[EM] Ties (was Condorcet Voting)

Alex Small asmall at physics.ucsb.edu
Tue Jan 7 20:01:52 PST 2003

Markus Schulze said:
> This "symmetry principle" is usually called "neutrality".
> "Anonymity" means that swapping voters should not change
> the result of the elections.

Thanks for the explanation.

> However, consider the following example:
>    40 voters vote A > B > C > D > E.
>    40 voters vote B > C > D > A > E.
>    40 voters vote C > A > D > E > B.
> Although this is not a symmetric situation, the used election
> method must violate Neutrality or Anonymity or Decisiveness or
> Local Independence from Irrelevant Alternatives in this example.

I'm not sure I see why.  And what is the local version of Independence
from Irrelevant Alternatives?  I'm aware of the standard version, and the
version that says adding a new candidate should not change the outcome
unless the new candidate can defeat the old winner pairwise.

I do see that A, B, and C all defeat D and E pairwise, and that A>B>C>A. 
If we got rid of D and E we'd have a situation that's symmetric under
rotations (A->B, B->C, C->A, where -> means "is replaced with").  I
suppose that if we use the modified IIA that I'm aware of we can make this
into such a symmetric situation.  Also, those rotations can be achieved
with a series of pairwise swaps, so I can see how one might work it out to
invoke neutrality here.

Anyway, I'm curious to learn more about how you can deduce that one of
those criteria must be flunked in this scenario.


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