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For 20 years, evidence about global warming has been directly and explicitly linked to a set of policy responses demanding international governance regimes, large-scale social engineering, and the redistribution of wealth. These are the sort of things that most Democrats welcome, and most Republicans hate. No wonder the Republicans are suspicious of the science.

Think about it: The results of climate science, delivered by scientists who are overwhelmingly Democratic, are used over a period of decades to advance a political agenda that happens to align precisely with the ideological preferences of Democrats. Coincidence—or causation?

How would a more politically diverse scientific community improve this situation? First, it could foster greater confidence among Republican politicians about the legitimacy of mainstream science. Second, it would cultivate more informed, creative, and challenging debates about the policy implications of scientific knowledge. This could help keep difficult problems like climate change from getting prematurely straitjacketed by ideology. A more politically diverse scientific community would, overall, support a healthier relationship between science and politics.

American society has long tended toward pragmatism, with a great deal of respect for the value and legitimacy not just of scientific facts, but of scientists themselves.

Yet this exceptional status could well be forfeit in the escalating fervor of national politics, given that most scientists are on one side of the partisan divide. If that public confidence is lost, it would be a huge and perhaps unrecoverable loss for a democratic society.

A democratic society needs Republican scientists.

I have to imagine 50 years ago there were a lot more Republican scientists, when the Democrats were still the party of Southern Baptists. As a rational person I find it impossible to support any candidate who panders to the religious right, and in current politics, that's every National Republican.

As Freedman put it in The Atlantic: “80 percent of non-randomized studies (by far the most common type) turn out to be wrong, as do 25 percent of supposedly gold-standard randomized trials, and as much as 10 percent of the platinum-standard large randomized trials.” Ioannidis himself was quoted uttering some sobering words for the medical community (and the public at large): “Science is a noble endeavor, but it’s also a low-yield endeavor. I’m not sure that more than a very small percentage of medical research is ever likely to lead to major improvements in clinical outcomes and quality of life. We should be very comfortable with that fact.”

Julia and I actually addressed this topic during a Rationally Speaking podcast, featuring as guest our friend Steve Novella, of Skeptics’ Guide to the Universe and Science-Based Medicine fame. But while Steve did quibble with the tone of the Atlantic article, he agreed that Ioannidis’ results are well known and accepted by the medical research community. Steve did point out that it should not be surprising that results get better and better as one moves toward more stringent protocols like large randomized trials, but it seems to me that one should be surprised (actually, appalled) by the fact that even there the percentage of flawed studies is high — not to mention the fact that most studies are in fact neither large nor properly randomized.

The second big recent blow to public perception of the reliability of scientific results is an article published in The New Yorker by Jonah Lehrer, entitled “The truth wears off.” Lehrer also mentions Ioannidis, but the bulk of his essay is about findings in psychiatry, psychology and evolutionary biology (and even in research on the paranormal!).

In these disciplines there are now several documented cases of results that were initially spectacularly positive — for instance the effects of second generation antipsychotic drugs, or the hypothesized relationship between a male’s body symmetry and the quality of his genes — that turned out to be increasingly difficult to replicate over time, with the original effect sizes being cut down dramatically, or even disappearing altogether.

As Lehrer concludes at the end of his article: “Such anomalies demonstrate the slipperiness of empiricism. Although many scientific ideas generate conflicting results and suffer from falling effect sizes, they continue to get cited in the textbooks and drive standard medical practice. Why? Because these ideas seem true. Because they make sense. Because we can’t bear to let them go. And this is why the decline effect is so troubling.”

None of this should actually be particularly surprising to any practicing scientist. If you have spent a significant time of your life in labs and reading the technical literature, you will appreciate the difficulties posed by empirical research, not to mention a number of issues such as the fact that few scientists ever actually bother to replicate someone else’s results, for the simple reason that there is no Nobel (or even funded grant, or tenured position) waiting for the guy who arrived second.

n the midst of this I was directed by a tweet by my colleague Neil deGrasse Tyson (who has also appeared on the RS podcast, though in a different context) to a recent ABC News article penned by John Allen Paulos, which meant to explain the decline effect in science.

Paulos’ article is indeed concise and on the mark (though several of the explanations he proposes were already brought up in both the Atlantic and New Yorker essays), but it doesn’t really make things much better.

