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<p>Steve,<br>
<br>
Earlier I responded briefly to your 4-point list: yes, yes, not
possible,yes.<br>
<br>
To expand a bit, MJ is a Median Ratings method with a relatively
complicated tie-breaker, justified by I've no idea what.<br>
<br>
Bucklin is likewise a Median Ratings method and will usually give
the same winner, but the "tie breaker" is simple.<br>
</p>
<p><br>
</p>
<p>An example I recently came up with to critique another
Bucklin-like proposal:<br>
<br>
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. <br>
</p>
<p><br>
To expand a bit my earlier response to your point 4, I think it's
highly desirable for a method to meet FBC (the Favorite Betrayal<br>
Criterion), especially in the current US situation.<br>
</p>
<p><br>
</p>
<p>Potentially popular candidates the mainstream media and political
establishment doesn't like can be sunk by fake polls and<br>
the voters' fear of some perceived Greater Evil. <br>
<br>
They can say "Forget candidate X! X is only polling at 1 or 2%.
That justifies us ignoring X. If you vote for X you'll just be
helping<br>
Greater Evil win!". And their prophesy that X won't be a viable
candidate tends to be self-fulfilling.<br>
<br>
But if the used voting method meets FBC, the voter can in response
reply (or at least think) "Ok, maybe I have to top-rate some<br>
'realistic' Compromise candidate to maximise the chance of
beating Greater Evil, but I like X and I know that it can't
possibly hurt <br>
me to also top-rate X so I will."<br>
<br>
If the method meets FBC no voter who knows and understands that
can be cowed into not voting their sincere favorite at least <br>
equal-top. FBC is met by Approval, MJ and the currently proposed
version of Bucklin, and IBIFA.<br>
<br>
Of those I judge IBIFA to be by far the best. IRV and all
Condorcet methods unfortunately fail FBC.<br>
<br>
For a method that doesn't meet FBC, I consider meeting the
Condorcet criterion to be desirable. Unfortunately all Condorcet <br>
methods are (to greatly varying degrees) vulnerable to Burial
strategy, i.e. insincerely down-ranking to make a higher (usually<br>
top) ranked candidate win.<br>
<br>
In my humble opinion the best of the methods that are invulnerable
to Burial is IRV.<br>
</p>
<p><br>
Chris Benham<br>
<br>
</p>
<div class="moz-cite-prefix">On 21/05/2019 5:16 am, steve bosworth
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:AM6PR06MB5795BF1BA275EFCFD1300EDDB6060@AM6PR06MB5795.eurprd06.prod.outlook.com">
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<span style="font-size:12.0pt;mso-bidi-font-family:
Calibri;mso-bidi-theme-font:minor-latin">Re: Best Single-
Winner Method</span></p>
<p style="margin: 0in 0in 8pt; line-height: 107%; font-family:
"Calibri",sans-serif; font-size:
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<span style="font-size:12.0pt;mso-bidi-font-family:
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</span></p>
<p style="margin: 0in 0in 8pt; line-height: 107%; font-family:
"Calibri",sans-serif; font-size:
11pt;margin-bottom:0in; margin-bottom:.0001pt; line-height:
normal">
<span style="font-size:12.0pt;mso-bidi-font-family:
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<p style="margin: 0in 0in 8pt; line-height: 107%; font-family:
"Calibri",sans-serif; font-size:
11pt;margin-bottom:0in; margin-bottom:.0001pt; line-height:
normal">
<span style="font-size:12.0pt;mso-fareast-font-family:
"Times New
Roman";mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:#323130;border:none
windowtext 1.0pt;mso-border-alt:none windowtext 0in;
padding:0in">Sennet Williams,<span style="mso-spacerun:yes">
</span>Forest Simmons, Robert Bristow-Johnson, Abd dul Raman
Lomax, and </span><span
style="font-size:12.0pt;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:#323130">Chris
Benham have recently addressed each others’ claims about
IRV, 3-slot Methods, IBIFA, and Asset.<span
style="mso-spacerun:yes"> </span>This discussion prompts
me to request some help later after I have clarified several
issues.</span></p>
<p style="margin: 0in 0in 8pt; line-height: 107%; font-family:
"Calibri",sans-serif; font-size:
11pt;margin-bottom:0in; margin-bottom:.0001pt; line-height:
