Dear Forest,
here is an example that shows that the Condorcet criterion
and the consistency criterion are incompatible.
40 voters vote A > B > C.
35 voters vote B > C > A.
25 voters vote C > A > B.
Case 1: Suppose that candidate A is elected. Then when you add
51 A > C > B voters and 49 C > B > A voters, the winner is
changed to candidate C.
Case 2: Suppose that candidate B is elected. Then when you add
51 B > A > C voters and 49 A > C > B voters, the winner is
changed to candidate A.
Case 3: Suppose that candidate C is elected. Then when you add
51 C > B > A voters and 49 B > A > C voters, the winner is
changed to candidate B.
******
You wrote (15 May 2001):
> As Richard says, IRV ignores and trashes valuable information
> willy nilly and still pretends to come up with a top notch
> winner. All of IRV's shortcomings can be traced back to this
> wasting of information.
It is not feasible to say that the one election method uses
more information than the other. All election methods use the
same information. They only interpret it differently. Election
methods only differ in how important they consider which part
of this information.
******
You wrote (15 May 2001):
> This is analogous to the fact that Condorcet methods violate
> the Reverse Symmetry Criterion.
The Condorcet criterion and the Reverse Symmetry Criterion
are not incompatible. There are good Condorcet methods that
meet Reversal Symmetry. Please read Blake Cretney's website
(http://www.fortunecity.com/meltingpot/harrow/124).
Markus Schulze
