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<span>
<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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">Hi Ted,</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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">Thank you both for your response to Cris’s IBIFA and for your discussion of your
proposed Relevant Rating (RR) method.</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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN"></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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">Of course, both IBIRA and RR are great improvements on the methods that are actually
being used to elect single-winners.<span style="mso-spacerun:yes"> </span>However, it still seems to me that both fall short of the advantages offered by MJ.
<span style="mso-spacerun:yes"> </span>With regard to your description of RR,<span style="mso-spacerun:yes">
</span>please correct any of the self [clarifications which I’ve added within the square brackets].<span style="mso-spacerun:yes">
</span>At the same time, I still seem to be misunderstanding RR because, as yet, I do not see how you have arrived at your conclusions with regard your example election.</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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN"></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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">In the hope of assisting our dialogue, below I have added a table which records
the way MJ would count that election.<span style="mso-spacerun:yes"> </span>That table uses Balinski’s recommended grading language. He argues that the following 6 grades provide a most discerning, meaningful, and informative way for voters to express their
judgments about the suitability of candidates for office: Excellent, Very Good, Good, Acceptable, Poor, or Reject.<span style="mso-spacerun:yes">
</span>These six follow the empirical evidence and arguments offered by </span><span style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Arial">G.A. Miller (1956,”The magical number seven, plus or minus two: Some limits on
our capacity for processing information”. <i>Psychological Review </i>63: 89-97) and</span><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:black;mso-ansi-language:EN">
<span lang="EN">use by Balinski and Laraki Majority Judgment, 2010 MIT. </span></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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN"></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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">Correct me if I’m mistaken, but in contrast to MJ, it currently seem to me that
your RR suffers from two major flaws:</span></p>
<ol style="margin-bottom: 0in">
<li><span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">RR does not guarantee that the winner is the one candidate who has received
the highest available grade on at least 50% plus one of all the ballots containing at least one rating other than 0 (i.e. other than Poor or Reject in the language suggested by Balinski).<span style="mso-spacerun:yes">
</span>Provided an MJ citizen marks their ballot at least with one of the following grades for one of the candidates (Excellent, Very Good, Good, or Acceptable), this grade together with all their default “Rejects” for all the other candidates are counted.
<span style="mso-spacerun:yes"> </span>Thus each and every voter equally and necessarily helps to determine each candidates median-grade.<span style="mso-spacerun:yes">
</span>The MJ candidate who has received the highest median-grade is the winner.<span style="mso-spacerun:yes">
</span>My previous post (copied below) explains the strong and relatively simple process by which any tie is broken.</span></li><li><span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">RR does not treat each citizen’s vote equally.<span style="mso-spacerun:yes">
</span>All the relatively small number of Rejects given to the most popular candidates who gave at least Acceptable to a much less popular candidate are ignored when determining the median-grade of all the candidates (or such median-grades have no relevance
for RR).<span style="mso-spacerun:yes"> </span>This is why RR seems both not to guarantee that the winner will be supported by an absolute majority of all those voting, and effectively wastes (ignores) all the votes of at least Acceptable given to unpopular
candidates.<span style="mso-spacerun:yes"> </span>This inequality encourages voters to vote dishonestly (tactically).</span></li></ol>
<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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">SEE BELOW PLEASE</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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">I look forward to your clarifications and/or refutations.</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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">Steve</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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>></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">
<b><span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">From:</span></b><span lang="EN" style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin;color:black;mso-ansi-language:EN">
Ted Stern <dodecatheon@gmail.com><br>
<b>Sent:</b> Friday, May 24, 2019 7:10 PM<br>
<b>To:</b> cbenham@adam.com.au<br>
<b>Cc:</b> election-methods@lists.electorama.com; steve bosworth<br>
<b>Subject:</b> Re: [EM] Best Single-Winner Method</span><span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:EN">
</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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN"> </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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">T:<span style="mso-spacerun:yes">
</span>Here's an attempt at a statement of Relevant Rating. I would welcome any improvements in the explanation.