normal">
<span style="font-size:12.0pt;mso-bidi-font-family:
Calibri;mso-bidi-theme-font:minor-latin;color:#323130"></span></p>
<p style="margin: 0in 0in 8pt; line-height: 107%; font-family:
"Calibri",sans-serif; font-size:
11pt;margin-bottom:0in; margin-bottom:.0001pt; line-height:
normal">
<span style="font-size:12.0pt;mso-bidi-font-family:
Calibri;mso-bidi-theme-font:minor-latin;color:#323130">Firstly,
please correct me if I am mistaken but currently I am
assuming that
<span style="mso-spacerun:yes"> </span>we all would ideally
want the Best Single-Winner Method:</span><span
style="font-size:12.0pt;mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin"></span></p>
<div style="color: rgb(0, 0, 0); font-family:
Calibri,Helvetica,sans-serif; font-size: 14pt;">
<ol style="margin-bottom: 0in">
<li><span style="font-size:12.0pt;mso-bidi-font-family:
Calibri;mso-bidi-theme-font:minor-latin;color:#323130">To
be simple enough so voters
<span style="mso-spacerun:yes"> </span>can both use it
and understand how it is counted;</span></li>
<li><span style="font-size:12.0pt;mso-bidi-font-family:
Calibri;mso-bidi-theme-font:minor-latin;color:#323130">To
minimize the wasting of citizens’ votes (see below),<span
style="mso-spacerun:yes">
</span>and</span></li>
<li><span style="font-size:12.0pt;mso-bidi-font-family:
Calibri;mso-bidi-theme-font:minor-latin;color:#323130">To
guarantee that the winner among 3 or more candidates is
the candidate most supported by at least 50% plus one
(an absolute majority) of all the citizens voting, and</span></li>
<li><span style="font-size:12.0pt;mso-bidi-font-family:
Calibri;mso-bidi-theme-font:minor-latin;color:#323130">To
offer as few incentives and possibilities for voting
tactical.</span><span style="font-family:
""",serif;mso-fareast-font-family:"Times New
Roman";mso-bidi-font-family:
"Times New Roman";color:#323130;border:none
windowtext 1.0pt;mso-border-alt:
none windowtext 0in;padding:0in">
</span></li>
</ol>
</div>
<p style="margin: 0in 0in 8pt; line-height: 107%; font-family:
"Calibri",sans-serif; font-size:
11pt;mso-margin-top-alt:auto; margin-bottom:19.5pt;
line-height:normal; background:white">
<span style="mso-bookmark:_Hlk536824540"><span
style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">Given
these desires, currently I see Majority Judgment (MJ) as
superior to all of the above methods on each of these
counts.<span style="mso-spacerun:yes"> </span>However,
since the above discussions have not mentioned MJ, I
assume that many contributors would reject this claim for
MJ.
<span style="mso-spacerun:yes"> </span>This is why I would
very much appreciate receiving any of your clarifications
or explanations of how my claim for MJ cannot be
sustained.<span style="mso-spacerun:yes">
</span>What important flaws to you see in MJ?</span></span></p>
<p style="margin: 0in 0in 8pt; line-height: 107%; font-family:
"Calibri",sans-serif; font-size:
11pt;mso-margin-top-alt:auto; margin-bottom:19.5pt;
line-height:normal; background:white">
<span style="mso-bookmark:_Hlk536824540"><span
style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">To
help you to marshal your criticisms of MJ, please let me
explain more full my own understandings and reasons for
favoring MJ.<span style="mso-spacerun:yes"> </span>Firstly,
I<a moz-do-not-send="true"> see a citizen’s vote as being
wasted
<i>quantitatively</i> to the degree that it fails
equally to help one of their most trusted candidates to
win. A citizen’s vote is wasted
<i>qualitatively</i> to the degree that it instead helps
to elect a candidate whom they judge less
<i>fit</i> for office, rather than an available
candidate judged to be more fit.</a></span></span></p>
<span style="mso-bookmark:_Hlk8778434"></span><span
style="mso-bookmark:_Hlk536824540"></span>
<p style="margin: 0in 0in 8pt; line-height: 107%; 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">Other
than in MJ, such waste is present in all the existing
methods, whether they ask voters to rank, score, or approve
as many of the candidates as they might wish.<span
style="mso-spacerun:yes"> </span>Of course, most
dramatic is the waste provided by plurality or
First-Past-The-Post voting.
