Vote of no confidence; No voting system is perfect, but why do we put up with one of the worst, asks Phil McKenna BYLINE: Phil McKenna. Phil McKenna is a writer based in Boston LENGTH: 2506 words. (NOTE: We laboriously typed in the full text of the article from New Scientist 12 April 2008 pages 30-33, and here it is as a local copy.) --------------------------------------- ONE person one vote is the mantra of democracy. And as Americans prepare to elect a new president this year, they'll be weighing up who to cast their precious vote for. Yet giving each citizen just one vote may not serve democracy's best interests. It can all too easily throw up a winner who in a straight fight with the runner-up would not be the majority's choice - surely a negation of democracy. How can this happen? It's to do with the way voters are allowed to express their preferences, and how those choices are turned into a winner. Most elections in the US, the UK, Canada, India and many other countries use what is technically called a plurality voting system (better known as first-past-the-post) for single-winner elections. Every voter chooses one candidate from those standing, and the candidate with the most votes wins. It's beautifully simple. But it can also be strongly influenced by fringe candidates with relatively little support. By taking votes that would otherwise go to one of the leading candidates, these "spoilers" can tip the outcome in favour of that candidate's main rival. In five of the last 45 US presidential elections, plurality voting has handed the White House to the second most popular candidate, according to William Poundstone, author of Gaming the Vote: Why elections aren't fair . "It's really the worst system. Its only virtue is that it is the simplest way of voting, which is why we put up with it," he says. Voting reform initiatives in the US usually focus on problems with voting machines and on the electoral college used in a presidential election - an antiquated system that gives more weight to voters from some states than from others. Yet arguably the larger problem with elections in America and elsewhere is plurality voting itself. Is there a fairer alternative? Researchers and politicians have long known of plurality's weaknesses, but until recently most believed the alternatives weren't any better. 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). First, Arrow assumed that all voters would vote honestly rather than try to manipulate the system. Then he identified five criteria that he felt a good voting system should meet. Three of them seem obvious: every election should result in a decisive winner; if a candidate is the unanimous favourite, he or she should win; all candidates should be treated equally. A fourth criterion stipulates that all voters should count equally and be anonymous, in order to guarantee freedom of expression and ensure that it is not only the wishes of a dictator or minority elite that count. Finally, Arrow's fifth criterion states that if you look at any three candidates, the way the system reflects voters' preferences for candidate A or B should be independent of their views about candidate C. That is, liking candidate C shouldn't force voters to desert either A or B. Plurality voting fails to meet the last criterion. One recent demonstration of this failure happened in the 2000 US presidential election. It is now widely accepted that the Green Party candidate Ralph Nader took votes that would otherwise have counted towards Al Gore. A voting system that met Arrow's fifth criterion would have ensured that the winner in the race between Al Gore and George W. Bush would not depend on whether Nader was standing too . Arrow applied his test to all the proposed voting systems that allowed voters to rank candidates in order of preference. He found that no voting scheme could meet all his criteria. The conclusion, which came to be known as Arrow's impossibility theorem, spawned a new field of study called social choice theory and earned Arrow the Nobel prize in economics in 1972. "It really caused decades of despair. It asserted that no voting system is going to be fair," says Poundstone. But could Arrow have overlooked better options? Warren Smith, a former mathematics professor at Temple University in Philidelphia, and co-founder of www.rangevoting.org, claims to have circumvented Arrow's theorem with a controversial voting system called range voting, which the theorem doesn't cover. According to Smith, range voting consistently yields the most satisfying result for the greatest number of voters. 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. 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, who won the 2007 Nobel prize in economics for work he did on the rules that govern voting systems. 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. 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." 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?" Ripe for manipulation 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. No system is entirely safe from such manipulation, 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. 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." 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. Smith says these effects would cancel out between the different candidates because a similar share of each candidate's constituency would vote strategically. 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. 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. 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. Crucially, this means that the Condorcet winner in an election need not necessarily be the candidate with the majority of first-choice rankings. Proponents of Condorcet say it is the fairest method because it elects the candidate that the greatest number of people find the least disagreeable. The downside is it can elect a candidate that no one wanted as their first choice. 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. 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. 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. 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. 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. 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. 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." 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. For example, suppose there is a tight three-way race in which candidate A leads but doesn't have an overall majority, while candidates B and C are vying for second, with B voters preferring A as their second choice and C voters preferring B as their second choice. If candidate A courts and wins too many of the C voters, then candidate C will be eliminated first and his or her votes will give candidate B the overall victory. "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. "In reality, you would have to have members of the Green Party voting for the Republican candidate," says Hill. Of all the alternatives to plurality voting, IRV is the only one that has gained a toehold in government elections. For example, San Francisco, California, and Takoma Park, Maryland, use it in municipal elections. And presidential hopefuls John McCain and Barack Obama have both supported efforts to adopt the system in state-wide elections. As campaigners try ever sneakier ways to manipulate the plurality system, so the need for change is growing more pronounced. Having seen how Ralph Nader split the liberal vote in the 2000 US election, Republicans helped fund his 2004 campaign in the hope that he might undermine the Democrats again. The practice has now become commonplace in American politics. 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." Could plurality voting have had its day? Perhaps it's time to give every man and woman more than one vote. ---end.