Paulos suggests that one explanation for the decline effect is the well known statistical phenomenon of the regression toward the mean. This phenomenon is responsible, among other things, for a fair number of superstitions: you’ve probably heard of some athletes’ and other celebrities’ fear of being featured on the cover of a magazine after a particularly impressive series of accomplishments, because this brings “bad luck,” meaning that the following year one will not be able to repeat the performance at the same level. This is actually true, not because of magical reasons, but simply as a result of the regression to the mean: extraordinary performances are the result of a large number of factors that have to line up just right for the spectacular result to be achieved. The statistical chances of such an alignment to repeat itself are low, so inevitably next year’s performance will likely be below par. Paulos correctly argues that this also explains some of the decline effect of scientific results: the first discovery might have been the result of a number of factors that are unlikely to repeat themselves in exactly the same way, thus reducing the effect size when the study is replicated.

nother major determinant of the unreliability of scientific results mentioned by Paulos is the well know problem of publication bias: crudely put, science journals (particularly the high-profile ones, like Nature and Science) are interested only in positive, spectacular, “sexy” results. Which creates a powerful filter against negative, or marginally significant results. What you see in science journals, in other words, isn’t a statistically representative sample of scientific results, but a highly biased one, in favor of positive outcomes. No wonder that when people try to repeat the feat they often come up empty handed.

A third cause for the problem, not mentioned by Paulos but addressed in the New Yorker article, is the selective reporting of results by scientists themselves. This is essentially the same phenomenon as the publication bias, except that this time it is scientists themselves, not editors and reviewers, who don’t bother to submit for publication results that are either negative or not strongly conclusive. Again, the outcome is that what we see in the literature isn’t all the science that we ought to see. And it’s no good to argue that it is the “best” science, because the quality of scientific research is measured by the appropriateness of the experimental protocols (including the use of large samples) and of the data analyses — not by whether the results happen to confirm the scientist’s favorite theory.

The conclusion of all this is not, of course, that we should throw the baby (science) out with the bath water (bad or unreliable results). But scientists should also be under no illusion that these are rare anomalies that do not affect scientific research at large. Too much emphasis is being put on the “publish or perish” culture of modern academia, with the result that graduate students are explicitly instructed to go for the SPU’s — Smallest Publishable Units — when they have to decide how much of their work to submit to a journal. That way they maximize the number of their publications, which maximizes the chances of landing a postdoc position, and then a tenure track one, and then of getting grants funded, and finally of getting tenure. The result is that, according to statistics published by Nature, it turns out that about ⅓ of published studies is never cited (not to mention replicated!).

“Scientists these days tend to keep up the polite fiction that all science is equal. Except for the work of the misguided opponent whose arguments we happen to be refuting at the time, we speak as though every scientist’s field and methods of study are as good as every other scientist’s, and perhaps a little better. This keeps us all cordial when it comes to recommending each other for government grants. ... We speak piously of taking measurements and making small studies that will ‘add another brick to the temple of science.’ Most such bricks lie around the brickyard.”

Most damning of all, however, is the potential effect that all of this may have on science’s already dubious reputation with the general public (think evolution-creation, vaccine-autism, or climate change)

“If we don’t tell the public about these problems, then we’re no better than non-scientists who falsely claim they can heal. If the drugs don’t work and we’re not sure how to treat something, why should we claim differently? Some fear that there may be less funding because we stop claiming we can prove we have miraculous treatments. But if we can’t really provide those miracles, how long will we be able to fool the public anyway? The scientific enterprise is probably the most fantastic achievement in human history, but that doesn’t mean we have a right to overstate what we’re accomplishing.”

Joseph T. Lapp said... But is any of this new for science? Perhaps science has operated this way all along, full of fits and starts, mostly duds. How do we know that this isn't the optimal way for science to operate?My issues are with the understanding of science that high school graduates have, and with the reporting of science.

What seems to have emerged in recent decades is a change in the institutional setting that got science advancing spectacularly since the establishment of the Royal Society. Flaws in the system such as corporate funded research, pal-review instead of peer-review, publication bias, science entangled with policy advocacy, and suchlike, may be distorting the environment, making it less suitable for the production of good science, especially in some fields.

Remedies should exist, but they should evolve rather than being imposed on a reluctant sociological-economic science establishment driven by powerful motives such as professional advance or funding. After all, who or what would have the authority to impose those rules, other than the scientific establishment itself?

