User:Andrewa/ABC voting
Why democracy can't work...[edit]
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.)[edit]
See also Condorcet paradox, Condorcet method and Condorcet criterion.