<div dir="ltr">Here's an attempt at a statement of Relevant Rating. I would welcome any improvements in the explanation.<div><ol><span class="gmail-im" style="color:rgb(80,0,80)"><li style="margin-left:15px">Voters rate each candidates a rating of max rating down to 0. Blank ballots will be counted as 0 / Disapproved. Any non-zero rating is counted as approved. A ballot can contain any number of candidates at any rating level, but all equal-bottom rated candidates will be counted as 0. In other words, a ballot must disapprove at least one candidate.</li><li style="margin-left:15px">A candidate's total approval rating on a set of ballots is the total number of those ballots rating the candidate above zero.</li><li style="margin-left:15px">For each candidate X, imagine dividing the ballots into MAXRATE+1 piles. In each pile are the ballots rating X at rating R from MAXRATE down to zero. For a particular rating R, we can see the total vote for X at and above that rating by adding up the sizes of the piles from MAXRATE down to R. Then, looking at the ballots in the remaining piles (R-1 down to 0), look for the candidate with highest total approval.</li><li style="margin-left:15px">If X's votes at and above a rating R exceed the highest total approval for any candidate on ballots that rate X below R, then X's relevant rating is R.</li><li style="margin-left:15px">Starting at the top rating, see if any candidates have that relevant rating (i.e., they satisfy criterion 4).</li><li style="margin-left:15px">If there is at least one such candidate, then see if there is among them a candidate Y for whom the total number of ballots rating Y <i style="font-weight:bold">above</i> R is also greater than the highest total approval for any candidate on the ballots that rate Y below R. If so, the candidate Y with highest total number of ballots rating Y above R is the winner. Otherwise, the candidate X satisfying criterion 5 with highest total number of ballots rating X at R and above is the winner.</li></span><li style="margin-left:15px">If there is no non-zero rating at which a candidate can be found who satisfies criterion 4, then the candidate with highest total approval is the winner.<br></li></ol>Here's a somewhat contrived example of an election in which Relevant Rating and IBIFA get a different result.</div><div><br></div><div>49: A > B</div><div>03: B > A > C</div><div>10: D > B > C</div><div>38: E > F > C</div><div>05: G > D > H</div><div><br></div><div>Ratings of 3, 2, 1, 0.</div><div><br></div><div>At rating 3, we see that A has 49 vs total approval C:51 on the complementary ballots, so A's relevant rating must be below 3.</div><div><br></div><div>At rating 2, A has 51 ballots at and above rating 2, as opposed to C's approval of 48 on complementary ballots, so A's relevant rating is 2. But we see that B has 61 ballots at and above rating 2, meeting the same criterion. If we are using IBIFA, B wins with 61 vs A's 48. But using Relevant Rating, we see that A's 3-level total of 49 is greater than the total for C on ballots voting for A below 2, and B's total at rating 3 does not exceed the highest approved candidate on ballots that exclude B at 3, so A wins the RR tie-breaker.</div><div><br></div><div>MJ and Median rating both choose B.</div><div><br></div><div>Condorcet winner is A.</div><div><br></div><div>Since I announced this method (as "EXACT") a year or so go, I've found a fairly natural way to extend this to quota-based multiwinner, also. If interested, I will describe details.</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, May 24, 2019 at 11:09 AM Ted Stern <<a href="mailto:dodecatheon@gmail.com">dodecatheon@gmail.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"><div dir="ltr"><div dir="ltr">Hi Chris,<div><br></div><div>You write (emphasis mine):<br><br></div></div><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, May 22, 2019 at 5:12 AM C.Benham <<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</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">
<div bgcolor="#FFFFFF">
<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, <b><i>justified by I've no idea what.</i></b><br>
<br>
Bucklin is likewise a Median Ratings method and will usually give
the same winner, but the "tie breaker" is simple.</p></div></blockquote><div><br></div><div>The justification for the Majority Judgment tie breaker is that when two candidates have the same median rating, the proper way to resolve the tie is to look at the minimal number of ballots that must be removed to change their median rating. So it is similar to Minimax Pairwise Margins justification of minimal change. This tie breaker leans towards those candidates with stronger support above the median rating.</div><div><br></div><div>My privately proposed method of Relevant Ratings (formerly known as EXACT) uses a MJ-like tie breaker with your IBIFA method to get a similar effect.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div bgcolor="#FFFFFF"><p>
</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="gmail-m_-2818294270155005541gmail-m_-2981034959420349233moz-cite-prefix">On 21/05/2019 5:16 am, steve bosworth
wrote:<br>
</div>
<blockquote type="cite">
<span>
<p style="margin:0in 0in 0.0001pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal">
