# [EM] Ties (was Condorcet Voting)

Alex Small asmall at physics.ucsb.edu
Tue Jan 7 17:58:36 PST 2003

```Markus Schulze said:
> I prefer to say: "The method should be prepared to declare a
> winner for everything except for situations where otherwise
> Anonymity, Neutrality, Monotonicity, Independence from Clones
> or Local Independence from Irrelevant Alternatives is violated."

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 principle can help us identify situations in which two candidates
must either be tied, or neither candidate wins, irrespective of the method
under consideration.

Example:

40 A>C>B
40 B>C>A
10 C>A>B
10 C>B>A

Suppose that the method selects A in this case.  If all voters swap A and
B on their ballots we still have the same situation.  Our symmetry
principle demands that B win, but our original supposition demands that A
wins.  We hence conclude one of two things.  Either

1) C wins (e.g. Condorcet, top 2 voting)
or
2) A and B are tied for victory (e.g. IRV, plurality)

Alex

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