Mike Ossipoff wrote (2 Nov 2011):
Kevin--
You wrote:
ER-IRV(whole) doesn't satisfy FBC. You may need to demote your
favorite in order
to get a preferable elimination order.
[endquote]
How? Say that there's a particular candidate whom you need to have win.
You can give him a vote by downrating your favorite in order to get
hir eliminated soon,
so that your ballot will give a vote to the compromise. But you could
also just give the
compromise an immediate vote, by ranking hir in 1st place. Why would
you need to do otherwise
in order to help hir win?
Here is Kevin Venzke's example from a June 2004 EM post:
6: A
3: C>B
2: C=B (sincere is C>B)
2: B
The method is ER-IRV(whole). If the 2 C=B voters sincerely vote C>B then
the first-round scores are
A6, C5, B2. B is eliminated and A wins.
As it is the first-round scores are A6, C5, B4. B is still eliminated
and A wins.
To meet FBC no voters should have any incentive to vote their sincere
favourite below equal-top.
6: A
3: C>B
2: B>C (sincere is C>B)
2: B
But if those 2 voters (sincere C>B, was C=B) do that and strictly
top-rank their compromise candidate B,
then the first-round scores are A6, B4, C3. C is eliminated and B
wins: B7, A6.
By down-ranking their sincere favourite those 2 voters have gained a
result they prefer that they couldn't have
got any other way, a clear failure of the Favorite Betrayal Criterion (FBC).
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-June/013434.html
Chris Benham
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