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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.

At the other end of the spectrum, scare stories are - of course - a stalwart of media science. Based on minimal evidence and expanded with poor understanding of its significance, they help perform the most crucial function for the media, which is selling you, the reader, to their advertisers. The MMR disaster was a fantasy entirely of the media's making (www.badscience.net/?p=23), which failed to go away. In fact the Daily Mail is still publishing hysterical anti-immunisation stories, including one calling the pneumococcus vaccine a "triple jab", presumably because they misunderstood that the meningitis, pneumonia, and septicaemia it protects against are all caused by the same pneumococcus bacteria (www.badscience.net/?p=118).

people periodically come up to me and say, isn't it funny how that Wakefield MMR paper turned out to be Bad Science after all? And I say: no. The paper always was and still remains a perfectly good small case series report, but it was systematically misrepresented as being more than that, by media that are incapable of interpreting and reporting scientific data.

Once journalists get their teeth into what they think is a scare story, trivial increases in risk are presented, often out of context, but always using one single way of expressing risk, the "relative risk increase", that makes the danger appear disproportionately large (www.badscience.net/?p=8).

he media obsession with "new breakthroughs": a more subtly destructive category of science story. It's quite understandable that newspapers should feel it's their job to write about new stuff. But in the aggregate, these stories sell the idea that science, and indeed the whole empirical world view, is only about tenuous, new, hotly-contested data

Articles about robustly-supported emerging themes and ideas would be more stimulating, of course, than most single experimental results, and these themes are, most people would agree, the real developments in science. But they emerge over months and several bits of evidence, not single rejiggable press releases. Often, a front page science story will emerge from a press release alone, and the formal academic paper may never appear, or appear much later, and then not even show what the press reports claimed it would (www.badscience.net/?p=159).

there was an interesting essay in the journal PLoS Medicine, about how most brand new research findings will turn out to be false (www.tinyurl.com/ceq33). It predictably generated a small flurry of ecstatic pieces from humanities graduates in the media, along the lines of science is made-up, self-aggrandising, hegemony-maintaining, transient fad nonsense; and this is the perfect example of the parody hypothesis that we'll see later. Scientists know how to read a paper. That's what they do for a living: read papers, pick them apart, pull out what's good and bad.

there is no useful information in most science stories. A piece in the Independent on Sunday from January 11 2004 suggested that mail-order Viagra is a rip-off because it does not contain the "correct form" of the drug. I don't use the stuff, but there were 1,147 words in that piece. Just tell me: was it a different salt, a different preparation, a different isomer, a related molecule, a completely different drug? No idea. No room for that one bit of information.

Remember all those stories about the danger of mobile phones? I was on holiday at the time, and not looking things up obsessively on PubMed; but off in the sunshine I must have read 15 newspaper articles on the subject. Not one told me what the experiment flagging up the danger was. What was the exposure, the measured outcome, was it human or animal data? Figures? Anything? Nothing. I've never bothered to look it up for myself, and so I'm still as much in the dark as you.

Because papers think you won't understand the "science bit", all stories involving science must be dumbed down, leaving pieces without enough content to stimulate the only people who are actually going to read them - that is, the people who know a bit about science.

Compare this with the book review section, in any newspaper. The more obscure references to Russian novelists and French philosophers you can bang in, the better writer everyone thinks you are. Nobody dumbs down the finance pages.

Statistics are what causes the most fear for reporters, and so they are usually just edited out, with interesting consequences. Because science isn't about something being true or not true: that's a humanities graduate parody. It's about the error bar, statistical significance, it's about how reliable and valid the experiment was, it's about coming to a verdict, about a hypothesis, on the back of lots of bits of evidence.

science journalists somehow don't understand the difference between the evidence and the hypothesis. The Times's health editor Nigel Hawkes recently covered an experiment which showed that having younger siblings was associated with a lower incidence of multiple sclerosis. MS is caused by the immune system turning on the body. "This is more likely to happen if a child at a key stage of development is not exposed to infections from younger siblings, says the study." That's what Hawkes said. Wrong! That's the "Hygiene Hypothesis", that's not what the study showed: the study just found that having younger siblings seemed to be somewhat protective against MS: it didn't say, couldn't say, what the mechanism was, like whether it happened through greater exposure to infections. He confused evidence with hypothesis (www.badscience.net/?p=112), and he is a "science communicator".

how do the media work around their inability to deliver scientific evidence? They use authority figures, the very antithesis of what science is about, as if they were priests, or politicians, or parent figures. "Scientists today said ... scientists revealed ... scientists warned." And if they want balance, you'll get two scientists disagreeing, although with no explanation of why (an approach at its most dangerous with the myth that scientists were "divided" over the safety of MMR). One scientist will "reveal" something, and then another will "challenge" it

The danger of authority figure coverage, in the absence of real evidence, is that it leaves the field wide open for questionable authority figures to waltz in. Gillian McKeith, Andrew Wakefield, Kevin Warwick and the rest can all get a whole lot further, in an environment where their authority is taken as read, because their reasoning and evidence is rarely publicly examined.

it also reinforces the humanities graduate journalists' parody of science, for which we now have all the ingredients: science is about groundless, incomprehensible, didactic truth statements from scientists, who themselves are socially powerful, arbitrary, unelected authority figures. They are detached from reality: they do work that is either wacky, or dangerous, but either way, everything in science is tenuous, contradictory and, most ridiculously, "hard to understand".

This misrepresentation of science is a direct descendant of the reaction, in the Romantic movement, against the birth of science and empiricism more than 200 years ago; it's exactly the same paranoid fantasy as Mary Shelley's Frankenstein, only not as well written. We say descendant, but of course, the humanities haven't really moved forward at all, except to invent cultural relativism, which exists largely as a pooh-pooh reaction against science. And humanities graduates in the media, who suspect themselves to be intellectuals, desperately need to reinforce the idea that science is nonsense: because they've denied themselves access to the most significant developments in the history of western thought for 200 years, and secretly, deep down, they're angry with themselves over that.

had a good spirited row with an eminent science journalist, who kept telling me that scientists needed to face up to the fact that they had to get better at communicating to a lay audience. She is a humanities graduate. "Since you describe yourself as a science communicator," I would invariably say, to the sound of derisory laughter: "isn't that your job?" But no, for there is a popular and grand idea about, that scientific ignorance is a useful tool: if even they can understand it, they think to themselves, the reader will. What kind of a communicator does that make you?

Science is done by scientists, who write it up. Then a press release is written by a non-scientist, who runs it by their non-scientist boss, who then sends it to journalists without a science education who try to convey difficult new ideas to an audience of either lay people, or more likely - since they'll be the ones interested in reading the stuff - people who know their way around a t-test a lot better than any of these intermediaries. Finally, it's edited by a whole team of people who don't understand it. You can be sure that at least one person in any given "science communication" chain is just juggling words about on a page, without having the first clue what they mean, pretending they've got a proper job, their pens all lined up neatly on the desk.