Friday, 31 August 2012
To give an example; in 2005 the Labour party got 57% of the seats in the British House of Commons with only 36% of the votes. Is that fair? This outcome is a consequence of the first-past-the-post electoral system, or winner-takes-all system, in multiple districts. In this case, the candidate that gets the most votes, whether he/she reaches a majority of votes or not ("first past the post") wins the seat in parliament. It was designed to support for a two-party electoral contest. It worked well when there were only Whigs and Tories it is however ill-suited to a multi-party political landscape. It thwarts the will of the voters, leaving millions without political representation in parliament.
Take a look at the vote and seat distribution of the 1994 elections. As you can see, CDA and PvdA suffered great losses, D66 and VVD won a lot of votes. Now consider the election matrix as retrieved prior to the elections (source Dutch Parliament Elections Studies). The cell (D66, PvdA) in this matrix contains the number of 655 while the cell (PvdA, D66) contains the number of 580. This means that 655 respondents strictly prefer D66 to PvdA and that 580 strictly prefer the PvdA.
Using this matrix a majority ranking can be constructed in such a way that the party higher in rank holds a majority over all parties at lower ranks. From the majority ranking it is immediately clear that although D66 has the majority vote it is only ranked fourth based on number of seats. This is an example of what is called The More-Preferred-Less-Seats Paradox.
Can’t we improve voting systems to overcome these kinds of paradoxes? Unfortunately not. Like Kurt Gödel's proof that there will always be facts which cannot be proved or disproved in any mathematical system, the Impossibility Theorem on social choice of Arrow precludes the ideal of a perfect democracy. So abolish democracy? Of course not! The perfect democracy doesn’t exist, the challenge is to find the best possible. With Arrow’s theorem available a trade-off can be made on the properties a voting system should have and whether the above paradox is acceptable or not. But how to decide on that? Take a vote?