# [EM] beatpath tiebreaking (question)

Markus Schulze markus.schulze at alumni.tu-berlin.de
Thu Sep 2 08:38:20 PDT 2004

```Dear Stephen,

you wrote (2 Sep 2004):
> My question is about tiebreaking in the Schulze method
> (beatpath method).
>
> Suppose the part before the tiebreak has yielded more
> than one potential winner, and at least one candidate
> has been eliminated.  Is there any reason why we can´t
> just iterate the method, the difference this time
> being that we do not allow paths through eliminated
> candidates?

This would violate monotonicity.

Example 1:

3 ABC
2 BCA
2 CAB
2 CBA

A:B=5:4
A:C=3:6
B:C=5:4

When the method is iterated then candidate B wins with
certainty.

Example 2:

One CAB voter is replaced by ACB.

3 ABC
1 ACB
2 BCA
1 CAB
2 CBA

A:B=5:4
A:C=4:5
B:C=5:4

Now, candidate A is elected with a probability of 4/9;
candidate B is elected with a probability of 2/9; and
candidate C is elected with a probability of 1/3.

Thus, ranking the candidate C lower increased his
probability of being elected.

Of course, it is arguable whether rather monotonicity or
decisiveness should be sacrificed in such a situation.

Markus Schulze

```