorcet.

Sorry, there is no such thing as "the Condorcet method." There are an infinite number of different Condorcet methods. And I assure you that the particular method McKenna/Maskin now state, was never stated by Condorcet.

Voters rank each candidate in order of preference. They can give two or more candidates the same rank, or not rank a candidate at all.

So as a result, the vote is quite range-like in format. In an N-candidate election, Maskin here now wants the votes to be the same as votes got by range voting on an N-point-scale (but the votes, once obtained, are used in a different way). Incidentally, I have seen previous writings by Maskin on voting, but this is the first time I have seen him advocate this sort of ballot, and the first time, indeed, I have seen him advocate allowing rank-equalities. Both of those probably are good developments.

This makes for a rather complex set of possible outcomes that requires computers to calculate the winner in all but the smallest elections. In essence it works like this: for every possible combination of two candidates, the computer scans through all the rankings and counts how many times each candidate is ranked higher than their adversary. The overall winner is the candidate who wins the most of these one-on-one comparisons.

The above is the "Copeland voting system with draws allowed." Maskin has written before about voting, but I never saw him previously come out in favor of the Copeland voting system. One of Copeland's problems is that it often yields tied winners.

Another problem with Copeland (which Borda Voting also is subject to in the same way) is its vulnerability to candidate-cloning. If a faction simply runs a large number of cloned candidates (but where there is a fairly clear quality-ordering among the clones) that can assure it wins the election, regardless of what the voters want.

A theorem by Smith (also proven a bit later in a weaker form by Simmons) states that

  1. Range voting is both cloneproof and favorite-betrayal-proof,
  2. No anonymous neutral rank-order voting system enjoys both those properties.

That is a way range voting is superior to every rank-order system. (Maskin's Condorcet rank-order system fails both clones and favorite-betrayal, while IRV only fails the latter.)

The computer simulations reported here indicate that, e.g, Copeland output 10342 Condorcet Winners in the same set of situations in which Range Voting output 11796 Condorcet Winners.

That is because this test was of precisely the sort of scenario Maskin was worried about – strategic imbalances among the voters (there was a mix of honest and strategic voters) and due to voter dishonesty Copeland could sometimes fail to elect Condorcet winners even though such winners (based on honest votes) exist.

The interesting result was that RANGE VOTING PRODUCES MORE CONDORCET WINNERS than Copeland.

Thus by Maskin's own measure of success, in exactly the sort of situation designed to make Maskin's worries about range voting be highly justified, Range Voting still outperforms Maskin's favorite voting method Copeland.

I would think this fact would have some impact on Maskin.

Also, there is a simple theorem that, under reasonable assumptions about strategic voters, Range Voting will always elect a Condorcet Winner whenever one exists. That is precisely what Maskin wants. It happens precisely when Maskin thinks range voting is in trouble (strategic voters). By theorem.

Again, I would think this fact would have some impact on Maskin.

Crucially, this means that the Condorcet winner in an election need not necessarily be the candidate with the majority of first-choice rankings.

That statement is false. Any candidate with a majority of first choice rankings (over 50%) will always win with any Condorcet method. Probably instead of the word "majority of" McKenna meant "plurality of" or "the most."

Proponents of Condorcet say it is the fairest method because it elects the candidate that the greatest number of people find the least disagreeable.

This last sentence is meaningless and bogus. To the extent it has meaning in a vague way, it is a better description of range than Condorcet.

A sentence which genuinely has precise meaning is "approval voting elects the candidate the greatest number of people approve."

The downside is it [Condorcet] can elect a candidate that no one wanted as their first choice.

I do not see why that is a "downside." Bayesian Regret enables a precise meaning to be ascribed to otherwise meaningless pejoratives like "downside." When you do that, you realize that "electing a candidate that no one wanted as their first choice" can happen with no Bayesian Regret at all. Therefore, when examined precisely, we find this is not necessarily a "downside." Also, in elections where you are allowed to vote for yourself, I find it essentially inconceivable that such a "downside" would ever occur. Name one substantial election ever in which

  1. candidates were allowed to vote for themselves,
  2. X won (or would have with some sensible voting system), and
  3. X received zero votes as first choice.
I doubt one ever existed. Therefore, this so-called downside is both not a downside, and also irrelevant to reality. It is sad that something so unimportant and misleading should be given such importance in the article.

Condorcet has yet to be used in any government elections, but there is another ranking system that has made that grade. Known variously as instant run-off voting (IRV), preferential voting and the alternative vote, it uses the same ranking system as Condorcet, but the count is different.

The statement is false in the sense that no IRV system in use today (to my knowledge) allows arbitrary equalities in rankings – which the article said we were going to have with Condorcet. (If IRV permitted equalities, then various new rules would be needed and various difficulties and additional property-failure-problems would arise...)

