## Condorcet voting

The Condorcet method is the most sophisticated voting method. Here, we will just give an informal description and a few examples. Condorcet method is a pairwise election method where each candidate runs against all the others separately, and one counts the “defeats” X/Y, i.e. the number of times candidates X beats candidates Y versus the number of times X is beaten by Y.

Defeats X/Y are ordered according their magnitude, the magnitude being the number of times candidates X beats candidates Y. For instance in this ballot with three candidates:

40: C 35: A B C 25: B A C

We have the following defeats:

B/C:60/40 (B beats C 60 times, C beats B 40 times, the magnitude is 60) A/C:60/40 (A beats C 60 times, C beats A 40 times, the magnitude is 60) A/B:35/25 (A beats B 35 times, B beats A 25 times, the magnitude is 35)

Since A beats all its opponents in separate races, it is the clear winner. In more complex situations, no candidate beats all the others. Then the counting proceeds by removing the weakest defeats until an unbeaten candidate is found, or we get a tie. For instance in this case:

40: C 35: A B C 25: B C

we get:

C/A: 65/35 B/C: 60/40 A/B: 35/25

and removing successively the weakest (smallest magnitude) defeat, we remain with the unbeaten candidate B which is the Condorcet winner. This is the algorithm describing the original Condorcet method, but actually PARTECS™ does not implement it (since it has some minor defects). PARTECS™ uses a state-of-the-art variation of Condorcet, the Cloneproof or Schwartz sequential dropping (SSD) Condorcet method.

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