I made it clear that I’m not concerned about simple underrepresentation. I did not even make the moral argument that we need ideological diversity to right an injustice. Rather, I focused on what happens when a scientific community shares sacred values. A tribal moral community arises, one that actively suppresses ideas that are sacrilegious, and that discourages non-believers from entering. I argued that my field has become a tribal moral community, and the absence of conservatives (not just their underrepresentation) has serious consequences for the quality of our science. We rely on our peers to find flaws in our arguments, but when there is essentially nobody out there to challenge liberal assumptions and interpretations of experimental findings, the peer review process breaks down, at least for work that is related to those sacred values. (

The fact that you criticized me without making an effort to understand me is not surprising.

Rather, what sets you apart from all other bloggers who are members of the academy is what you did next. You accused me of professional misconduct—lying, essentially–and you speculated as to my true motive: I suspect that Haidt is either an incompetent psychologist (not likely) or is disingenuously saying the sort of things controversial enough to get him in the New York Times (more likely).

As far as I can tell your evidence for these accusations is that my argument was so bad that I couldn’t have believed it myself. Here is how you justified your accusations: A serious social scientist doesn’t go around crying out discrimination just on the basis of unequal numbers. If that were the case, the NBA would be sued for discriminating against short people, dance companies against people without spatial coordination, and newspapers against dyslexics

Accusations of professional misconduct are sensibly made only if one has a reasonable and detailed understanding of the facts of the case, and can bring forth evidence of misconduct. Pigliucci has made no effort to acquire such an understanding, nor has he presented any evidence to support his accusation. He simply took one claim from the Tierney article and then ran wild with speculation about Haidt’s motives. It was pretty silly of him, and down right irresponsible of Pigliucci to publish that garbage without even knowing what Haidt said.

I challenge you to watch the video of my talk (click here) and then either 1) Retract your blog post and apologize publicly for calling me a liar or 2) State on your blog that you stand by your original post. If you do stand by your post, even after hearing my argument, then the world can decide for itself which of us is right, and which of us best models the ideals of science, philosophy, and the Enlightenment which you claim for yourself in the header of your blog, “Rationally Speaking.” Jonathan Haidt

Casasanto found, in the new study, that these biases are also easily manipulated. First he studies stroke patients who were paralyzed on one side of the body or the other. If a right-hander were weak on the left side (as a control) this had no effect on their choice. But if their right side were weak, then their preference shifted to their intact left side. This, however, can be due to damage to the brain, rather than the fact that they are now obligate left-handers. So he did a follow up experiment in which subjects were made to perform a task with a ski-glove on one hand. If right-handers wore the glove on their left hand, again this had no effect on their choices. But if they wore it on their right hand while performing tasks for as little as 12 minutes, then their cognitive bias shifted to that of a left-hander.

Casasanto observes: ‘People generally think their judgments are rational, and their concepts are stable. But if wearing a glove for a few minutes can reverse people’s usual judgments about what’s good and bad, perhaps the mind is more malleable than we thought.’

The typical establishment individual would refuse to contribute an article to an independent medium that is known to carry opposition party voices, for example. In Singapore’s political culture, it is assumed that any such medium would be blacklisted by people at the top, and that anyone who cooperates with it will be guilty by association. Or, perhaps it is simply that most establishment types lack the confidence to engage in debate on a truly level playing field.

The theory of motivated reasoning builds on a key insight of modern neuroscience (PDF): Reasoning is actually suffused with emotion (or what researchers often call "affect"). Not only are the two inseparable, but our positive or negative feelings about people, things, and ideas arise much more rapidly than our conscious thoughts, in a matter of milliseconds—fast enough to detect with an EEG device, but long before we're aware of it. That shouldn't be surprising: Evolution required us to react very quickly to stimuli in our environment. It's a "basic human survival skill," explains political scientist Arthur Lupia of the University of Michigan. We push threatening information away; we pull friendly information close. We apply fight-or-flight reflexes not only to predators, but to data itself.

We're not driven only by emotions, of course—we also reason, deliberate. But reasoning comes later, works slower—and even then, it doesn't take place in an emotional vacuum. Rather, our quick-fire emotions can set us on a course of thinking that's highly biased, especially on topics we care a great deal about.

