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<p style="margin: 0in 0in 8pt; line-height: normal; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-outline-level: 2;">
<span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">Re: “goal of a better election method”
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<p style="margin: 0in 0in 8pt; line-height: normal; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-outline-level: 2;">
<font face="Calibri"><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">To all (but prompted by Sennet Williams and Rober Bristow-Johnson,
and earlier by </span><span style="mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-fareast-language: EN-GB;">Michael Ossipoff,
</span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: "Times New Roman";">Richard Fobes,
</span><span style="font-size: 12pt;">Kristofer Munsterhjelm,<span style="mso-spacerun: yes;">
</span></span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: "Times New Roman";">Steve Eppley,</span><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman";">
Jameson Quinn, and </span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: "Times New Roman";">Kevin Venzke)</span></font></p>
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<span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">Since January 9<sup>th
</sup>(Election-Methods Digest, Vol 151, Issue 12) there have been several answers to Sennet Williams’ question: “What is the goal of a "better" election method?”<span style="mso-spacerun: yes;">
</span>Please correct me if I am mistaken but the answer that I would like to suggest below would effectively satisfy the answers given by, e.g. Robert Bristow-Johnson’s:<span style="mso-spacerun: yes;">
</span>“The end goal of a "better" election method … is FAIRNESS and INCLUSION.<span style="mso-spacerun: yes;">
</span>Fairness for voters means<br>
1. Level playing field<br>
for *all* voters ("One person, one vote")<br>
2. No burden of tactical voting (therefore no punishment for voting sincerely) in a multi-candidate election. ?No voter regret.?<br>
3. …. 10 ….”</font></span></p>
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<font face="Calibri"><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">My suggested goal for</span><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">
a single-winner election (e.g. for a president, governor, or major) is Balinski and Laraki’s:</span></font></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">“The purpose of … an election is to select, if possible, some candidate who shall, in the opinion
of a majority of the electors, be most fit for the post…” (E. J. Nanson, quoted by Balinski and Laraki,
<i style="mso-bidi-font-style: normal;">Majority Judgment</i>, MIT, 2011, p.209).</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Also, “to gather as precisely as possible, the true opinions and evaluations of individuals, and
to determine as precisely as possible, the true aggregate wills of electorates ….” (Ibid, p. 388).</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Accordingly, I also seem to be coming to the conclusion that a refined improvement on Balinski and
Laraki’s Majority Judgment (MJ) method called Highest Majority Judgment (HMJ) by me would be the most efficient way of electing this “most fit” candidate.<span style="mso-spacerun: yes;">
</span>As will be explained below, HMJ guarantees that the winner will be the candidate most valued for the job by at least an absolute majority of all the voters, i.e. the candidate believed on average by at least an absolute majority to be the most qualified
for the office.<span style="mso-spacerun: yes;"> </span>Thus, HMJ also seems to be the “easiest single-winner voting method to tolerate”. Please explain any mistakes I might be making if I see HMJ as superior to the other good methods, e.g. any known variant
of Immediate Run-Off Voting (IRV), SCORE (Range), Maximized Affirmed Majorities (MAM), or APPROVAL.</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Firstly, I believe that Balinski and Laraki
<span style="mso-spacerun: yes;"> </span>explain how MJ avoids both “Condorcet paradox” and the “Arrow paradox” (ibid, pp.182-3).<span style="mso-spacerun: yes;">
</span>Secondly, I believe that B&L “prove” (pp. 15, 19, 186-198) that MJ provides only about “half” the incentives or opportunities for anti-democratic “strategic” voting to be successful. If you disagree, please explain the flaw in their argument. Until I
see such a flaw, MJ would seem to offer no reason for a savvy voter to expect to have a probable “strategic” advantage over less savvy voters, i.e. if and when they might choose to misuse MJ’s ballot, in effect, to “rank” rather than to “grade” the candidates.
