The first-past-the-post system, as mathematician Donald Saari (University of California) has demonstrated, favours the party that has even the slightest edge over its opponents in most electoral divisions, even if overall, i.e. when the results of all electoral divisions are taken into account, that party does not collect the majority of the votes. Sounds like a conundrum?
In fact, it's a question of reasonably simple arithmetic. And because it looks convincingly fair, even though it doesn't pass the litmus test of maths, it's frequently used. This systems is especially favourable to likely losers in touch-and-go elections, a notable example being the 2000 US presidential election, which G. W. Bush won by a slim margin over Al Gore.
Here's how it works: suppose that you ask 15 voters to rank their preference for milk (M), beer (B) and wine (W). Say that the ranking looks like this:
M-W-B: 6 people
B-W-M: 5 people
W-B-M: 4 people
According to the first-past-the post system, milk is the clear winner, while wine is the clear loser. In fact, 10 of the 15 voters would much rather drink wine (first and third sets) than beer, while 9 out of 15 rank wine above milk (second and third sets). Wine, not milk, is what these people really want (understandably too), except that the plurality system exploits the fact that alcohol drinkers almost inevitably will name their favourite booze as their first choice, and the closest alternative as their second choice (see second and third pairs). 'Similar things happen in politics', points out Ian Stewart, '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.'
As you'd expect, the exploitable quirks of voting maths have not got lost on politicians. You've probably known this intuitively all along but Saari's calculations provide mathematical proof: 'given a set of voter preferences you can design a system that produces any result you desire'.
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