Consider a person who has heard about a scientific discovery that deeply challenges her belief in divine creation—a new hominid, say, that confirms our evolutionary origins. What happens next, explains political scientist Charles Taber of Stony Brook University, is a subconscious negative response to the new information—and that response, in turn, guides the type of memories and associations formed in the conscious mind. "They retrieve thoughts that are consistent with their previous beliefs," says Taber, "and that will lead them to build an argument and challenge what they're hearing."

when we think we're reasoning, we may instead be rationalizing. Or to use an analogy offered by University of Virginia psychologist Jonathan Haidt: We may think we're being scientists, but we're actually being lawyers (PDF). Our "reasoning" is a means to a predetermined end—winning our "case"—and is shot through with biases. They include "confirmation bias," in which we give greater heed to evidence and arguments that bolster our beliefs, and "disconfirmation bias," in which we expend disproportionate energy trying to debunk or refute views and arguments that we find uncongenial.

1. The harm principle bases our ethical considerations on other beings’ capacity for higher-level subjective experience. Human beings (and some animals) have the potential — and desire — to experience deep pleasure and happiness while seeking to avoid pain and suffering. We have the obligation, then, to afford creatures with these capacities, desires and relations a certain level of respect. They also have other emotional and social interests: for instance, friends and families concerned with their health and enjoyment. These actors also deserve consideration.

2. If we have a moral obligation to act a certain way toward someone, that should be reflected in law. Rights theory is the idea that there are certain rights worth granting to people with very few, if any, caveats. Many of these rights were spelled out in the founding documents of this country, the Declaration of Independence (which admittedly has no legal pull) and the Constitution (which does). They have been defended in a long history of U.S. Supreme Court rulings. They have also been expanded on in the U.N.’s 1948 Universal Declaration of Human Rights and in the founding documents of other countries around the world. To name a few, they include: freedom of belief, speech and expression, due process, equal treatment, health care, and education.

3. While we ought to consider our broader moral efforts, and focus on our obligations to others, it is also important to place attention on our quality as moral agents. A vital part of fostering a respectable pluralist moral framework is to encourage virtues, and cultivate moral character. A short list of these virtues would include prudence, justice, wisdom, honesty, compassion, and courage. One should study these, and strive to put these into practice and work to be a better human being, as Aristotle advised us to do.

most people already are ethical pluralists. Life and society are complex to navigate, and one cannot rely on a single idea for guidance. It is probably accurate to say that people lean more toward one theory, rather than practice it to the exclusion of all others. Of course, this only describes the fact that people think about morality in a pluralistic way. But the outlined approach is supported, sound reasoning — that is, unless you are ready to entirely dismiss 2,500 years of Western moral philosophy.

in many cases, the offensive messages were spread further by those reporting the offence.

What is the justification for strong police action against any form of speech? Why do we sometimes feel that it may not be enough to counter bad speech with good speech in free and open debate, and that we must instead use the law to stop the bad speech? Surely, it must be because we think the bad speech is so dangerous that it can cause immediate harm; or because we don’t trust the public to respond rationally, so we don’t know if good speech would indeed triumph in open debate. Usually, if we call in the authorities, it must be because we have a mental picture of offensive speech being like lighting a match in a combustible atmosphere. It is dangerous and there’s no time to debate the merits of that match – we just have to put it out. The irony of most of the cases that we have seen in the past few years is that the people demanding government action, as if the offensive words were explosive, were also those who helped to spread them. It is like helping to spread a fire while calling for the fire brigade.

their act of spreading the offensive content must mean that they did not actually believe that the expression was really that dangerous in the sense of prompting violence through reprisal attacks or riots. In reposting the offensive words or pictures, they showed that they actually trusted the public enough to respond sympathetically – they had faith that enough people would add their voices to the outrage that they themselves felt when they saw the offensive images or videos or words.

This then raises the question, why the need to involve the police at all? If Singaporeans are grown-up enough to defend their society against offensive speech, why have calls for prosecution and censorship become the automatic response? I wonder if this is an example of the well-known habit of unthinkingly relying on government to solve all our problems even when, with a little bit of effort in the form of grassroots action can do the job.

