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<blockquote type="cite">46: A<br>
03: A>B<br>
25: C>B<br>
23: D>B<br>
<br>
97 ballots (majority threshold = 48)<br>
<br>
(If you want MJ-style multi-slot ratings ballots, assume that
all the voters have given their favourite the highest possible<br>
rating and those that rated B above bottom all gave B the same
middle rating and that truncating here signifies giving the<br>
lowest possible rating).<br>
<br>
MJ and Bucklin both rightly elect A. IBIFA and IRV also
elect A. A is the Condorcet winner: A>B 49-48, A>C 49-25,
A>D 49-23,<br>
A>E 49>0.<br>
<br>
A is the most Top-rated candidate: A49, C25, D23, B0, E0.<br>
<br>
So suppose the votes are counted and it is announced that A has
won, but just before this is officially and irrevocably
confirmed<br>
someone pipes up, "Hang on a minute, we found a few more
ballots!" (Maybe they are late-arriving postal votes that had
been<br>
thought lost.) <br>
<br>
These 3 new ballots are inspected and found that all they do is
give the highest possible rating to E, a candidate with no
support<br>
on any of the other 97 ballots. What do we do now? Laugh and
carry on with confirming A as still the winner? No.<br>
<br>
46: A<br>
03: A>B<br>
25: C>B<br>
23: D>B<br>
03: E<br>
<br>
100 ballots (majority threshold = 51)<br>
<br>
Now MJ and Bucklin and any other Median Ratings method elects
B. All methods that I find acceptable elect A both with<br>
and without those 3E ballots. </blockquote>
<br>
Steve,<br>
<br>
On 12/06/2019 6:34 am, steve bosworth wrote:<br>
<blockquote type="cite"><span><span
style="mso-bidi-font-weight:bold">Your concept of
“irrelevant ballots” seems to be central to your IBIFA
method of counting.<span style="mso-spacerun:yes">
</span>Do you also see this concept as conflicting with my
own assumption that in a workable and ideal democracy, each
citizen’s vote would count equally – one-person-one-vote?</span></span></blockquote>
<br>
Of course not. But "count" only has some positive sensible
meaning if we are talking about counting towards a result that the
voter prefers <br>
(as expressed on the voter's ballot) over what would have resulted
if the voter had stayed home.<br>
<br>
<blockquote type="cite"><span><span
style="mso-bidi-font-weight:bold"><span
style="mso-spacerun:yes">
</span>No citizen’s vote would be needlessly wasted either
quantitatively or qualitatively.</span></span></blockquote>
Refreshing our memories on what you mean by that:<br>
<blockquote type="cite">I see a citizen’s vote as being wasted
quantitatively to the degree that it fails equally to help one
of their most trusted candidates to win. A citizen’s vote is
wasted qualitatively to the degree that it instead helps to
elect a candidate whom they judge less fit for office, rather
than an available candidate judged to be more fit.
</blockquote>
<br>
If we cross out "most trusted" and replace it with 'preferred (for
whatever reason)', that is fine.<br>
<br>
<blockquote type="cite"><span><span
style="mso-bidi-font-weight:bold"><span
style="mso-spacerun:yes"></span>This also means that
whenever possible, the single-winner in an election will
have received at least 50% plus one of all the citizens’
votes cast.</span></span></blockquote>
<br>
No it doesn't. Why doesn't it mean that the winner should
preferably come from the Smith set (be the Condorcet winner or
come from the smallest<br>
set S of candidates that pairwise beat all the outside-S
candidates)?<br>
<br>
<blockquote type="cite"><span>In contrast to MJ, the trouble in my
view with IBIFA is that it gives more weight to higher
preferences than lower preferences, e.g. a citizen’s Top-rated
vote for a candidate is given more weight than a citizen’s
Middle-rated vote for a different candidate.</span></blockquote>
<br>
Yes, I can imagine the voters would hate that.<br>
<br>
<blockquote type="cite"><span><span style="mso-spacerun:yes"></span>This
leads to the demeaning identification of some citizens votes
as being “irrelevant”. </span></blockquote>
<br>
</div>
<div class="moz-cite-prefix">MJ brilliantly avoids that by
"counting" those ballots so that they cause the winner to change
from A (perhaps a Condorcet winner) to B,<br>
when those ballots express indifference between A and B.<br>
<br>
<blockquote type="cite"><span> It also prompts dishonest voting
(tactical voting) because a Top-rating counts more than a
Middle-rating when using IBIFA.