<span></span></p>
<p style="margin:0in 0in 0.0001pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal">
<span style="font-size:12pt">Re: Best Single-
Winner Method</span></p>
<p style="margin:0in 0in 0.0001pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal">
<span style="font-size:12pt"><br>
</span></p>
<p style="margin:0in 0in 0.0001pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal">
<span style="font-size:12pt"></span></p>
<p style="margin:0in 0in 0.0001pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal">
<span>Sennet Williams,<span>
</span>Forest Simmons, Robert Bristow-Johnson, Abd dul Raman
Lomax, and </span><span style="font-size:12pt;color:rgb(50,49,48)">Chris
Benham have recently addressed each others’ claims about
IRV, 3-slot Methods, IBIFA, and Asset.<span> </span>This discussion prompts
me to request some help later after I have clarified several
issues.</span></p>
<p style="margin:0in 0in 0.0001pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal">
<span style="font-size:12pt;color:rgb(50,49,48)"></span></p>
<p style="margin:0in 0in 0.0001pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal">
<span style="font-size:12pt;color:rgb(50,49,48)">Firstly,
please correct me if I am mistaken but currently I am
assuming that
<span> </span>we all would ideally
want the Best Single-Winner Method:</span><span style="font-size:12pt"></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:12pt;color:rgb(50,49,48)">To
be simple enough so voters
<span> </span>can both use it
and understand how it is counted;</span></li>
<li><span style="font-size:12pt;color:rgb(50,49,48)">To
minimize the wasting of citizens’ votes (see below),<span>
</span>and</span></li>
<li><span style="font-size:12pt;color:rgb(50,49,48)">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:12pt;color:rgb(50,49,48)">To
offer as few incentives and possibilities for voting
tactical.</span><span>
</span></li>
</ol>
</div>
<p style="margin:0in 0in 19.5pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal;background:white">
<span><span style="font-size:12pt">Given
these desires, currently I see Majority Judgment (MJ) as
superior to all of the above methods on each of these
counts.<span> </span>However,
since the above discussions have not mentioned MJ, I
assume that many contributors would reject this claim for
MJ.
<span> </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>
</span>What important flaws to you see in MJ?</span></span></p>
<p style="margin:0in 0in 19.5pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal;background:white">
<span><span style="font-size:12pt">To
help you to marshal your criticisms of MJ, please let me
explain more full my own understandings and reasons for
favoring MJ.<span> </span>Firstly,
I<a> 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></span><span></span>
<p style="margin:0in 0in 19.5pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal;background:white">
<span style="font-size:12pt">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> </span>Of course, most
dramatic is the waste provided by plurality or
First-Past-The-Post voting.
</span></p>
<p style="margin:0in 0in 19.5pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal;background:white">
<span style="font-size:12pt">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> </span>
These grades are more discerning, meaningful, and
informative than merely expressing preferences or using
numeric
<a>scores</a></span><span><span style="font-size:8pt"><a href="#m_-2818294270155005541_m_-2981034959420349233__msocom_1">[MOU1]</a><span> </span></span></span><span style="font-size:12pt">,
X’s or ticks.<span> </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 19.5pt;font-family:Calibri,sans-serif;font-size:11pt;line-height:normal;background:white">
<span style="font-size:12pt">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>
</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>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>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:12pt">
<div><br>
</div>
</span>
<div><span style="font-size:12pt">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:12pt">Also,
in contrast to the alternatives, Balinski
<span> </span>explains how MJ
reduces by almost half, both the incentives and
opportunities for effective tactical voting.<span>
</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:12pt">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>
</span>Also, finding and comparing the median-grades of all
the candidate is quite simple.<span>
</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>
</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:12pt">I
look forward to your comments.</span></div>
<span style="font-size:12pt">
<div><br>
</div>
</span>
<div><span style="font-size:12pt">Steve<br>
</span></div>
<div>
<hr width="33%" size="1" align="left">
<div>
<div><span></span>
<p style="margin:0in 0in 8pt;font-family:Calibri,sans-serif;font-size:10pt">
<span><span style="font-size:8pt"><span> <a href="#m_-2818294270155005541_m_-2981034959420349233__msoanchor_1">[MOU1]</a></span></span></span>Numerical
scores</p>
</div>
</div>
</div>
<br>
</span>
<br>
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