</span></p>
<p style="margin: 0in 0in 8pt; line-height: 107%; 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">To
counter qualitative waste, Balinski and Laraki (<i>Majority
Judgment,
</i>2010 MIT) argue that our capacity for judging qualities
of human behavior can be most meaningfully expressed in an
election by each voter grading each candidate’s suitability
for office as either Excellent (<i>ideal</i>), Very Good,
Good, Acceptable, Poor, or “Reject” (<i>entirely unsuitable</i>).<span
style="mso-spacerun:yes"> </span>
These grades are more discerning, meaningful, and
informative than merely expressing preferences or using
numeric
<a
style="mso-comment-reference:MOU_1;mso-comment-date:20180924T1043"
moz-do-not-send="true">scores</a></span><span><span
style="font-size:8.0pt"><a href="#_msocom_1"
moz-do-not-send="true">[MOU1]</a><span
style="mso-special-character:
comment"> </span></span></span><span
style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">,
X’s or ticks.<span style="mso-spacerun:yes"> </span>Such
grading makes it more likely that the highest quality
candidate will be elected in the eyes of the electorate.
</span></p>
<p style="margin: 0in 0in 8pt; line-height: 107%; 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">Each
candidate who is not explicitly graded is counted as
”Reject” by that voter. As a result, all the candidates
will receiv the same number of evaluations, but a different
set of grades from the voters.<span style="mso-spacerun:yes">
</span>
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></li>
</ul>
<span style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">
<div><br>
</div>
</span>
<div><span style="font-size:12.0pt;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 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>
</div>
<div><br>
<span style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">Also,
in contrast to the alternatives, Balinski
<span style="mso-spacerun:yes"> </span>explains how MJ
reduces by almost half, both the incentives and
opportunities for effective tactical voting.<span
style="mso-spacerun:yes">
</span>Thus, each voter has every appropriate incentive, not
only to vote but to reveal their honest evaluations of each
candidate.</span><br>
<br>
<span style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">Thus,
to me, using MJ should be simpler and more satisfying
because grading many candidates is both easier and more
meaningful than ranking or scoring them.<span
style="mso-spacerun:yes">
</span>Also, finding and comparing the median-grades of all
the candidate is quite simple.<span style="mso-spacerun:yes">
</span>Unlike MJ, IRV, Condorcet methods, and Scoring do not
guarantee the election of the candidate most preferred by at
least 50% plus one of all the citizens voting.<span
style="mso-spacerun:yes">
</span>Unlike IRV but like Condorcet methods and Score, MJ
does not eliminate any candidate until the winner is
discovered.</span></div>
<div><br>
</div>
<div>Finally, I would favor the following Asset option to be
added at the bottom of each MJ ballot: Any citizen who
currently feels that they do not yet know enough about any of
the candidates to grade them, can instead give their proxy
vote to the Register Elector who will do this for them. They
could do this by WRITING-IN the published code of that
Registered Elector.<br>
<br>
<span style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">I
look forward to your comments.</span></div>
<span style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">
<div><br>
</div>
</span>
<div><span style="font-size:12.0pt;mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:Arial">Steve<br>
</span></div>
<div style="mso-element:comment-list">
<hr width="33%" size="1" align="left">
<div style="mso-element:comment">
<div><span style="mso-comment-author:
"Microsoft Office
User";mso-comment-providerid:None;mso-comment-userid:"Microsoft
Office User""></span>
<p style="margin: 0in 0in 8pt; font-family:
"Calibri",sans-serif; font-size: 10pt">
<span><span style="font-size:
8.0pt"><span style="mso-special-character:comment"> <a
href="#_msoanchor_1" moz-do-not-send="true">[MOU1]</a></span></span></span>Numerical
scores</p>
</div>
</div>
</div>
<br>
</span>
<br>
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