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<div id="divRplyFwdMsg" dir="ltr"><font color="#000000" face="Calibri, sans-serif" style="font-size:11pt"><b>From:</b> steve bosworth <stevebosworth@hotmail.com><br>
<b>Sent:</b> Wednesday, July 3, 2019 12:45 AM<br>
<b>To:</b> election-methods@lists.electorama.com<br>
<b>Subject:</b> Best Single-Winner Method: RR vs. MJ+</font>
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<div id="divRplyFwdMsg" dir="ltr"><font color="#000000" face="Calibri, sans-serif" style="font-size:11pt"><b>From:</b> steve bosworth <stevebosworth@hotmail.com><br>
<b>Sent:</b> Sunday, June 30, 2019 3:00 AM<br>
<b>To:</b> Ted Stern<br>
<b>Subject:</b> Steve's request for clarification: Best Single-Winner Method: RR vs. MJ+</font> </div>
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<span lang="EN" style="font-family:"Segoe UI",sans-serif">Hi Ted, </span></p>
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<span lang="EN" style="font-family:"Segoe UI",sans-serif">Thank you for giving me an additional concept to think about, namely, the *centroid of the population*.<span style="">
</span><span style=""> </span>Perhaps my need to seek some clarification about this has made my reply to you later than expected.
<span style=""> </span>Such clarifications may enabling our next dialogue to be even more productive.</span></p>
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<span lang="EN" style="font-family:"Segoe UI",sans-serif">Of course, initially I saw the *centroid* as best expressed by Balinski’s definition of the MJ winner.<span style="">
</span>However, given your apt reference to the wikipedia <span style=""> </span>article on MJ, I can see that one might instead argue that the centroid would be more completely expressed and represented by the candidate who had received the l<i>argest</i>
absolute majority of grades equal to or above the highest median-grade received by any candidate<span style="display:inline!important; font-family:"Segoe UI",sans-serif; font-size-adjust:none; font-stretch:100%">, e.g. candidate C in the wikipedia example</span>.
<span style=""> </span>Balinski's tie breaking procedure would not be used unless there were also a tie between two or more candidates because they have exactly the same number of such grades.<span style="">
</span>We might call this modification MJ+.</span></p>
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<span lang="EN" style="font-family:"Segoe UI",sans-serif">Assuming for the moment that I now prefer MJ+, are we in total agreement with each other?</span></p>
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<span lang="EN" style="font-family:"Segoe UI",sans-serif">If you have a different concept of the *centroid*, please give me your definition and explain the process by which it can be discovered for any given population.<span style=""> E</span>xactly what data
would we have to collect before we could <span style=""> </span>minimize *the sum of the distance squared from all voters to the winning candidate*. How would we process this date so we could make this calculation?</span></p>
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<span lang="EN" style="font-family:"Segoe UI",sans-serif">I look forward to your ideas.</span></p>
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<span lang="EN" style="font-family:"Segoe UI",sans-serif">Steve</span></p>
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