</span></p>
<ol style="margin-bottom: 0in">
<li><span lang="EN" style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin;mso-ansi-language:EN">Voters rate each candidates a rating of max rating down to 0. Blank ballots [regarding
any particular candidate] will be counted as 0 / Disapproved <span style="mso-spacerun:yes">
</span>[i.e. Reject]. Any non-zero rating is counted as approved [i.e. Acceptable, Good, Very Good, or Excellent]. A ballot can contain any number of candidates at any rating level, but all equal-bottom rated candidates [Poor or Reject] will be counted as
0. In other words, a ballot must disapprove at least one candidate [no, must grade at least one candidate as Acceptable, and by doing so will be counted as also graded every other candidate as Reject].</span></li><li><span lang="EN" style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin;mso-ansi-language:EN">A candidate's total approval rating on a set of ballots is the total number of those ballots
rating the candidate above zero.</span></li><li><span lang="EN" style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin;mso-ansi-language:EN">For each candidate X, imagine dividing the ballots into MAXRATE+1 piles [i.e. ballots
that give each candidate either Excellent or one of the other 5 Balinski grades ]. [I.e.] In each pile are [all] the ballots rating X<s> at rating R</s> [with any of Balinski’s grades] from MAXRATE down to zero [i.e. Reject]. For a particular rating R [i.e.
median-rating], 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 [number of] ballots in the remaining piles (R-1 down to 0) [i.e. the number lower than the median-rating
grade], look for the candidate with highest total approval [i.e. the number higher than the median-grade plus the median-grade].</span></li><li><span lang="EN" style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin;mso-ansi-language:EN">If [the number of] X's votes at and above a rating R [i.e. X’s median-grade] exceed the
highest total [number of ballots which approve <s>approval for</s> any candidate on ballots that rate X below R [i.e. X’s median-grade], then X's relevant rating is R [?].</span></li><li><span lang="EN" style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin;mso-ansi-language:EN">Starting at the top rating, see if any candidates have that relevant rating (i.e., they
satisfy criterion 4).</span></li><li><span lang="EN" style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin;mso-ansi-language:EN">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 <b><i>above</i></b> R is also greater [in number] 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 [I am still not clear whether this description might only be a more cumbersome way of expressing the count used by
MJ and which I presented in the last paragraph of my earlier post as copied at the end of this post – please clarify?].</span></li><li><span lang="EN" style="font-size:12.0pt;
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Calibri;
mso-bidi-theme-font:minor-latin;mso-ansi-language:EN">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.</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>></span><br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130">S:<span style="mso-spacerun:yes">
</span>Stern’s example election :</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130">Converted to Balinisk’s MJ vocabulary (Excellent (e), Very Good (vg), Good (g), Acceptable (a), Poor (p), or Reject (r).</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130">Possible translation by Balinski’’s MJ:<span style="mso-spacerun:yes">
</span></span><br>
<br>
<span lang="EN" style="color: rgb(0, 0, 0); font-size: 12pt;">49: A > B</span><br>
<span lang="EN" style="color: rgb(0, 0, 0); font-size: 12pt;">03: B > A > C</span><br>
<span lang="EN" style="color: rgb(0, 0, 0); font-size: 12pt;">10: D > B > C</span><br>
<span lang="EN" style="color: rgb(0, 0, 0); font-size: 12pt;">38: E > F > C</span><br>
<span lang="EN" style="color: rgb(0, 0, 0); font-size: 12pt;">05: G > D</span><span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN"> > H</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130">Candidates:<span style="mso-tab-count:1">
</span>A <span style="mso-tab-count:1"> </span>B<span style="mso-tab-count:1">
</span>C<span style="mso-tab-count:1"> </span>D<span style="mso-tab-count:1">
</span>E<span style="mso-tab-count:1"> </span>F<span style="mso-tab-count:1">
</span>G<span style="mso-tab-count:1"> </span>H</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"><span style="mso-tab-count:2">
</span>49:e<span style="mso-tab-count:1"> </span>49:vg<span style="mso-tab-count:1">
</span>03:a<span style="mso-tab-count:1"> </span>10:e<span style="mso-tab-count:1">
</span>38:e<span style="mso-tab-count:1"> </span>38:vg<span style="mso-tab-count:1">
</span>05:e<span style="mso-tab-count:1"> </span>05:a</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"> 03:vg<span style="mso-tab-count:1">
</span>03:e<span style="mso-tab-count:1"> </span>10:a<span style="mso-tab-count:1">
