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<p>Ted,<br>
<br>
Why does your example have the "B>F>C" voters divided into
two groups?<br>
<br>
<blockquote type="cite">
<div>04: B > F > C</div>
<div>25: B > F > C</div>
</blockquote>
Is there a typo?<br>
<br>
Chris Benham<br>
</p>
<div class="moz-cite-prefix">On 4/06/2019 7:12 am, Ted Stern wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAHGFzOSftj62pYBTAo=ir4eunSvH_-81M_=AC_R7SkRxuMQMYQ@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">
<div dir="ltr">Hi Chris,
<div><br>
</div>
<div>You are <i>so</i> close to Relevant Ratings in your
proposal. I just want to point out how close and why the
one missing factor is important.</div>
<div><br>
</div>
<div>You write:</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">My idea (originally my
misunderstanding of Ted's Relevant Ratings method) is that
if at some (quasi-Bucklin) IBIFA round after the first (but
before we have reached just counting total approval scores)
we find more than one candidate Q qualified to win then
instead of (Bucklin-like) giving the win to the Q with the
highest score in that round we elect the Q with the highest
score in the round before.</blockquote>
<div><br>
</div>
<div>Where this differs from RR is as follows:</div>
<div>
<ul>
<li>For each candidate Q qualified to win IBIFA, their
total ballots from highest rating down to the current
round rating exceed some highest total approval on
complementary ballots excluding Q down to that rating.
Say that the highest total approval on such
complementary ballots is TC.</li>
<li>Your modified IBIFA just looks at the Q totals from
the previous round.</li>
<li>My Relevant Ratings method looks only at the previous
round Q totals that are larger than their respective TC
opposition <i>in the current round!</i></li>
</ul>
<div>In most situations, the Q you find with your modified
IBIFA would be the same. But it is possible that they
might not be. Let's carefully construct a 4 slot example,
working backwards:</div>
</div>
<div><br>
</div>
<div>Say we want at least 3 candidates, ratings 3 = Excellent
("A"), 2 = Very Good ("B"), 1 = OK ("C"), 0 = disapproved
("D").</div>
<div>
<ul>
<li>round 1 totals (scores at 3) of A48, B49, with other
candidates below that (and not qualifying in any method)</li>
<li>round 2 totals (scores at 2 and above) of A52, B51,
with other candidates below that (and not qualifying in
any method)</li>
<li>round 3 totals (scores above 0) of A52, B52, and C
> 54, with other candidates below that (only C
qualifying under MCA or MJ)</li>
<li>In round 1, we want A48's most approved complementary
candidate to be B or C with at least 49</li>
<li>In round 1, we want B49's most approved complementary
candidate to be A or C with at least 50</li>
<li>In round 2, we want A52's most approved complementary
candidate to be C with at most 47</li>
<li>In round 2, we want B51's most approved complementary
candidate to be C with exactly 50.</li>
<li>We want A and B's total approval to be less than 50%,
so there must be at least 105 ballots. So we expect at
least 5 irrelevant ballots.</li>
</ul>
<div>Under this scenario, C will win both MCA and MJ in
round 3. B will win in modified IBIFA, as round 2
qualifier with the highest round 1 score.</div>
</div>
<div><br>
</div>
<div>But A will win both original IBIFA and relevant rating
because while both A and B qualify in round 2, only A's
round 1 score exceeds A's round 2 complementary approval
winner C's approval of 47, while B's round 2 score of 49 is
below B's complementary approval winner C's score of 50.</div>
<div><br>
</div>
<div>Here is a set of ballots that I think satisfies those
constraints.</div>
<div><br>
</div>
<div>02: A > B > C</div>
<div>24: A > D > C</div>
<div>22: A > E > C</div>
<div><b>04: B > F > C</b></div>
<div><b>25: B > F > C</b></div>
<div>21: B > G > C</div>
<div>02: E > D=A > C</div>
<div>02: F > E=A > H</div>
<div>06: G > F > H</div>
<div><br>
</div>
<div>Round 1: A48 vs complementary approval winner C with 51,
B49 vs complementary approval winner C with 50. Neither
qualifies</div>
<div>Round 2: A52 vs complementary approval winner C with 47,
B51 vs complementary approval winner C with 48. Both
qualify in IBIFA-derived methods, but not in MCA or MJ with
less than 50% of ballots</div>
<div>Round 3: C99 passes 50% threshold, while A and B still
less than 50% threshold for tiebreaker.</div>
<div><br>
</div>
<div>A52 pairwise beats B51 and is the Condorcet winner
(Please check my arithmetic!)</div>
<div><br>
</div>
<div>The main point here is that while both IBIFA, modified
IBIFA and Relevant Ratings can avoid electing a non-CW
candidate C, the lowest level compromise approval winner
elected by standard median ratings, your modified IBIFA will
fail to choose the CW while relevant ratings and original
IBIFA will find that candidate.</div>
<div><br>
</div>
<div>You suggestion of using undefeated tied-at-top winner
first, then falling back to some IBI method, is an
interesting one, however.</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sun, Jun 2, 2019 at 8:16
PM Chris Benham <a href="mailto:cbenhamau@yahoo.com.au"
moz-do-not-send="true">cbenhamau@yahoo.com.au</a>
[RangeVoting] <<a
href="mailto:RangeVoting@yahoogroups.com"
moz-do-not-send="true">RangeVoting@yahoogroups.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex"><br>
IBIFA was conceived as an Irrelevant Ballot independent
version of <br>
Bucklin, with the added benefits of having a less<br>
