<div dir="auto">Ted,<div dir="auto"><br></div><div dir="auto">I'm anxious to see how it does in simulations.</div><div dir="auto"><br></div><div dir="auto">Thanks!</div></div><br><div class="gmail_quote"><div dir="ltr">El mié., 6 de oct. de 2021 11:42 a. m., Ted Stern <<a href="mailto:dodecatheon@gmail.com">dodecatheon@gmail.com</a>> escribió:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">X-ASM! I like it.<br><br>I'll see if I can modify my ASM code to do X-ASM as well. Should be a small change.</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Oct 5, 2021 at 4:32 PM Forest Simmons <<a href="mailto:forest.simmons21@gmail.com" target="_blank" rel="noreferrer">forest.simmons21@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="auto"><div>Steve, </div><div dir="auto"><br></div><div dir="auto">Great questions and suggestion! </div><div dir="auto"><br></div><div dir="auto">However, in some venues not every voter has the patience to grade potentially dozens if not hundreds of candidates as in past California governor recall elections which were plenty cumbersome with FPTP style ballots (which should have been voted and tallied under Approval rules). In that context many more voters will have enough patience to vote in the final round.</div><div dir="auto"><div dir="auto"><br></div><div dir="auto">In my opinion MJ is a great improvement on most Cardinal Ratings/Score based methods, but the certainty of tied median grades is a drawback despite its signature clever method for resolving such ties.</div><div dir="auto"><br></div><div dir="auto">A closely related but more robust method invented by Andy Jennings makes ties vanishingly rare while preserving all of the<span style="font-family:sans-serif"> advantages of MJ including use of familiar, easy to understand grade style ballots with minimal strategic incentive for grade inflation/exaggeration.</span></div><div dir="auto"><br></div><div dir="auto">The voter instructions and other features of the voter interface environment for Jennings' method are identical to those of MJ. </div><div dir="auto"><br></div><div dir="auto">The method is called Chiastic Approval (XA) because of an X shaped (i.e. Chi shaped) graphical interpretation showing how MJ, Approval, and XA are related to the candidates' grade distributions.</div><div dir="auto"><br></div><div dir="auto">[Those distributions are discontinuous graphs that stair step down through the six grade levels. A vertical line through the middle of such a graph crosses at the midrange approval cutoff point between acceptable and poor. An horizontal line through the middle of the graph crosses it at the median ... which illustrates the ambiguity of the median, since an horizontal line will either miss the stair stepping graph entirely, or will intersect it along an entire line segment. On the other hand, a diagonal line of unit slope will cross the graph at precisely one point .. at the instant it crosses from below to above the graph. The descending distribution graph and the ascending diagonal line (segment) form the shape of the Greek letter chi.]</div><div dir="auto"><br></div><div dir="auto">It is pleasant for election geeks to contemplate such schematic diagrams, but the beauty will be lost on anybody else ... best to save it for those who might appreciate it :-)</div><div dir="auto"><br></div><div dir="auto">The algebraic representation will be even more of an imposition ... best to shred any reference to it except as documentation of the software:</div><div dir="auto"><br></div><div dir="auto">The distribution function F whose graph forms the descending staircase alluded to above is defined as follows:</div><div dir="auto"><br></div><div dir="auto">F(x) is the percentage of ballots that rate candidate C greater than or equal to x ... as x increases F(x) decreases.</div><div dir="auto"><br></div><div dir="auto">So the chiastic approval of candidate C is the greatest value of x such F(x) is no greater than x.</div><div dir="auto"><br></div><div dir="auto">Putting it all together we have ...</div><div dir="auto"><br></div><div dir="auto"><div dir="auto" style="font-family:sans-serif">The chiastic approval for candidate C is the greatest value of x such that x is less than or equal to the percentage of ballots that rate (i.e. grade) candidate C at or above x.</div><div dir="auto" style="font-family:sans-serif"><br></div><div dir="auto" style="font-family:sans-serif">I warned you!</div><div dir="auto" style="font-family:sans-serif"><br></div><div dir="auto" style="font-family:sans-serif">How many of you understand the Huntingto-Hill method of apportionment? Yet that is the official method for determining how many representatives each state gets in Congress and the Electoral College. And people trust in it unquestioningly just as they implicitly trust the medical pharmaceutical complex.</div><div dir="auto" style="font-family:sans-serif"><br></div><div dir="auto" style="font-family:sans-serif">Chiastic Approval is arguably easier to explain than MJ except perhaps at a superficial level that avoids the tie breaking details of MJ.</div><div dir="auto" style="font-family:sans-serif"><br></div><div dir="auto" style="font-family:sans-serif">Once you understand the beauty and efficiency of both Chiastic Approval and Approval Sorted Margins it becomes apparent that no Condorcet compliant deterministic social order (single winner order of finish) can surpass XASM, Chiastic Approval Sorted Margins, IMHO:-)</div></div><div dir="auto"><br></div>Forest<br><br><div class="gmail_quote" dir="auto"><div dir="ltr">El mar., 5 de oct. de 2021 11:33 a. m., steve bosworth <<a href="mailto:stevebosworth@hotmail.com" target="_blank" rel="noreferrer">stevebosworth@hotmail.com</a>> escribió:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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<div>Today's Topics: Replacing Top Two primaries</div>
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<div>From: Steve Bosworth</div>
<div>TO: Kevin Venzke</div>
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<div>Kevin Venzke wants to replace Top Two Primaries.<br>
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<div>Could not the objections to top two primaries be optimally satisfied by removing such primaries altogether, and instead electing the winner in the general election
<font size="2"><span style="font-size:11pt">by using Majority Judgment (MJ)</span></font>? Regardless of the number of candidates,<span lang="en-US"> MJ guarantees that the winner has received the highest median grade from at least 50% plus 1 of all the ballots
cast. As you know, </span>MJ invites each voter to judge the suitability for office of at least one of the candidates as either Excellent (<i>ideal</i>), Very Good, Good, Acceptable, Poor, or Reject (<i>entirely unsuitable</i>). Voters may give the same grade
to any number of candidates. Each candidate who is not explicitly graded is counted as a ‘Reject’ by that voter. As a result, all candidates have the same number of evaluations but a different set of grades awarded from all voters. The MJ winner is the one
who receives an absolute majority of all the grades equal to, or higher than, the highest
<i>median grade</i> given to any candidate. This median grade can be found as follows:</div>
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Place all the grades given to each candidate, high to low, left to right in a row, with the name of each candidate on the left of each row.</p>
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The median grade for each candidate is in the middle of each row. Specifically, the middle grade for an odd number of voters, or the grade on the right in the middle for an even number of voters.</p>
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<font face="Times New Roman, serif">The winner is the candidate with the highest median grade. If more than one candidate has the same highest median grade, remove the current median grade from each tied candidate and start again at step 1 with those tied candidates.</font></blockquote>
</li><li style="display:block"><font face="Times New Roman, serif">What do you think?</font></li><li style="display:block"><font face="Times New Roman, serif">Steve Bosworth (<a href="mailto:stevebosworth@hotmail.com" rel="noreferrer noreferrer" target="_blank">stevebosworth@hotmail.com</a></font></li></ol>
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