</span>05:vg<span style="mso-tab-count:1"> </span>03:E</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"><span style="mso-tab-count:2">
</span>0<span style="mso-tab-count:
1"> </span>10:vg<span style="mso-tab-count:1">
</span>38:a<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"><span style="mso-tab-count:1">
</span><span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130">Total High:<span style="mso-tab-count:1">
</span>52<span style="mso-tab-count:
1"> </span>62<span style="mso-tab-count:1">
</span>51<span style="mso-tab-count:1"> </span>15<span style="mso-tab-count:1">
</span>41<span style="mso-tab-count:1"> </span>38<span style="mso-tab-count:1">
</span>05<span style="mso-tab-count:1"> </span>05</span><br>
<br>
<u><span style="font-family:"Segoe UI",sans-serif;color:#323130">Median:<span style="mso-tab-count:1">
</span>r<span style="mso-tab-count:1"> </span>vg<span style="mso-tab-count:1">
</span>r<span style="mso-tab-count:1"> </span>r<span style="mso-tab-count:1">
</span>r<span style="mso-tab-count:1"> </span>r<span style="mso-tab-count:1">
</span>r<span style="mso-tab-count:1"> </span>r<span style="mso-tab-count:1">
</span></span></u><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130">Total Low:<span style="mso-tab-count:1">
</span>53<span style="mso-tab-count:1"> </span>43<span style="mso-tab-count:1">
</span>54<span style="mso-tab-count:1"> </span>90<span style="mso-tab-count:1">
</span>67<span style="mso-tab-count:1"> </span>67<span style="mso-tab-count:1">
</span>100<span style="mso-tab-count:1"> </span>100</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"><span style="mso-tab-count:2">
</span>0<span style="mso-tab-count:
1"> </span>0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>05:r<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"> 0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0:<span style="mso-tab-count:1"> </span>05:r<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>38:r<span style="mso-tab-count:1">
</span>38:r<span style="mso-tab-count:1"> </span><span style="mso-tab-count:1">
</span></span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"> 05:r<span style="mso-tab-count:1">
</span>05:r<span style="mso-tab-count:1"> </span>05:r<span style="mso-tab-count:1">
</span>38:r <span style="mso-tab-count:1"> </span>10:r<span style="mso-tab-count:1">
</span>10:r<span style="mso-tab-count:1"> </span>10:r<span style="mso-tab-count:1">
</span>10:r<span style="mso-tab-count:1"> </span><span style="mso-tab-count:1">
</span></span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"><span style="mso-tab-count:1">
</span><span style="mso-tab-count:1"> </span>38:r<span style="mso-tab-count:1">
</span>38:r<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>03:r<span style="mso-tab-count:1"> </span>03:r<span style="mso-tab-count:1">
</span>03:r<span style="mso-tab-count:1"> </span>03:r<span style="mso-tab-count:1">
</span>03:r<span style="mso-tab-count:2"> </span></span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130"><span style="mso-tab-count:2">
</span>10:r<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>49:r<span style="mso-tab-count:1"> </span>49:r<span style="mso-tab-count:1">
</span>49:r<span style="mso-tab-count:1"> </span>49:r<span style="mso-tab-count:1">
</span>49:r<span style="mso-tab-count:1"> </span>49:r</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#323130">B is the winner with a median-grade of Very Good.<span style="mso-spacerun:yes">
</span>However, if the 5 citizens who voted for GDH were absent or entirely ignored as seems to be the case with RR, A would be the winner with a new median-grade of Excellent (e).<span style="mso-spacerun:yes">
</span>At the same time, since these 5 citizens did vote, but RR elects A, A is being elected by a large minority of all the votes cast.<span style="mso-spacerun:yes">
</span>How can this be justified if every citizens’ vote must be treated with equal respect in a democracy?</span><br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">T:<span style="mso-spacerun:yes">
</span>Here's a somewhat contrived example of an election in which Relevant Rating and IBIFA get a different result.</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">49: A > B</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">03: B > A > C</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">10: D > B > C</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">38: E > F > C</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">05: G > D > H</span><br>
<br>
<br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">Ratings of 3, 2, 1, 0.</span><br>
<br>
<br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">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.</span><br>
<br>
<br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">At rating 2, A has 51 [?52] ballots at and above rating 2, as opposed to C's approval of 48
[?51] on complementary ballots, so A's relevant rating is 2. But we see that B has 61 [62] ballots at and above rating 2, meeting the same criterion. If we are using IBIFA, B wins with 61 [?62] 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.