First candidates are ranked according to how many first choices they received, as in plurality. If no candidate has an overall majority, the candidate with the least number of first- choice votes is eliminated and their votes are reallocated according to the second choices on the eliminated candidate's ballots.

Then what? Process continues, but article does not say so, thus incorrectly describing IRV's rules.. Or are we now speaking only of 2-round runoff? (Anyway, I can tell you that San Francisco neither used the rules here, nor standard IRV rules, despite assertion by the article that SF used IRV. SF in fact used rules with some similarity to these, but that is all.)

IRV's strength is that it places great value on voters' first preferences. "IRV will never elect a candidate who doesn't have substantial first-choice support," says Richie, whose organisation FairVote promotes the system.

That is a downside for IRV that can lead to substantial Bayesian Regret. (The article unfortunately may have made it sound like an upside. This whole "strength" is just vague propaganda designed to appeal to those with some naive attachment to Plurality Voting.)

Richie points to the method's proven track record in Australia, where it has been used since 1918 to elect the country's House of Representatives.

Its "proven track record" is: it has led to massive 2-party domination in IRV seats.

According to Ben Reilly, director of the Centre for Democratic Institutions at the Australian National University in Canberra, preferential voting was brought in to replace plurality and prevent fringe candidates from spoiling the election.

Australian voting expert Chris Benham provides what he thinks is the actual story, as opposed to the feel-good propaganda pseudo-history: "I understand it was brought in to lessen the chance of Labor candidates winning due to the fact that the anti-Labor 'side' was fielding more than one candidate in each seat."

Another major advantage of IRV is that it allows smaller parties to campaign for election and present their views without the risk of splitting the votes of larger parties. "The smaller parties have a really strong interest in running candidates even where they can't win the election, because they can have a strong influence on policy," Reilly says.

No supporting evidence has been offered here to support that claim. The truth is, third-parties can almost never win an IRV seat. In Australian House right now, zero seats are held by third-party members. Further, third-parties in Australia almost always get tiny vote-fractions for Richie's all-important "first place support." None managed to reach 16% in any 2007 house election, and most were a lot lower. Therefore, if God magically killed every third party candidate in Australia and eliminated them from all ballots, it might well be (from properties of IRV and the fact voting is compulsory in Australia), the exact same winners would have happened in e.g. every House race. Therefore, the existence of third parties seems irrelevant and there is no "really strong interest in running candidates even where they can't win the election, because they can have a strong influence on policy."

I don't see how you can have a strong influence on policy by running somebody who cannot win and who cannot alter the winner either. Do you see how? Because I don't.

At least with plurality voting, third party candidates with tiny vote fractions, by running, can alter the winner, and thus have a strong influence on policy. Only problem is that influence can have the wrong sign, like the way Nader's 2000 run influenced policy (it could have had the right sign if the major candidates had granted policy concessions to Nader to pull out, but they did not do so). So actually, the Reilly quote was exactly wrong – in practice IRV actually diminishes the effect a third party run has on policy.

Australian voting expert Chris Benham provides the following fascinating argument against me: "[this argument by Smith] may be true or nearly true of recent House of Reps. general elections. But there was quite a long period (during the Cold War) when it was generally accepted that a right-wing Catholic ('anti-Communist') split-off from the ALP, the Democratic Labour Party (DLP) kept ALP out of power by directing their preferences (via their 'how-to-vote card' recommendations) away from Labor to the conservative parties. If the DLP hadn't existed, it is thought that enough of their supporters would have voted Labor (on class grounds) for Labor to win enough seats to form government."
Smith ripostes: if Australia had been using plurality voting, then the DLP could have recommended its supporters vote for some other anti-labor party – or just, more straightforwardly, recommended they vote DLP – and the result would have been as Benham described. Therefore, still, I see no way in which IRV improves over plain plurality voting with respect to incentivizing third parties to run candidates to "have a strong influence on policy" in Australia.
Benham counters: (a) Not quite, since the effect of voting for DLP thus denying Labor a vote, is not as powerful as also voting for Labor's competitor. Incidentally at this time for this reason, Labor's policy was to oppose Instant Runoff Voting and return to plain-plurality voting for House elections.
(b) So why do you think the Australian third-parties keep running candidates in IRV races, then?
Smith: Re (a), true. Re (b), I do not know. Because Australia's upper house is elected via PR, Australia's third parties do not die out like in the USA, and hence they have enough resources to run, if they so choose (unlike in the USA, where they usually cannot).

IRV is not without its faults. "It's not quite as vulnerable as plurality," Maskin says, "but it doesn't rule out spoilers or the chance that a candidate without a majority might win."

