Why Democracy is Always Unfair

Believe it or not, that’s the New Scientist’s headline, not mine. I guess it depends what you mean by fair. In the April 28th edition, Ian Stewart lays out a good summary of all the different problems intrinsic to democratic voting procedures. Arrow’s Impossibility Theorem, Condorcet‘s theorem, the Alabama Paradox, and gerrymandering, among other ballot box nettles, all make an appearance. Stewart’s intro:

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”…