[EM] Fw: Best Single-Winner Method: RR vs. MJ+

[steve bosworth]

________________________________
From: steve bosworth <stevebosworth at hotmail.com>
Sent: Wednesday, July 3, 2019 12:45 AM
To: election-methods at lists.electorama.com
Subject: Best Single-Winner Method: RR vs. MJ+



________________________________
From: steve bosworth <stevebosworth at hotmail.com>
Sent: Sunday, June 30, 2019 3:00 AM
To: Ted Stern
Subject: Steve's request for clarification: Best Single-Winner Method: RR vs. MJ+



Hi Ted,


Thank you for giving me an additional concept to think about, namely, the *centroid of the population*.   Perhaps my need to seek some clarification about this has made my reply to you later than expected.  Such clarifications may enabling our next dialogue to be even more productive.


Of course, initially I saw the *centroid* as best expressed by Balinski’s definition of the MJ winner.  However, given your apt reference to the wikipedia  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 largest absolute majority of grades equal to or above the highest median-grade received by any candidate, e.g. candidate C in the wikipedia example.  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.  We might call this modification MJ+.


Assuming for the moment that I now prefer MJ+, are we in total agreement with each other?


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.  Exactly what data would we have to collect before we could  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?


I look forward to your ideas.


Steve

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20190703/668b9ab1/attachment.html>