</span></blockquote>
<br>
I've already explained, and gave an example, that MJ has a much
stronger truncation incentive than does IBIFA.<br>
<br>
45: A>B<br>
30: B<br>
25: C<br>
<br>
IBIFA elects A (the CW: A>B 45-30, A>C 45-25). <br>
<br>
Imagine how happy the A>B voters are that MJ doesn't "<span>give
more weight to higher preferences than lower preferences" and<br>
ensures </span><span><span><span
style="mso-bidi-font-weight:bold">that "whenever possible,
the single-winner in an election will have received at least
50% plus one of all the citizens’ votes cast."<br>
<br>
MJ elects B. Obviously MJ punished the A>B voters for
not "dishonestly" simply voting A, and IBIFA didn't.<br>
<br>
IBIFA is much more Condorcet-ish than MJ. In the example no
Condorcet method would punish those A>B voters like MJ
does.<br>
<br>
That is one of the reasons that "some people" </span></span></span><span><span><span
style="mso-bidi-font-weight:bold"><span>continue to propose
the "less than satisfactory Condorcet methods."<br>
<br>
I think you'll find that the Balinski claim that MJ is so
wonderful at resisting tactical voting is mainly based on
the comparison with<br>
Average Rating (now aka Score Voting) which gives voters a
very strong incentive to just submit approval ballots
(i.e. only use the<br>
top and bottom grades).<br>
<br>
MJ just gives voters a weaker (but still quite strong)
incentive to do that. I would say that in general the
best Condorcet<br>
methods plus IRV plus IBIFA are all somewhat better than
MJ at not penalising voters for voting sincerely.<br>
<br>
Chris Benham<br>
<br>
</span></span></span></span></div>
<div class="moz-cite-prefix"><span><span><span
style="mso-bidi-font-weight:bold"></span></span></span><br>
<br>
<br>
On 12/06/2019 6:34 am, steve bosworth wrote:<br>
</div>
<blockquote type="cite"
cite="mid:AM6PR06MB47247C0E64DFC44367229E74B6ED0@AM6PR06MB4724.eurprd06.prod.outlook.com">
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<span>
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</p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
<span style="mso-bidi-font-weight:bold">Hi Chris,</span></p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
<span style="mso-bidi-font-weight:bold">Your concept of
“irrelevant ballots” seems to be central to your IBIFA
method of counting.<span style="mso-spacerun:yes">
</span>Do you also see this concept as conflicting with my
own assumption that in a workable and ideal democracy,
each citizen’s vote would count equally –
one-person-one-vote?<span style="mso-spacerun:yes">
</span>No citizen’s vote would be needlessly wasted either
quantitatively or qualitatively.
<span style="mso-spacerun:yes"> </span>This also means
that whenever possible, the single-winner in an election
will have received at least 50% plus one of all the
citizens’ votes cast.</span></p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
<span style="mso-bidi-font-weight:bold">If we do disagree,
how to you justify IBIFA’s violations of the above
democratic principles, especially when MJ provides a
simpler and more meaningful method which guarantees that
its elections conform to the above democratic principles?</span></p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
In contrast to MJ, the trouble in my view with IBIFA is that
it gives more weight to higher preferences than lower
preferences, e.g. a citizen’s Top-rated vote for a candidate
is given more weight than a citizen’s Middle-rated vote for
a different candidate.
<span style="mso-spacerun:yes"> </span>This leads to the
demeaning identification of some citizens votes as being
“irrelevant”. It also prompts dishonest voting (tactical
voting) because a Top-rating counts more than a
Middle-rating when using IBIFA.
