On 06/09/2012 12:27 AM, Nicholas Buckner wrote:
Hello,
I am Nicholas Buckner. I developed an alternative method that takes
the Independence of Irrelevant Alternatives path over the Condorcet
path. It handles single-winner elections and multiple-winner
elections. I believe it satisfies a great number of criterions,
including difficult ones like Clone Independence and Participation.
I don't think this passes IIA.
Consider the following CSV:
25,1,2,3
40,2,3,1
35,3,1,2
i.e. 25 A>B>C, 40 B>C>A, 35 C>A>B.
According to your program, the ordering is {0,2} > 3 > 1 or B > C > A,
so B wins.
So let's remove irrelevant candidate C (3):
25,1,2
40,2,1
35,1,2
Now the ordering is {0,1} > 2 or A > B, as enforced by the Majority
criterion.
So eliminating irrelevant candidate C shifted the win from B to A.
The example above is engineered so that no matter who you pick in the
three-candidate election, one can remove an irrelevant alternative and
force someone else to win by the majority criterion.
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