<div dir="auto"><div>Yes, I fully agree on that point; nobody I know likes it when the nurse asks how much it hurts on a scale of one to ten!<br><br><div class="gmail_quote"><div dir="ltr">El mié., 6 de oct. de 2021 9:49 p. m., steve bosworth <<a href="mailto:stevebosworth@hotmail.com">stevebosworth@hotmail.com</a>> escribió:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt">TO: Forest</span><br>
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<span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt">FROM: Steve</span></div>
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<span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt">Thank you for forcing me to see that no voting method, including MJ, can "guarantee" that its winner will be supported by an absolute majority of all the ballots cast. MJ guarantees
this only if</span><font size="3"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt">
</span></font></font><font style="font-size:12pt" size="3"><font color="#000000"><font face="Liberation Serif, serif"><span lang="en-US"></span></font></font><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">an
absolute majority</span></font></font><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US"> of all the ballots cast for a</span></font></font><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">t</span></font></font><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">
least one candidate </span></font></font><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">have awarded them a grade of at least Acceptable.
</span></font></font><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">Otherwise, the MJ winner is the candidate who has received a plurality of such grades.
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<div style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt;color:rgb(0,0,0)">
<font style="font-size:12pt" size="3"><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">In these circumstances, electing this plurality candidate is justified
by the democratic assumption that other things being equal, a candidate with more votes than other candidates is probably more suited for office. For the same reason, an absolute majority candidate is probably more suited than a winning candidate with less
support <font style="font-size:12pt" size="3"><font color="#000000"><font face="Liberation Serif, serif"><span style="font-size:14pt" lang="en-US">than a majority</span></font></font></font>.</span></font></font></font></div>
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<font style="font-size:12pt" size="3"><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US"><br>
</span></font></font></font></div>
<div><font style="font-size:12pt" size="3"><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">At the same time, do you disagree with me that compared to voting
by using marks, numbers, or rankings; grading candidates allows voters more meaningfully and informatively to express their qualitative judgments about the candidates?</span></font></font></font></div>
<div><font style="font-size:12pt" size="3"><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US"><br>
</span></font></font></font></div>
<div><font style="font-size:12pt" size="3"><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">I look forward to our next dialogue.</span></font></font></font></div>
<div><font style="font-size:12pt" size="3"><font color="#000000"><font face="Liberation Serif, serif"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:14pt" lang="en-US">Steve<br>
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<div id="m_-370812665081396604divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Forest Simmons <<a href="mailto:forest.simmons21@gmail.com" target="_blank" rel="noreferrer">forest.simmons21@gmail.com</a>><br>
<b>Sent:</b> Wednesday, October 6, 2021 7:38 PM<br>
<b>To:</b> steve bosworth <<a href="mailto:stevebosworth@hotmail.com" target="_blank" rel="noreferrer">stevebosworth@hotmail.com</a>><br>
<b>Cc:</b> EM <<a href="mailto:Election-methods@lists.electorama.com" target="_blank" rel="noreferrer">Election-methods@lists.electorama.com</a>><br>
<b>Subject:</b> Deterministic Epsilon Consensus Idea stimulated by a question of Steve Bosworth (was Election-Methods Digest, Vol 207, Issue 9)</font>
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<div dir="auto">Steve's query about Chiastic Approval included the following ....
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<div dir="auto"> <span style="font-family:sans-serif;font-size:14.6667px">Also, correct me if I'm mistaken that XA does not guarantee that its winner will be elected with the support of a majority of all the votes (ballots) cast.</span></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">The short answer is "no" ... no method can guarantee majority voter support for its winner, unless they can guarantee that at least one candidate is ranked, rated, scored, or graded
above bottom on more than half of the ballots submitted.</span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">The long answer is, "Why stop at half or two-thirds, as some methods require ... why not go for full 100% consensus?"</span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">But, you may object, full consensus is not always possible. Well, neither is forty percent support always possible, but that doesn't stop the Constitution from requiring two-thirds of
the voters' support for certain kinds of amendments, etc.</span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">One expedient that has been suggested is the NOTA option for the case when the quota is not met. This option gives new meaning to the word "approval" ... as Mike Ossipoff used to say,
you approve a candidate if you would rather see her elected than have to come back next month to vote for someone else.</span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">I would like to suggest another option based on the standard MJ grade ballot ...</span></font></div>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">Each candidate X gets a score that is given by the sum ..</span></font></div>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">S(X) = Sum (over j from zero to five) of the product</span></font></div>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">a(j)*epsilon^j,</span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">where epsilon is a value to be determined by the voters ... and the respective values of a(j), for j in {0, 1, 2, 3, 4} are the number of ballots on which candidate X is graded strictly
above reject, poor, acceptable, good, or very good, respectively.</span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">Also each voter has the option of voting for a value of epsilon in the set {.01, .02, ... .99, 1.00}. The median of the distribution of these votes determines the value of epsilon. </span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">Elect the candidate X with the max value of S(X) (once the epsilon value has been determined).</span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">Note that if, for some j, the coefficient a(j) is the total number of ballots, then we can say candidate X is a full consensus candidate at level j.</span></font></div>
<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px"><br>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">If there are several full consensus level j candidates, then the higher degree terms will determine the winner.</span></font></div>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">Thanks!</span></font></div>
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<div dir="auto"><font face="sans-serif"><span style="font-size:14.6667px">FWS</span></font></div>
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