The New Scientist (28th April 2010) carried a most timely article on dysfunctions in voting. Their example ran basically as follows. Assume that 15 people vote for the Liberal Democrats, Labor, and the Conservatives and they end up with 6 in favor of the Conservatives, 5 in favor of Labor, and 4 in favor of the Liberal Democrats, then under the current voting scheme the Conservatives win. Consider however if they ranked their choices as follows:
6: Conservative – Liberal Democrat – Labor
5: Labor – Liberal Democrat – Conservative
4: Liberal Democrat – Labor – Conservative
It is then apparent that 9 people preferred Labor to the Conservatives; and 10 people preferred the Liberal Democrats to Labor. In short, the “real” voting was Liberal Democrats first, Labor second, and the Conservatives last. In other words, the Conservatives would not have got in if rank order had been taken into account. Unfortunately, it is not quite as easy as shifting from a winner takes all system to a rank-order system. It is not hard to show, and the article by Ian Stewart does it, that there are a number of different voting schemes — and each one of them produces a potentially different answer. Nobel Prize Winner Kenneth Arrow demonstrated many years ago the sheer impossibility of finding the perfect voting system hence the provocative title of the New Scientist article: Why democracy is always unfair!