</span><br>
<br>
<br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">S: Please clarify all the above reasoning.</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>></span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#C00000">Stern’s RESULTs (printed in red:???????????????????????):</span><br>
<br>
<br>
<br>
<br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#C00000">Candidates:<span style="mso-tab-count:1">
</span>A <span style="mso-tab-count:1"> </span>B<span style="mso-tab-count:1">
</span>C<span style="mso-tab-count:1"> </span></span><span style="font-family:"Segoe UI",sans-serif">D<span style="mso-tab-count:1">
</span>E<span style="mso-tab-count:1"> </span>F<span style="mso-tab-count:1">
</span>G<span style="mso-tab-count:1"> </span>H</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#C00000"><span style="mso-tab-count:2">
</span>49:3<span style="mso-tab-count:1"> </span>49:2<span style="mso-tab-count:1">
</span>03:1<span style="mso-tab-count:1"> </span></span><span style="font-family:"Segoe UI",sans-serif">10:e<span style="mso-tab-count:1">
</span>38:e<span style="mso-tab-count:1"> </span>38:vg<span style="mso-tab-count:1">
</span>05:e<span style="mso-tab-count:1"> </span>05:a</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#C00000"> 03:2<span style="mso-tab-count:1">
</span>03:3<span style="mso-tab-count:1"> </span>10:1<span style="mso-tab-count:1">
</span></span><span style="font-family:"Segoe UI",sans-serif">05:vg<span style="mso-tab-count:1">
</span>03:e</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#C00000"><span style="mso-tab-count:2">
</span>0<span style="mso-tab-count:
1"> </span>10:2<span style="mso-tab-count:1">
</span>38:1<span style="mso-tab-count:1"> </span></span><span style="font-family:"Segoe UI",sans-serif">0<span style="mso-tab-count:1">
</span>0</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#C00000"><span style="mso-tab-count:1">
</span><span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span></span><span style="font-family:"Segoe UI",sans-serif">0<span style="mso-tab-count:1">
</span>0</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif;color:#C00000">Total High:<span style="mso-tab-count:1">
</span>52<span style="mso-tab-count:
1"> </span>62<span style="mso-tab-count:1">
</span>51<span style="mso-tab-count:1"> </span></span><span style="font-family:"Segoe UI",sans-serif">15<span style="mso-tab-count:1">
</span>41<span style="mso-tab-count:1"> </span>38<span style="mso-tab-count:1">
</span>05<span style="mso-tab-count:1"> </span>05</span><br>
<br>
<u><span style="font-family:"Segoe UI",sans-serif">Median:<span style="mso-tab-count:1">
</span>r<span style="mso-tab-count:1"> </span>vg<span style="mso-tab-count:1">
</span>approval<span style="mso-tab-count:1"> </span></span></u><br>
<br>
<span style="font-family:"Segoe UI",sans-serif">Total Low:<span style="mso-tab-count:1">
</span>48<span style="mso-tab-count:1"> </span>38<span style="mso-tab-count:1">
</span>49<span style="mso-tab-count:1"> </span>90<span style="mso-tab-count:1">
</span>67<span style="mso-tab-count:1"> </span>67<span style="mso-tab-count:1">
</span>100<span style="mso-tab-count:1"> </span>100</span><br>
<br>
<br>
<span style="font-family:"Segoe UI",sans-serif"><span style="mso-tab-count:
2">
</span>0<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>05:r<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0</span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif"> 0<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>0:<span style="mso-tab-count:1"> </span>05:r<span style="mso-tab-count:1">
</span>0<span style="mso-tab-count:1"> </span>38:r<span style="mso-tab-count:1">
</span>38:r<span style="mso-tab-count:1"> </span><span style="mso-tab-count:1">
</span></span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif"> 05:r<span style="mso-tab-count:1">
</span>05:r<span style="mso-tab-count:1"> </span>05:r<span style="mso-tab-count:1">
</span>38:r <span style="mso-tab-count:1"> </span>10:r<span style="mso-tab-count:1">
</span>10:r<span style="mso-tab-count:1"> </span>10:r<span style="mso-tab-count:1">
</span>10:r<span style="mso-tab-count:1"> </span><span style="mso-tab-count:1">
</span></span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif"><span style="mso-tab-count:
1">
</span><span style="mso-tab-count:1"> </span>38:r<span style="mso-tab-count:1">
</span>38:r<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>03:r<span style="mso-tab-count:1"> </span>03:r<span style="mso-tab-count:1">
</span>03:r<span style="mso-tab-count:1"> </span>03:r<span style="mso-tab-count:1">
</span>03:r<span style="mso-tab-count:2"> </span></span><br>
<br>
<span style="font-family:"Segoe UI",sans-serif"><span style="mso-tab-count:
2">
</span>10:r<span style="mso-tab-count:1"> </span>0<span style="mso-tab-count:1">
</span>49:r<span style="mso-tab-count:1"> </span>49:r<span style="mso-tab-count:1">
</span>49:r<span style="mso-tab-count:1"> </span>49:r<span style="mso-tab-count:1">
</span>49:r<span style="mso-tab-count:1"> </span>49:r<span style="mso-tab-count:2">
</span></span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">[….]</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>></span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">On 21/05/2019 5:16 am, steve bosworth wrote:</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">Re: Best Single- Winner Method</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">[….]</span><br>
<br>
<span lang="EN" 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;
mso-ansi-language:EN">Firstly, please correct me if I am mistaken but currently I am assuming that
we all would ideally want the Best Single-Winner Method:</span></li></ol>
<ol style="margin-bottom: 0in">
<li><span lang="EN" 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;mso-ansi-language:EN">To be simple enough so voters can both use it and understand how it is
counted;</span></li><li><span lang="EN" 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;mso-ansi-language:EN">To minimize the wasting of citizens’ votes (see below), and</span></li><li><span lang="EN" 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;mso-ansi-language:EN">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 lang="EN" 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;mso-ansi-language:EN">To offer as few incentives and opportunities as possible to vote tactical.</span><span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;color:black;
mso-ansi-language:EN">
</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">Given these desires, currently I see Majority Judgment (MJ) as superior to all of the above
methods on each of these counts. However, since the above discussions have not mentioned MJ, I assume that many contributors would reject this claim for MJ. This is why I would very much appreciate receiving any of your clarifications or explanations of
how my claim for MJ cannot be sustained. What important flaws to you see in MJ?</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">To help you to marshal your criticisms of MJ, please let me explain more full my own understandings
and reasons for favoring MJ. Firstly, I 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.</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">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. Of course, most dramatic is the waste provided by plurality or First-Past-The-Post voting.
</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">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>). These grades are more discerning, meaningful, and informative than merely expressing preferences or using numeric scores , X’s or ticks. Such grading makes it more likely that the highest quality candidate will be
elected in the eyes of the electorate. </span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">Each candidate who is not explicitly graded is counted as ”Reject” by that voter. As a result,
all the candidates will receive the same number of evaluations, but a different set of grades from the voters. 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></li></ol>
<ul style="margin-bottom: 0in">
<li><span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">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 lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">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>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN"><br>
Also, in contrast to the alternatives, Balinski explains how MJ reduces by almost half, both the incentives and opportunities for effective tactical voting. Thus, each voter has every appropriate incentive, not only to vote but to reveal their honest evaluations
of each candidate.<br>
<br>
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. Also, finding and comparing the median-grades of all the candidate is quite simple. 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. Unlike IRV but like Condorcet methods and Score, MJ does not eliminate any candidate until the winner is discovered.</span><br>
<br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">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>
I look forward to your comments.</span><br>
<span lang="EN" style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;mso-ansi-language:
EN">Steve</span></li></ul>
<br>
</span></div>
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