severe truncation and/or compress at the top incentive and
also being <br>
much more (and absolutely more) Condorcet-consistent.<br>
<br>
Inspired by an example from Ted Stern of?? his "Relevant
Ratings" method <br>
(which I gather is IBIFA<br>
modified to more closely resemble Majority Judgement), I've
come to <br>
believe that if ratings ballots<br>
with four or more slots (or grades) are used then a simple
rule change <br>
can make the method still<br>
more Condorcet-consistent?? at no cost.<br>
<br>
My idea (originally my misunderstanding of Ted's Relevant
Ratings <br>
method) is that if at some<br>
(quasi-Bucklin) IBIFA round after the first (but before we
have reached <br>
just counting total approval scores)<br>
we find more than one candidate Q qualified to win then
instead of?? <br>
(Bucklin-like) giving the win to the Q<br>
with the highest score in that round we elect the Q with the
highest <br>
score in the round before.<br>
<br>
A link to the electowiki entry on my original version of
IBIFA:<br>
<br>
<a href="https://wiki.electorama.com/wiki/IBIFA"
rel="noreferrer" target="_blank" moz-do-not-send="true">https://wiki.electorama.com/wiki/IBIFA</a><br>
<br>
And the EM post in which I first suggested it:<br>
<a
href="http://lists.electorama.com/pipermail/election-methods-electorama.com//2010-May/091807.html"
rel="noreferrer" target="_blank" moz-do-not-send="true">http://lists.electorama.com/pipermail/election-methods-electorama.com//2010-May/091807.html</a><br>
<br>
Here is the description of the revised 4-slot version,
referring to <br>
A-B-C-D grading ballots:<br>
<br>
*Voters fill out 4-slot ratings ballots, say with A B C D
grades.<br>
??Default rating/grade is D, signifying least preferred and
unapproved.<br>
<br>
Any grade above D is interpreted as Approval.<br>
<br>
If any candidate/s X has an A score that is higher than any
other <br>
candidate's approval<br>
score on ballots that?? don't give X an A grade, elect the X
with the <br>
highest A score.<br>
<br>
Otherwise, if any candidate/s X has a A+B score that is
higher than any <br>
other candidate's<br>
approval score on ballots that don't give X an A or B grade,
elect the X <br>
with the highest<br>
??A score.<br>
<br>
Otherwise, elect the candidate with the highest Approval
score.*<br>
<br>
??35: A<br>
??10: A=B<br>
??30: B>C<br>
??25: C<br>
<br>
With my Condorcet hat on, in this example I've said that B
is the <br>
weakest candidate.?? A bit unfortunately<br>
IBIFA here elects B, but FBC is a bit more "expensive" than
Condorcet, <br>
and so does Winning Votes and Margins.<br>
Bucklin elects the most approved candidate C, but at least B
both <br>
pairwise beats and is more top-rated than C.<br>
<br>
Ted Stern's eye-opening example:<br>
<br>
49: A > B<br>
03: B > A > C<br>
10: D > B > C<br>
38: E > F > C<br>
05: G > D > H<br>
<br>
The Condorcet winner is A.?? Ted's Relevant Ratings and my
revised 4+ <br>
slot IBIFA elect A.<br>
My original version of IBIFA?? and?? Median Ratings methods
such as <br>
Bucklin and MJ elect B.<br>
<br>
Top Ratings (A) scores:?? A49,?? E38,?? D10,?? G5,?? B3,??
C0<br>
A + B scores:???????????????????????????????????? A51,??
E38,?? D15,?? G5,?? B62,?? C0<br>
<br>
In the second round A and B both "qualify".???? On ballots
that don't?? <br>
give A one of the two<br>
top grades the most approved candidate is E with a score of
38, lower <br>
than 51 so A qualifies.<br>
<br>
On ballots that don't give B one of the top two grades the
most approved <br>
candidate is again<br>
E with again a score of 38, lower than 62 so B qualifies. In
the "round <br>
before" A?? has the<br>
higher score (49 versus 3) so revised IBIFA gives the win to
A.<br>
<br>
A>B 49-13,???? A>E 51-38,?? A>D 51-15,?? A>G
51>5, A>C?? 51-48.<br>
<br>
At the cost of being a quite a bit more complicated,?? IBIFA
can be <br>
combined?? with Kevin Venzke's<br>
special "tied-at-the-top" rule used in his "Improved
Condorcet Approval" <br>
method to make<br>
the method even more Condorcet-consistent?? (possibly as
much as it <br>
possible for a FBC method<br>
to be).<br>
<a
href="https://wiki.electorama.com/wiki/Improved_Condorcet_Approval"
rel="noreferrer" target="_blank" moz-do-not-send="true">https://wiki.electorama.com/wiki/Improved_Condorcet_Approval</a><br>
<br>
*If one candidate T pairwise beats all others by the
tied-at-the-top <br>
rule then T wins. If there is no<br>
such T then we elect the (revised) IBIFA winner.<br>
If there is more than one T then we elect the one that
"qualifies" <br>
(according to IBIFA) in the earliest<br>
IBIFA round. If there is more than one of these, then elect
the one with <br>
the highest score in the previous<br>
round if there was one, otherwise simply with the highest
top-ratings <br>
score.*<br>
<br>
4: A>B<br>
6: A>C<br>
6: B>A<br>
2: B>C<br>
3: C>B<br>
<br>
B is the narrow Condorcet winner:?? B>A 11-10,?? B>C??
12-9. No ballots <br>
have any candidates tied at the top,<br>
so B wins.?? Plain IBIFA elects A, which is positionally
dominant: Top <br>
scores: A10, B8, C2. Approval scores: A16,?? B13,?? C10.<br>
<br>
For the time being the name I suggest?? for?? this is
Quasi-Condorcet IBIFA.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
<br>
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------------------------------------<br>
Posted by: Chris Benham <<a
href="mailto:cbenhamau@yahoo.com.au" target="_blank"
moz-do-not-send="true">cbenhamau@yahoo.com.au</a>><br>
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