The next time people encounter racist or religiously offensive speech, it would be nice to see swift responses from credible and respected civil society groups, Members of Parliament, and other ordinary citizens. If the speaker doesn’t get the message, organise boycotts, for example, and give him or her the clear message that our society isn’t going to take such offence lying down. The more we can respond ourselves through open debate and grassroots action, without the need to ask law and order to step in, the stronger our society will be.

how long should political liberals have let debate last? Here we reach another issue to parse, that of dividing the spheres of discourse of politics and society.The political sphere includes lawmakers, who have their name for a reason: they make laws. They cannot sit around and debate endlessly. They must, at some point, push legislation through (which is at the center of the debate over filibuster reform).

take note of another passage from Mill: “It is the duty of governments, and of individuals, to form the truest opinions they can; to form them carefully, and never impose them on others unless they are quite sure of being right. But when they are sure … it is not conscientiousness but cowardice to shrink from acting on their opinions. ... Men, and governments, must act to the best of their ability. There is no such thing as absolute certainty, but there is assurance sufficient for the purposes of human life." (Mill, 25-26, emphasis added).

Yet our division of spheres of discourse means passage of a bill – or even defeat – does not mark the end of debate. Indeed, many Americans continued to discuss the merits of the legislation, with some even filing lawsuits arguing it was unconstitutional (I think these stand little chance of going anywhere). American society at large can and will continue to have the conversation about health insurance reform. Then, in the next election, they will bring their beliefs to the polls. They will expect those voted in to act. And then, the conversation will continue. Politics is a continuous process. By dividing up spheres of discourse into political and societal, we see that debate never really ends – it’s just that sometimes lawmakers need to get on with their job, and leave debate to the public.

even if authors were all trying to faithfully represent the world as they perceived it, why would we expect their perceptions to be any more universally true than anyone else's?

I can't see any reason to give any more weight to the implicit arguments of a novel than we would give to the explicit arguments of any individual person. And yet when we read a novel or study it in school, especially if it's a hallowed classic, we tend to treat its arguments as truths.

Constraining imagination by knowledge does not make it redundant. We rarely know an explicit formula that tells us what to do in a complex situation. We have to work out what to do by thinking through the possibilities in ways that are simultaneously imaginative and realistic, and not less imaginative when more realistic. Knowledge, far from limiting imagination, enables it to serve its central function.

we can borrow a distinction from the philosophy of science, between contexts of discovery and contexts of justification. In the context of discovery, we get ideas, no matter how — dreams or drugs will do. Then, in the context of justification, we assemble objective evidence to determine whether the ideas are correct. On this picture, standards of rationality apply only to the context of justification, not to the context of discovery. Those who downplay the cognitive role of the imagination restrict it to the context of discovery, excluding it from the context of justification. But they are wrong. Imagination plays a vital role in justifying ideas as well as generating them in the first place.

finding counterexamples can, in general, weaken our confidence in our own arguments. Forms of reasoning that are good for solving logic puzzles but bad for winning arguments lost out, over the course of evolution, to those that help us be persuasive but cause us to struggle with abstract syllogisms. Interestingly, syllogisms are easier to evaluate in the form “No flying things are penguins; all penguins are birds; so some birds are not fliers.” That’s because we are more likely to argue about animals than A, B, and C.

The sort of faulty thinking called motivated reasoning also impedes our search for truth but advances arguments. For instance, we tend to look harder for flaws in a study when we don’t agree with its conclusions and are more critical of evidence that undermines our point of view.

Second of all, fields naturally select for people who accept their foundational assumptions. People who don't accept those assumptions are likely not to have gone into that field in the first place, or to have left it already.

Sometimes those foundational assumptions are simple enough that an outsider can evaluate them - for instance, I may not be an expert in astrology or theology, but I can understand their starting premises (stars affect human fates; we should accept the Bible as the truth) well enough to confidently dismiss them, and the fields that rest on them. But when the foundational assumptions get more complex - like the assumption that we can reliably model future temperatures - it becomes much harder for an outsider to judge their soundness.

we almost seem to be stuck in a Catch-22: The only people who are qualified to evaluate the validity of a complex field are the ones who have studied that field in depth - in other words, experts. Yet the experts are also the people who have the strongest incentives not to reject the foundational assumptions of the field, and the ones who have self-selected for believing those assumptions. So the closer you are to a field, the more biased you are, which makes you a poor judge of it; the farther away you are, the less relevant knowledge you have, which makes you a poor judge of it. What to do?

luckily, the Catch-22 isn't quite as stark as I made it sound. For example, you can often find people who are experts in the particular methodology used by a field without actually being a member of the field, so they can be much more unbiased judges of whether that field is applying the methodology soundly. So for example, a foundational principle underlying a lot of empirical social science research is that linear regression is a valid tool for modeling most phenomena. I strongly recommend asking a statistics professor about that. 

there are some general criteria that outsiders can use to evaluate the validity of a technical field, even without “technical scientific expertise” in that field. For example, can the field make testable predictions, and does it have a good track record of predicting things correctly? This seems like a good criterion by which an outsider can judge the field of climate modeling (and "predictions" here includes using your model to predict past data accurately). I don't need to know how the insanely-complicated models work to know that successful prediction is a good sign.

