| ELECTIONS NOT FAIR Electoral dysfunction: Why democracy is always unfair28 April 2010 by Ian StewartMagazine issue 2758. Subscribe and get 4 free issues.Read full article Continue reading page |1 |2Editorial: Giving democracy a shot in the armIN AN ideal world, elections should be two things: free and fair. Every adult, with a few sensible exceptions, should be able to vote for a candidate of their choice, and each single vote should be worth the same.Ensuring a free vote is a matter for the law. Making elections fair is more a matter for mathematicians. They have been studying voting systems for hundreds of years, looking for sources of bias that distort the value of individual votes, and ways to avoid them. Along the way, they have turned up many paradoxes and surprises. What they have not done is come up with the answer. With good reason: it probably doesn’t exist.The many democratic electoral systems in use around the world attempt to strike a balance between mathematical fairness and political considerations such as accountability and the need for strong, stable government. Take first-past-the-post or “plurality” voting, which used for national elections in the US, Canada, India – and the UK, which goes to the polls next week. Its principle is simple: each electoral division elects one representative, the candidate who gained the most votes.This system scores well on stability and accountability, but in terms of mathematical fairness it is a dud. Votes for anyone other than the winning candidate are disregarded. If more than two parties with substantial support contest a constituency, as is typical in Canada, India and the UK, a candidate does not have to get anything like 50 per cent of the votes to win, so a majority of votes are “lost”.Dividing a nation or city into bite-sized chunks for an election is itself a fraught business (see “Borderline case”) that invites other distortions, too. A party can win outright by being only marginally ahead of its competitors in most electoral divisions. In the UK general election in 2005, the ruling Labour party won 55 per cent of the seats on just 35 per cent of the total votes. If a candidate or party is slightly ahead in a bare majority of electoral divisions but a long way behind in others, they can win even if a competitor gets more votes overall – as happened most notoriously in recent history in the US presidential election of 2000, when George W. Bush narrowly defeated Al Gore.The anomalies of a plurality voting system can be more subtle, though, as mathematician Donald Saari at the University of California, Irvine, showed. Suppose 15 people are asked to rank their liking for milk (M), beer (B), or wine (W). Six rank them M-W-B, five B-W-M, and four W-B-M. In a plurality system where only first preferences count, the outcome is simple: milk wins with 40 per cent of the vote, followed by beer, with wine trailing in last.So do voters actually prefer milk? Not a bit of it. Nine voters prefer beer to milk, and nine prefer wine to milk – clear majorities in both cases. Meanwhile, 10 people prefer wine to beer. By pairing off all these preferences, we see the truly preferred order to be W-B-M – the exact reverse of what the voting system produced. In fact Saari showed that given a set of voter preferences you can design a system that produces any result you desire.In the example above, simple plurality voting produced an anomalous outcome because the alcohol drinkers stuck together: wine and beer drinkers both nominated the other as their second preference and gave milk a big thumbs-down. Similar things happen in politics when two parties appeal to the same kind of voters, splitting their votes between them and allowing a third party unpopular with the majority to win the election.Can we avoid that kind of unfairness while keeping the advantages of a first-past-the-post system? Only to an extent. One possibility is a second “run-off” election between the two top-ranked candidates, as happens in France and in many presidential elections elsewhere. But there is no guarantee that the two candidates with the widest potential support even make the run-off. In the 2002 French presidential election, for example, so many left-wing candidates stood in the first round that all of them were eliminated, leaving two right-wing candidates, Jacques Chirac and Jean-Marie Le Pen, to contest the run-off.Order, orderAnother strategy allows voters to place candidates in order of preference, with a 1, 2, 3 and so on. After the first-preference votes have been counted, the candidate with the lowest score is eliminated and the votes reapportioned to the next-choice candidates on those ballot papers. This process goes on until one candidate has the support of over 50 per cent of the voters. This system, called the instant run-off or alternative or preferential vote, is used in elections to the Australian House of Representatives, as well as in several US cities. It has also been suggested for the UK. |
