[EM] Ties (was Condorcet Voting)

[Markus Schulze]

Dear Alex,

you wrote (7 Jan 2003):
> The situations giving rise to ties can be derived from a symmetry
> principle (without definitions I don't know whether your criteria
> amount to the same): If candidate A wins, and all voters then
> interchange candidates A and B in their rankings, candidate B should
> win.  If candidate C wins, and all voters then interchange candidates
> A and B in their rankings, candidate C should still win.

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

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.

Markus Schulze

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