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Jameson,<br>
<br>
In response to Forest asking if there was a method that satisfies
something plus FBC you<br>
responded:<br>
<br>
<blockquote type="cite">Yes. 321 voting
<a class="moz-txt-link-rfc2396E" href="http://wiki.electorama.com/wiki/321_voting"><http://wiki.electorama.com/wiki/321_voting></a></blockquote>
<br>
<br>
<blockquote type="cite">
<h1 id="firstHeading" class="firstHeading">321 voting</h1>
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<p>3-level rated ballots. Of the 3 candidates with the most ratings,
take the 2 candidates with the most top-ratings, and then take the 1
pairwise winner among those. </p>
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</blockquote>
<br>
This fails FBC in the same way that ER-IRV(whole) does. From my 2 Nov.
EM post:<br>
<br>
<snip><br>
<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 <br>
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 <br>
and A wins.<br>
<br>
To meet FBC no voters should have any incentive to vote their sincere <br>
favourite below equal-top.<br>
<br>
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 <br>
top-rank their compromise candidate B, then the first-round scores are
<br>
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 <br>
result they prefer that they couldn't have got any other way, a clear
failure of the <br>
Favorite Betrayal Criterion (FBC).<br>
<br>
<snip><br>
<br>
Even if 321 voting met FBC with 3 candidates it it wouldn't with
more, because <br>
sincerely rating your sincere favourite Top instead of Bottom could
mean that your <br>
favourite displaces your compromise candidate from the top 3 most
rated candidates and <br>
goes on to lose when your compromise would have won.<br>
<br>
Chris Benham<br>
.<br>
<br>
<br>
Forest Simmons wrote (9 Nov 2011):<br>
<br>
I'm assuming "approval bad example" is typified by the implicit
approval order in the scenario<br>
<br>
49 C<br>
27 A>B<br>
24 B<br>
<br>
It seems to me that IF we (1) want to respect the Plurality Criterion,
(2) discourage "chicken" strategy, <br>
(3) stick with determinism, and (4) not take advantage of proxy ideas,
then our method must allow <br>
equal-rank-top and elect C in the above scenario, but elect B when B is
advanced to top equal with A in <br>
the middle faction:<br>
<br>
49 C<br>
27 A=B<br>
24 B<br>
<br>
Then if sincere preferences are<br>
<br>
49 C<br>
27 A>B<br>
24 B>A,<br>
<br>
the B faction will be deterred from truncating A. While if the B
supporters are sincerely indifferent <br>
between A and C, the A supporters can vote approval style (A=B) to get
B elected.<br>
<br>
Do we agree on this?<br>
<br>
Note that IRV (=whole) satisfies this, but now the question remains ...
is there a method that satisfies <br>
this which also satisfies the FBC?<br>
<br>
Forest<br>
<br>
<br>
<br>
<br>
<br>
<br>
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