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<font size="2"><span style="font-size: 12pt;">TO: Forest</span><span style="font-size:11pt"><br>
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<font size="2"><span style="font-size: 12pt;">FROM: Steve</span><span style="font-size:11pt"><br>
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<font size="2"><span style="font-size: 12pt;">Currently, I understand your pursuit of the optimal "Epsilon" to be an interesting mathematical challenge for you. However, I do not yet see it as having the prospect of improving the use MJ. Partly, my question
follows from you previously agreeing that voting using grades is more meaningful than using numbers. You answered: "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!"</span></font></div>
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<span style="font-size: 12pt;">If so, the highest median-grade of any MJ election must be either Excellent, Very Good, Good, Acceptable, Poor, or Reject. How could an election benefit from replacing these judgments with numbers?</span></div>
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<span style="font-size: 12pt;">In any case, what portion of the electorate is going to understand an explanation of a new voting system that includes one of your phrases below like: "... the winning votes consist of fractions greater than (1 - 1/k) of the ballots."</span></div>
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<span style="font-size: 12pt;">I look forward to our dialogue.</span></div>
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<span style="font-size: 12pt;">Steve</span><br>
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<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Forest Simmons <forest.simmons21@gmail.com><br>
<b>Sent:</b> Thursday, October 7, 2021 3:50 PM<br>
<b>To:</b> steve bosworth <stevebosworth@hotmail.com><br>
<b>Cc:</b> EM <Election-methods@lists.electorama.com><br>
<b>Subject:</b> Re: Deterministic Epsilon Consensus Idea stimulated by a question of Steve Bosworth</font>
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<div>Note that if epsilon is one, the method is just Range Voting on a scale of zero to five ... which gives a clear incentive for concentrating ratings to the extremes of zero and five, or the extremes of "reject" and "excellent" in the MJ terminology.</div>
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<div dir="auto">On the other hand, if epsilon were infinitesimal, the grades above "poor" would serve merely as tie breakers ... not a bad idea for a general purpose tie breaker method!</div>
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<div dir="auto">But as a stand alone method, it might be best to limit the choice of epsilon to a value between zero and 1/6.</div>
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<div dir="auto">Why 1/6? Because of the six levels of grades, a five-sixths majority is a reasonable partial consensus quota. In particular, an initial step that disqualified every alternative pairwise defeated by more than a five-sixths majority of the ballots
could never disqualify all candidates when there are only six levels. </div>
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<div dir="auto">[In general, if there are only k levels, there cannot be a beat cycle where all of the winning votes consist of fractions greater than (1 - 1/k) of the ballots.]</div>
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<div dir="auto">This and other considerations make me think that in general when there are k levels of approval, 1/k might be a good nominal value for epsilon.</div>
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<div dir="auto">This "method" is still in the brainstorming stage, so all suggestions are worth considering!</div>
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<div dir="ltr">El mié., 6 de oct. de 2021 7:38 p. m., Forest Simmons <<a href="mailto:forest.simmons21@gmail.com" target="_blank" rel="noreferrer">forest.simmons21@gmail.com</a>> escribió:<br>
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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>
<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">Each candidate X gets a score that is given by the sum ..</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">S(X) = Sum (over j from zero to five) of the product</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">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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