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<span style="right: auto;" id="yui_3_2_0_16_1320291528046201"><br>
Mike Ossipoff wrote (2 Nov 2011):<br>
<br>
<blockquote type="cite"><span style="right: auto;"
id="yui_3_2_0_16_1320291528046201">Kevin--<br>
<br>
You wrote:<br>
<br>
ER-IRV(whole) doesn't satisfy FBC. You may need to demote your favorite
in order<br>
to get a preferable elimination order.<br>
<br>
[endquote]<br>
<br>
How? Say that there's a particular candidate whom you need to have win.
<br>
<br>
You can give him a vote by downrating your favorite in order to get hir
eliminated soon,<br>
so that your ballot will give a vote to the compromise. But you could
also just give the<br>
compromise an immediate vote, by ranking hir in 1st place. Why would
you need to do otherwise<br>
in order to help hir win?<br>
</span></blockquote>
<br>
Here is Kevin Venzke's example from a June 2004 EM post:<br>
<br>
6: A<br>
3: C>B<br>
2: C=B (sincere is C>B)<br>
2: B<br>
<br>
The method is ER-IRV(whole). If the 2 C=B voters sincerely vote C>B
then the first-round scores are<br>
A6, C5, B2. B is eliminated and A wins.<br>
<br>
As it is the first-round scores are A6, C5, B4. B is still eliminated
and A wins.<br>
<br>
To meet FBC no voters should have any incentive to vote their sincere
favourite below equal-top.<br>
<br>
</span><span style="right: auto;" id="yui_3_2_0_16_1320291528046201">6:
A<br>
3: C>B<br>
2: B>C (sincere is C>B)<br>
2: B<br>
<br>
But if those 2 voters (sincere C>B, was C=B) do that and strictly
top-rank their compromise candidate B,<br>
then the first-round scores are A6, B4, C3. C is eliminated and B
wins: B7, A6.<br>
<br>
By down-ranking their sincere favourite those 2 voters have gained a
result they prefer that they couldn't have<br>
got any other way, a clear failure of the Favorite Betrayal Criterion
(FBC).<br>
<br>
<a class="moz-txt-link-freetext" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-June/013434.html">http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-June/013434.html</a><br>
<br>
Chris Benham<br>
</span>
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