<span style="mso-spacerun: yes;"> </span>If B&L’s proof is valid (and it is also true for HMJ), it, more than the above methods, largely frees voters from the burden of perhaps having to dishonestly ‘grade’ some of the candidates. This is because with HMJ,
it is probable that their honest ‘grades’ will do all they can to help elect the best candidate in their view.<span style="mso-spacerun: yes;">
</span>This is why Balinski and Laraki say that voting “honestly” with MJ is likely to be the “dominant strategy” (pp.190).<span style="mso-spacerun: yes;">
</span>Unfortunately, IRV, SCORE, MAM, and APPROVAL sometimes truly offer some very complicated reasons for very savvy citizens to vote dishonestly while hoping to make the election of their most preferred candidate more likely. By largely removing this burden,
HMJ would seem to help to minimize such distortions to the democratic process, i.e. to make the election of the best candidate as likely as possible.</font></span></p>
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<p style="margin: 0in 0in 8pt;"><span style="line-height: 107%; font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">I will now explain in more detail how HMJ works:
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<span style="line-height: 115%; font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">Uniquely, HMJ (and MJ) asks each voter simply to record their “evaluation” of each candidate by giving each candidate one of the following “grades”
depending on how closely each candidate comes to fitting the citizen’s own image of an “excellent” candidate:
</span><span style="line-height: 115%; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">EXCELLENT (5), VERY GOOD (4), GOOD (3), ACCEPTABLE (2), POOR (1), or REJECT (0) – each blank
is interpreted as REJECT.<span style="mso-spacerun: yes;"> </span>Such grades are likely to be meaningful at least to any person who has gone to school.<span style="mso-spacerun: yes;">
</span>It is easier to grade many candidates than to rank them.<span style="mso-spacerun: yes;">
</span>E</span><span style="line-height: 115%; font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">very citizens’ “grade” for every candidate continues to be part of the count until the absolute majority winner is discovered.
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<p style="color: rgb(0, 0, 0); font-family: "Calibri",sans-serif; font-size: 11pt; font-style: normal; font-weight: normal; margin-top: 0in; margin-bottom: 0pt; mso-list: l0 level1 lfo2;">
<span style="line-height: 115%; font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">Each candidate receives the same number of “grades”.<span style="mso-spacerun: yes;">
</span>To begin the count, all of each candidate’s “grades” are listed from highest to lowest, left to right.<span style="mso-spacerun: yes;">
</span>Next, each candidate’s “median-grade” is identified (i.e. the middle one on the right if there is an even number of voters).</span></p>
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<p style="color: rgb(0, 0, 0); font-family: "Calibri",sans-serif; font-size: 11pt; font-style: normal; font-weight: normal; margin-top: 0in; margin-bottom: 10pt; mso-list: l0 level1 lfo2;">
<span style="line-height: 115%; font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">The
HMJ winner is the candidate discovered to have the highest average of all the grades she has receive to the left of her “median-grade” and including her “median-grade”.<span style="mso-spacerun: yes;">
</span>If there is more than one candidate with this same highest average grade, each is a potential winner (see Example 1 below).<span style="mso-spacerun: yes;">
</span>In this event, HMJ discovers the winner by </span><span style="line-height: 115%; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">comparing, one by one, the next grade that
each has received immediately to the right of their respective medians.<span style="mso-spacerun: yes;">
</span>The winner is the first candidate in this sequential comparison discovered to have a next grade higher than any of the other previously tied potential winners
</span><span style="line-height: 115%; font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(see
Example 2 below)</span><span style="line-height: 115%; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">.</span><span style="line-height: 115%; font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Example 1:</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Y wins with HMJ, but X wins with MJ & Bucklin MJ</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">X:<span style="mso-spacerun: yes;">
</span>VGGPP or 43311………..10/3 = 3.66</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Y:<span style="mso-spacerun: yes;">
</span>EEAAP or 55221 …………12/3 = 4</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Example 2:</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">X wins with MJ & BMJ, but with HMJ, X & Y are initially tied.<span style="mso-spacerun: yes;">
</span>However, by comparing the grades to the right of the median, Y is discovered to be the HMJ winner.
