[EM] ER-IRV(whole) fails FBC (was "no subject")

[C.Benham]

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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