Kathy Dopp wrote:
Thanks Kristofer for the explanations. Do you know a good place that
discusses the Ranked Pairs method of resolving cycles, or all the
methods of resolving cycles? I would still like an example of a
spoiler in Condorcet no matter how unlikely if possible. Thank you.
Wikipedia explains Ranked Pairs well enough:
http://en.wikipedia.org/wiki/Ranked_Pairs
It doesn't explain River, because that method is less known. In both
Ranked Pairs and River, you first sort the majorities ("A beats B") by
magnitude, greatest first.
In Ranked Pairs, you then go down the list, "locking" majorities except
those that lead to a contradiction with what you've already locked (e.g.
if you lock "A beats B" and "B beats C", you can't lock "C beats A"),
and at the end you have an ordering, and the candidate at the top of
this ordering is the winner.
In River, you do the same, except that you're also forbidden from
locking a victory against someone who has already had a victory locked
against him (e.g. "A beats B", then you can't lock "C beats B"). The
root of the tree diagram (base of the river) is the winner.
As for a spoiler in your terms, consider this very simple election
(showing the Condorcet paradox):
10: A>B>C
10: B>C>A
11: C>A>B
If the method picks A, then B is a spoiler for C, because removing B
leads C to win:
21: C>A
10: A>C
If the method picks B, then C is a spoiler for A, because removing C
leads A to win:
21: A>B
10: B>A
If the method picks C, then A is a spoiler for B, because removing A
leads B to win:
20: B>C
11: C>B.
That should work for any election method that reduces to a majority vote
when there are only two candidates, because, as I've shown, it doesn't
matter which candidate is elected - you can still show there's a spoiler.
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