User:Andrewa/ABC voting

Why democracy can't work...

Consider three parties, A, B and C.

If we have a two-way election:

A will beat B

B will beat C

C will beat A

but, all three run. Who should win?

It's easy to have an electorate in which this may happen. Say we have three voters. One prefers A to B to C. One prefers B to C to A. The third prefers C to A to B.

If A and B run, voters one and three vote A.

If B and C run, voters one and two vote B.

If C and A run, voters two and three vote C.

If all three run, then they get one vote each.

With a reasonable number of voters, it's easy to get a system which eliminates one of the three in round one on some pretext or other. But it's then not possible to overcome the possibility that, in a two-horse race against either of the others, the eliminated party would win.

It can't work...

(...but it does.)

See also Condorcet paradox, Condorcet method and Condorcet criterion.