The voting method that is used in Britain—and that has been kept on in some of its former colonies, including the United States—may finally be replaced. ... a national referendum on changing the country’s main voting system ... will be held in 2011. If Britain does switch, as most other developed countries already have, the cause of voting reform in holdouts like the United States, India, and Canada could get a boost.
["First Past the Post" or "Winner Takes All" ]
In the standard British style of voting, each elector casts one vote, and the candidate with more votes than any other is elected. This is known as “first past the post”; the winner just needs to get more votes than anyone else, not achieve any threshold (such as a two-thirds majority). It is also called “winner takes all,” to distinguish it from some other methods, which elect the top two or more candidates.
In a contest between two people for one job, first past the post seems to be merely common sense. But, as soon as there are three or more candidates on the slate, it can quickly go awry. ...
Add political parties to the picture, and the winner-take-all system looks even worse. A party’s share of seats in a parliament or a congress can diverge wildly from its over-all share of votes. ... In this year’s election, the Liberal Democrat Party won more than a fifth of the votes and less than a tenth of the seats. That’s because Lib-Dem supporters today ... are thinly scattered across the land.
In a country with just two political parties, winner takes all can deliver a proportionate parliament or congress. But that’s only because the supporters of political parties tend to live in clusters. Say that fifty-three per cent of American voters are Democrats and forty-six per cent are Republicans (mirroring the vote in last year’s Presidential election). Then imagine that the supporters of the two parties were spread evenly throughout the country’s districts ... In that case, the Democrats would win every seat and there would be no Republicans in Congress.
[Rank Voting and Two-Stage Votes]
... Jean-Charles de Borda, a French mathematician and a naval hero of the American Revolutionary War, ... Borda’s main suggestion was to require voters to rank candidates, rather than just choose one favorite, so that a winner could be calculated by counting points awarded according to the rankings. The key idea was to find a way of taking lower preferences, as well as first preferences, into account....
Unfortunately, this method may fail to elect the majority’s favorite—it could, in theory, elect someone who was nobody’s favorite. It is also easy to manipulate by strategic voting. ...
... [T]he astronomer and mathematician Pierre-Simon Laplace, who was an important contributor to the theory of probability ... insisted on an over-all majority: at least half the votes plus one. ... Elections to the French National Assembly, and to the French Presidency, currently borrow from both Laplace and Condorcet. They use a two-stage method that guarantees a winning candidate with an over-all majority, by conducting a runoff round between the top two candidates from the first round. ...
[Proportional Representation]
... 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 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. ...
The alternative voting method that will be put to a referendum in Britain is not proportional representation ... Known in the United States as instant-runoff voting, the method was developed around 1870 by William Ware ...
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[Instant Runoff]
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. ...
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. ... In short, a candidate may lose if certain voters back him, and would have won if they hadn’t.
... [R]ecent work by Robert Norman, a mathematician at Dartmouth, suggests [a topsy-turvy result] 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. ... Burlington’s ... 2009 mayoral elections ... 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. ...
[Grade Voting]
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. ...
[Approval Voting]
Approval voting, as used in the last round of old Venetian elections, is a rating system with just two grades: approved and not approved. ... The American Mathematical Society and the Mathematical Association of America, among others, use it for internal elections, though the larger Institute of Electrical and Electronics Engineers, which also adopted it, came to have second thoughts.
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.
The fact that they escape Arrow’s proof, though, doesn’t mean that approval and range voting have no hidden kinks or paradoxes. 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. ... 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. ...
... 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....