</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">X:<span style="mso-spacerun: yes;">
</span>EVGPP or 54311………..12/3 = 4; 13/4 = 3.33</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Y:<span style="mso-spacerun: yes;">
</span>EEAAA or 55222…………12/3 = 4; 14/4 = 3.66</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">In this way, HMJ guarantees that the winner will be the candidate most highly valued by at least
an absolute majority of the electorate. </font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">While Balinski and Laraki clearly explain their own methods for breaking MJ ties, I see their methods
to be much more laborious and less efficient than HMJ’s.<span style="mso-spacerun: yes;">
</span>Firstly, MJ identifies all the candidates who have received the “highest majority-grade”.<span style="mso-spacerun: yes;">
</span>If there is more than one such candidate, MJ’s simplest tie breaking process uses “majority-guages” (pp.9ff).<span style="mso-spacerun: yes;">
</span>This differs from HMJ’s by simply comparing each such candidate’s number of grades listed to the left and to the right of all the grades each such candidate has received which are the same as their common “highest median-grade”.<span style="mso-spacerun: yes;">
</span>If and when this comparison fails to discover a winner, then the “majority-values” (pp. 6ff) of the tied candidates are compared instead.<span style="mso-spacerun: yes;">
</span>This is done by sequentially discovery and listing each tied candidate’s new “median-grade” upon the removal of the current median-grade from the total list of all the grades each such candidate had initially received.<span style="mso-spacerun: yes;">
</span>This is repeated until one of these candidates is found to have the highest new median-grade.<span style="mso-spacerun: yes;">
</span>Thus, unlike HMJ, MJ does not average the variety of different degrees of “evaluation” listed to the left of each candidate’s “median-grade”, i.e. the grades that may be distributed differently among this group of grades received by each of the tied
candidates.<span style="mso-spacerun: yes;"> </span></font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Therefore, in contrast to the above rival methods, HMJ</font></span></p>
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<span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">offers the greatest encouragement
for each citizen to vote;</span></p>
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<p style="color: rgb(0, 0, 0); font-family: "Calibri",sans-serif; font-size: 11pt; font-style: normal; font-weight: normal; margin-top: 0in; margin-bottom: 0pt; mso-list: l2 level1 lfo1;">
<span style="line-height: 115%; font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">allows</span><span style="line-height: 115%; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">
and most strongly encourages (with MJ)</span><span style="line-height: 115%; font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"> each citizen most fully, exactly and honestly to express their different “evaluations” of each
candidate;<span style="mso-spacerun: yes;"> </span></span></p>
</li><li style="color: rgb(0, 0, 0); font-family: "Calibri",sans-serif; font-size: 12pt; font-style: normal; font-weight: normal;">
<p style="color: rgb(0, 0, 0); line-height: normal; font-family: "Calibri",sans-serif; font-size: 11pt; font-style: normal; font-weight: normal; margin-top: 0in; margin-bottom: 0pt; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-list: l2 level1 lfo1; mso-add-space: auto;">
<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">again, (with MJ) offers
</span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">only
about </span><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">“</span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">half</span><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">”</span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">
the incentives or opportunities for anti-democratic </span><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">“</span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">strategic</span><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">”</span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">
voting to be successful. Thus, B&L argue that for most citizens, “sincere voting” will be the “dominant strategy” (pp. 190); and</span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">has the virtue (with MJ) of not requiring any arbitrary procedure to discover the absolute majority winner among any
initially tied candidates</span><span style="font-size: 12pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">
unless every voter has “graded” each candidate identically.</span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Also, I note that in contrast to HMJ:</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">IRV can eliminate some candidates before the winner is discovered.<span style="mso-spacerun: yes;">
</span>Unfortunately, one of these eliminated candidates might be the one who is preferred by more voters than any other candidate.<span style="mso-spacerun: yes;">
</span>This is true even though IRV also guarantees that its winner will have been explicitly preferred by a majority over all the remaining candidates;</span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">SCORE’s winner has not necessarily received ratings higher than 0 from a majority of the voters.<span style="mso-spacerun: yes;">
</span>Its number ratings of candidates are less meaningful than “grades”.<span style="mso-spacerun: yes;">
</span>Also, especially if its highest rating is more than “7”, they would also be less “discerning”</span><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"> (Ibid, p.283)</span><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">
than the 6 different “grades” used by HMJ.<span style="mso-spacerun: yes;"> </span>
This is because empirical studies have discovered that most people cannot meaningfully distinguish between more than seven “grades” of valued human behavior;</span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">MAM’s aggregation of all the voter’s preferences ignores some of the different ordinal preferences recorded on each voter’s
ballot.<span style="mso-spacerun: yes;"> </span>In contrast, all the different degrees of evaluation of all voters used by HMJ (i.e. “grades”) contribute to the discovery of its absolute majority winner.<span style="mso-spacerun: yes;">
</span>Also, many ordinary voters would find it much harder to understand how their MAM preferences are aggregated in an attempt to find the Condorcet winner (or the one produced by its tie breaking procedure). Finally, an MAM winner may not have been explicitly
preferred by a majority of the voters;</span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">APPROVAL does not allow citizens to express the full range of different degrees of “approval” that voters may feel with
regard to the available candidates.<span style="mso-spacerun: yes;"> </span>Consequently, a voter’s marking of the candidates she only weakly favors may help to defeat the candidate she most enthusiastically favors.<span style="mso-spacerun: yes;">
</span>Also, the APPROVAL winner may not have been “approved” by a majority of the voters.
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">I look forward to your feedback.</font></span></p>
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<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Steve</font></span></p>
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