And there are other more field-specific criteria outsiders can often use. For example, I've barely studied postmodernism at all, but I don't have to know much about the field to recognize that the fact that they borrow concepts from complex disciplines which they themselves haven't studied is a red flag.

the issue with AGW is less the science and all about the political solutions. Most every solution we hear in the public conversation requires some level of sacrifice and uncertainty in the future.Politicians, neither experts in climatology nor economics, craft legislation to solve the problem through the lens of their own political ideology. At TAM8, this was pretty apparent. My honest opinion is that people who are AGW skeptics are mainly skeptics of the political solutions. If AGW was said to increase the GDP of the country by two to three times, I'm guessing you'd see a lot less climate change skeptics.

After the Academy dropped Borda’s method, it plumped for a simple suggestion by the astronomer and mathematician Pierre-Simon Laplace, who was an important contributor to the theory of probability. Laplace’s rule insisted on an over-all majority: at least half the votes plus one. If no candidate achieved this, nobody was elected to the Academy.

Another early advocate of proportional representation was John Stuart Mill, who, in 1861, wrote about the critical distinction between “government of the whole people by the whole people, equally represented,” which was the ideal, and “government of the whole people by a mere majority of the people exclusively represented,” which is what winner-takes-all elections produce. (The minority that Mill was most concerned to protect was the “superior intellects and characters,” who he feared would be swamped as more citizens got the vote.)

The key to proportional representation is to enlarge constituencies so that more than one winner is elected in each, and then try to align the share of seats won by a party with the share of votes it receives. These days, a few small countries, including Israel and the Netherlands, treat their entire populations as single constituencies, and thereby get almost perfectly proportional representation. Some places require a party to cross a certain threshold of votes before it gets any seats, in order to filter out extremists.

The main criticisms of proportional representation are that it can lead to unstable coalition governments, because more parties are successful in elections, and that it can weaken the local ties between electors and their representatives. Conveniently for its critics, and for its defenders, there are so many flavors of proportional representation around the globe that you can usually find an example of whatever point you want to make. Still, more than three-quarters of the world’s rich countries seem to manage with such schemes.

The alternative voting method that will be put to a referendum in Britain is not proportional representation: it would elect a single winner in each constituency, and thus steer clear of what foreigners put up with. Known in the United States as instant-runoff voting, the method was developed around 1870 by William Ware

In instant-runoff elections, voters rank all or some of the candidates in order of preference, and votes may be transferred between candidates. The idea is that your vote may count even if your favorite loses. If any candidate gets more than half of all the first-preference votes, he or she wins, and the game is over. But, if there is no majority winner, the candidate with the fewest first-preference votes is eliminated. Then the second-preference votes of his or her supporters are distributed to the other candidates. If there is still nobody with more than half the votes, another candidate is eliminated, and the process is repeated until either someone has a majority or there are only two candidates left, in which case the one with the most votes wins. Third, fourth, and lower preferences will be redistributed if a voter’s higher preferences have already been transferred to candidates who were eliminated earlier.

At first glance, this is an appealing approach: it is guaranteed to produce a clear winner, and more voters will have a say in the election’s outcome. Look more closely, though, and you start to see how peculiar the logic behind it is. Although more people’s votes contribute to the result, they do so in strange ways. Some people’s second, third, or even lower preferences count for as much as other people’s first preferences. If you back the loser of the first tally, then in the subsequent tallies your second (and maybe lower) preferences will be added to that candidate’s first preferences. The winner’s pile of votes may well be a jumble of first, second, and third preferences.

