Friday, April 23, 2010

The three-party voting paradox

Take a closer look at the mathematics behind a three-way race – and particularly at the Condorcet paradox, the technical name of the situation I (almost) described.
Named after the Marquis de Condorcet (an 18th-century French nobleman who, Fisher writes, “had more fun with voting systems than most politicians”), the simplest Condorcet paradox occurs when there are three voters and three political parties A, B and C:
Voter 1 prefers A to B, but would rather have B than C
Voter 2 prefers B to C, but would rather have C than A
Voter 3 prefers C to A, but would rather have A than B

In these circumstances, no matter who is declared the winner, two-thirds of the electorate will have preferred someone else. There is no “Condorcet winner” – no party which, when compared to all others, is preferred by more people.

Source: Condorcet Paradox