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Shortcomings of the Condorcet Voting method

Condorcet Voting is probably the soundest ordinal method available today and it is favoured by many academics. Nevertheless it has its own shortcomings users should be aware of.

  • The Condorcet voting method is rather complex, difficult to explain and to grasp. Also, PARTECS™ does not implement its simplest version, Plain Condorcet, but implements the SSD Condorcet method, which is even more complex to explain;
  • Condorcet results cannot easily be converted in percentages, so are difficult to read for people used to the more common voting methods;
  • Condorcet is inferior to the Borda method in the case of sincere voters, since relevant information about the relative rating is lost (but this very fact increases the robustness against insincere votes);
  • Still there are cases where Condorcet is not 100% robust against insincere voters. Below is an example of such a case.

A case where Condorcet Voting is not robust

Consider this (sincere) ballot:

40: C
35: ABC
25: BAC

Here the winner is A, who beats both B (35/25) and C (60/40). However, if the B voters strategically refuse to rank A while the A voters sincerely rank B, that will let B steal the election from A since

40: C
35: ABC
25: BC

would give the defeats:

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

Removing the weakest defeat leaves B as the unbeaten candidate. Instant runoff and Borda method do not have this problem: voting C insincerely will go against the interest of B voters, since C will win, not B. However, it may be argued that these methods have even worse problems than Condorcet.

What about ties?

In elections with a small number of voters (typical of decision making process in small committees), ties are relatively frequent and must be managed in some way. There are various ways to solve the ambiguities, for instance the President may decide, or a different voting method can be used to see if the ambiguity disappears. Here is an example with four candidates A, B, C, D and these votes by a six members committee:

3: A C
3: B A

Nobody likes D, whereas three voters like A and three voters like B, but B voters also like A as a second choice, so we would expect A to win. However this is not the case using the Condorcet method, nor the Instant Runoff method. Let us consider first the Condorcet method tallying procedure. The defeats are:

A / D : 6/0
A / C : 6/0
C / D : 3/0
B / D : 3/0

Dropping the weakest defeats we still have a tie between A and B since they are both unbeaten. Still, it is clear that A must be winner, since it gets both first and second choices. The ambiguity is removed by the Borda method:

A: 15
B: 9
C: 6
D: 0

Condorcet Voting tends to give more ties than other methods. This is a good thing in general, since it is better to return a tie in dubious cases, leaving the decision to a human, than to return a wrong result. Now, let’s check if the Instant Runoff method gives a tie too:

This election required 2 rounds.
Round #1:
Removing D ...
3: A C -
3: B A -
Round #2:
Removing C ...
.TIE EXCEPTION: 

No winner can be established, since the algorithm cannot decide the weakest candidate between A and B.

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