Such transferrable-vote elections can behave in topsy-turvy ways: they are what mathematicians call “non-monotonic,” which means that something can go up when it should go down, or vice versa. Whether a candidate who gets through the first round of counting will ultimately be elected may depend on which of his rivals he has to face in subsequent rounds, and some votes for a weaker challenger may do a candidate more good than a vote for that candidate himself. In short, a candidate may lose if certain voters back him, and would have won if they hadn’t. Supporters of instant-runoff voting say that the problem is much too rare to worry about in real elections, but recent work by Robert Norman, a mathematician at Dartmouth, suggests otherwise. By Norman’s calculations, it would happen in one in five close contests among three candidates who each have between twenty-five and forty per cent of first-preference votes. With larger numbers of candidates, it would happen even more often. It’s rarely possible to tell whether past instant-runoff elections have gone topsy-turvy in this way, because full ballot data aren’t usually published. But, in Burlington’s 2006 and 2009 mayoral elections, the data were published, and the 2009 election did go topsy-turvy.

Kenneth Arrow, an economist at Stanford, examined a set of requirements that you’d think any reasonable voting system could satisfy, and proved that nothing can meet them all when there are more than two candidates. So designing elections is always a matter of choosing a lesser evil. When the Royal Swedish Academy of Sciences awarded Arrow a Nobel Prize, in 1972, it called his result “a rather discouraging one, as regards the dream of a perfect democracy.” Szpiro goes so far as to write that “the democratic world would never be the same again,

There is something of a loophole in Arrow’s demonstration. His proof applies only when voters rank candidates; it would not apply if, instead, they rated candidates by giving them grades. First-past-the-post voting is, in effect, a crude ranking method in which voters put one candidate in first place and everyone else last. Similarly, in the standard forms of proportional representation voters rank one party or group of candidates first, and all other parties and candidates last. With rating methods, on the other hand, voters would give all or some candidates a score, to say how much they like them. They would not have to say which is their favorite—though they could in effect do so, by giving only him or her their highest score—and they would not have to decide on an order of preference for the other candidates.

One such method is widely used on the Internet—to rate restaurants, movies, books, or other people’s comments or reviews, for example. You give numbers of stars or points to mark how much you like something. To convert this into an election method, count each candidate’s stars or points, and the winner is the one with the highest average score (or the highest total score, if voters are allowed to leave some candidates unrated). This is known as range voting, and it goes back to an idea considered by Laplace at the start of the nineteenth century. It also resembles ancient forms of acclamation in Sparta. The more you like something, the louder you bash your shield with your spear, and the biggest noise wins. A recent variant, developed by two mathematicians in Paris, Michel Balinski and Rida Laraki, uses familiar language rather than numbers for its rating scale. Voters are asked to grade each candidate as, for example, “Excellent,” “Very Good,” “Good,” “Insufficient,” or “Bad.” Judging politicians thus becomes like judging wines, except that you can drive afterward.

Range and approval voting deal neatly with the problem of vote-splitting: if a voter likes Nader best, and would rather have Gore than Bush, he or she can approve Nader and Gore but not Bush. Above all, their advocates say, both schemes give voters more options, and would elect the candidate with the most over-all support, rather than the one preferred by the largest minority. Both can be modified to deliver forms of proportional representation.

Whether such ideas can work depends on how people use them. If enough people are carelessly generous with their approval votes, for example, there could be some nasty surprises. In an unlikely set of circumstances, the candidate who is the favorite of more than half the voters could lose. Parties in an approval election might spend less time attacking their opponents, in order to pick up positive ratings from rivals’ supporters, and critics worry that it would favor bland politicians who don’t stand for anything much. Defenders insist that such a strategy would backfire in subsequent elections, if not before, and the case of Ronald Reagan suggests that broad appeal and strong views aren’t mutually exclusive.

Why are the effects of an unfamiliar electoral system so hard to puzzle out in advance? One reason is that political parties will change their campaign strategies, and voters the way they vote, to adapt to the new rules, and such variables put us in the realm of behavior and culture. Meanwhile, the technical debate about electoral systems generally takes place in a vacuum from which voters’ capriciousness and local circumstances have been pumped out. Although almost any alternative voting scheme now on offer is likely to be better than first past the post, it’s unrealistic to think that one voting method would work equally well for, say, the legislature of a young African republic, the Presidency of an island in Oceania, the school board of a New England town, and the assembly of a country still scarred by civil war. If winner takes all is a poor electoral system, one size fits all is a poor way to pick its replacements.

Mathematics can suggest what approaches are worth trying, but it can’t reveal what will suit a particular place, and best deliver what we want from a democratic voting system: to create a government that feels legitimate to people—to reconcile people to being governed, and give them reason to feel that, win or lose (especially lose), the game is fair.