Correct. (Albeit by "without a majority" I think Maskin probably worried, more precisely, that IRV might fail to elect a "beats-all" Condorcet winner.) And those pathologies have happened many times. In San Francisco, which the article claims uses IRV, every candidate (or almost every?) so far elected with IRV has failed to have a majority in every case in which they would not have won with plain plurality voting, i.e. in which IRV mattered. In Australia's 2007 House elections I found 9 cases where it appears the Condorcet winner existed but was not elected, and these 9 include every case where the IRV and plain-plurality winner differed.

Stranger yet, when things get really close in an instant run-off vote, selecting your favourite candidate could in theory do more harm than good. "If you increase your vote for somebody in IRV it can make them lose," says Smith.

I'd tried to tell McKenna that favorite betrayal was a more-important IRV pathology than non-monotonicity – and also every Condorcet method exhibits favorite-betrayal failures – but McKenna insisted on using only nonmonotonicity in his article, then had Hill supposedly shoot it down:

"The problem I have with these little paradoxes is that they break down in the real world," says Steven Hill, director of the Political Reform Program with the New America Foundation, a political advocacy group that supports IRV – and there is indeed no record of the scenario described above ever having happened in practice.

Hill's statement is false. The Louisiana 1991 election described in Poundstone's book and on this web page is one example. As he well knew. And Hill's organization FairVote got Burlingotn VT to adopt IRV, whereupon its 2009 election featured numerous pathologies including non-monotonicity, whereupon Burlington repealed IRV.

Hill just flat-out lied. Further, many other "little paradoxes" with IRV have occurred, including all the ones Maskin mentioned (see above for some links to examples), even though the article thinks there is "no record" of them, and as we saw above, not only did they occur, but they were very common.

Of all the alternatives to plurality voting, IRV is the only one that has gained a toehold in government elections.

That statement is false. Range voting has been used in Venice and Sparta, for hundreds of years, for example, and Approval Voting in the Soviet Union, and Borda voting in Kiribati.

For example, San Francisco, California, and Takoma Park, Maryland, use it in municipal elections.

And somehow I think the above examples (Venice, Sparta, Soviet Union – in their day world-leading powers) are a little more important than San Francisco, California, and Takoma Park, Maryland, municipal elections.

But change is in the air. After casting a half-century-long shadow of despair over the field of voting theory, even Arrow seems to be softening his stance. "Most systems are not going to work badly all of the time," he admits. "All I proved is that all can work badly at times."

True. Although I don't see how that was a "softening" since Arrow had always said this.

Two closing points

1. A common thread in this article in claims by Hill, Richie, Maskin, Arrow etc is that such and such is "not common," is "rare," or such and such is "important" or "psychologically important" etc. But the trouble is, those people don't provide quantitative evidence about how rare, common, important, or psychologically important something is. They base all those solely on their intuition (or in Hill's case, he simply lies), and intuition is well known to be very misleading in the voting area. As far as I can tell in Arrow's entire career he never tried to quantitatively assess these things (and ditto for Maskin's career) – as Arrow in the above quote is (somewhat) admitting. Now I, unlike those others, have actually found out how important things and common are. I have thus gone beyond mere intuition to enter the realm of actual measurement. There are several ways to measure. First, you can look at the actual historical record. I have the largest available database of national-level elections for this purpose, and based on it, e.g, I estimate that plurality elections yield the "wrong winner" approximately 1 time in 8. (Poundstone's estimate mentioned in the article was 1 time in 9.) Second, you can do polling. (I have collected the largest database database of polls for that purpose.) Third, you can do computer simulations. I have done the largest and most complete available simulations. These simulations can assess how often named-pathologies happen, how often unnamed-and uninvented-pathologies happen, and how serious they are when they happen. All of these quantitative assessments were not made by Maskin, Arrow, Hill and Richie, at any level beyond merely consulting their intuition.

2. The whole "property based" approach to comparing voting systems was sort of started by Ken Arrow, or at least, he's as big a figure as anyone. But unfortunately what I did not see mentioned here is: that approach is largely obsolete. It is not utterly valueless, but since it is nonquantitative (often absurdly so) and based on subjective judgements about the importance of this or that property, it soon runs into a brick wall and stops dead, trapped in a permanent morass of controversy. Which is exactly what happened. Bayesian Regret is the quantitative approach which gets us past that quagmire. That is major progress,and this New Scientist piece completely missed that story and just uselessly regurgitated the usual he said/she said stuff that's been happening for the last 50 years.

I am not the only inventor of Bayesian Regret methodology. Several people invented and used it independently in the voting area, and before that it was well known in other areas. I would like to see a recognition by the likes of Maskin, Arrow, et al, that Bayesian Regret is the right path forward, can escape the otherwise-permanent quagmire, and that my Bayesian Regret measurements and findings are correct. Sadly, so far, I see no so such recognition from either, and indeed see no evidence either even knows what Bayesian Regret is. That is sad not merely because of my bruised ego, but because millions of lives are at stake.

Return to main page