[EM] Condorcet methods - should the cycle order always determine the result order?

Toby Pereira tdp201b at yahoo.co.uk
Mon Nov 3 17:00:22 PST 2014

```In a lot of the more preferred Condorcet methods (e.g. I think all of Schulze, Ranked Pairs, River, Kemeny), if you have, for example, an A>B>C>A cycle, then if, say, A wins then B will automatically finish second and C third (if B wins, C will be second etc.). But you could have a similar number of A>B>C, B>C>A and C>A>B ballots but then also a lot of A>C>B ballots, meaning that in some sense C looks better than B. But as long as this doesn't break the cycle and A wins, then B will still finish second. I think the following example does it:

11: A>B>C
10: B>C>A
10: C>A>B
8: A>C>B

A beats B 29:10
C beats A 20:19
B beats C 21:18

I'm not saying these methods are wrong for doing this, but there is an intuitive sense in which C is arguably a better choice than B. So is it:

1. There is a reasonable Condorcet method that would rank them A>C>B
2. The intuition that C should finish ahead of B is poorly thought out.
3. It is in a sense reasonable to think that C should finish ahead of B, but doing so would cause a method to fail certain criteria and end up worse as a result.
4. Other?
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