</p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
<span style="font-size:12.0pt; mso-fareast-font-family:
"Times New Roman"; mso-bidi-font-family:Arial">In
contrast to IBIFA, please n</span><span
style="mso-bidi-font-weight:bold">ote that MJ gives the
same weight to each of the different grades that might be
given to the its winner. Only one of the grades given by a
voter can be added to the total which defines the winner’s
majority.<span style="mso-spacerun:yes">
</span>An Excellent only has the priority of being looked
for first.</span></p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
<span style="mso-bidi-font-weight:bold">What do you think of
the following possible explanation of how you have been
needlessly lead to adopt your idea of “irrelevant
ballots”.<span style="mso-spacerun:yes">
</span></span>As I see it, perhaps this flaw in IBIFA
stems from a Condorcet habit of minds which mistakenly
assumes that the primary electoral concern is to find the
candidate who is preferred, head to head, over each of the
other candidates.<span style="mso-spacerun:yes">
</span>The voter is only to focus on comparing and ranking
the particular candidates in the race.<span
style="mso-spacerun:yes">
</span>These comparisons and rankings presumably proceed
upon the qualities intuitively identified by the voter as
needed for an ideal candidate for the office being sought.<span
style="mso-spacerun:yes">
</span>Alternatively, it would proceed most rationally after
the voter analyzes and clarifies the hierarchy of such ideal
qualities.
</p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
In contrast, Balinski suggests that each candidate should,
in the light of these qualities, be given one of the 6
grades regarding their suitability for office (Excellent,
Very Good, Good, Acceptable, Poor, or Reject).<span
style="mso-spacerun:yes">
</span>However, a follower of Condorcet does not grade the
candidates but simply proceeds to ranking them.<span
style="mso-spacerun:yes">
</span>Next he uses a Condorcet method to see if a Condorcet
winner exists.<span style="mso-spacerun:yes">
</span>However, this is less than satisfactory because we
all know that each Condorcet method sometimes fails to find
such a winner, let alone a winner who has received an
absolute majority of the preferences.</p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
Given that MJ guarantees the election of the candidate who
is judged to be most fit for the office by an absolute
majority of the grades given to this winner, (i.e. grades
equal to or higher than the highest median-grade given to
any of the candidate), why does anyone continues to propose
the less than satisfactory Condorcet methods?</p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt">
<span style="mso-bidi-font-weight:bold">Finally, you have
also said that you do not understand MJ's procedure for
breaking ties.
<span style="mso-spacerun:yes"> </span><span
style="mso-spacerun:yes"> </span>Please let me try to
clarify this again:</span></p>
<p style="margin: 0in 0in 10pt; line-height: 115%;
font-family: "Calibri",sans-serif; font-size:
11pt;mso-margin-top-alt:auto;margin-bottom:19.5pt;
line-height:normal;background:white">
<span style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">In
a single-office election, the Majority Judgment (MJ)
winner is the one who has received grades from an absolute
majority of all the voters that are equal to, or higher
than, the highest <i>median-grade</i> given to any
candidate. This median-grade is found as follows:</span></p>
<ul style="margin-bottom: 0in">
<li><span
style="font-size:12.0pt;mso-fareast-font-family:"Times
New Roman";mso-bidi-font-family:
Arial">Place all the grades, high to low, top to bottom,
in side-by-side columns, the name of each candidate at
the top of each of these columns.</span></li>
<li><span
style="font-size:12.0pt;mso-fareast-font-family:"Times
New Roman";mso-bidi-font-family:
Arial">The median-grade for each candidate is the grade
located half way down each column, i.e. in the middle if
there is an odd number of voters, the lower middle if
the number is even.</span><br>
<br>
<span
style="font-size:12.0pt;line-height:115%;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">If
more than one candidate has the same highest
median-grade, the MJ winner is discovered by temporarily
removing (one-by-one) any grades equal in value to the
current highest median grade from each tied candidate’s
total until only one of the previously tied candidates
currently has the highest remaining median-grade.</span><br>
<br>
What do you think?<span style="mso-spacerun:yes"> </span>What
telling criticism of MJ can be made?<br>
<br>
<span style="mso-bidi-font-weight:bold">I look forward to
the next step in our dialogue.</span><br>
<br>
<span style="mso-bidi-font-weight:bold">Steve</span></li>
</ul>
<br>
</span></div>
</blockquote>
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