From: steve bosworth <[hidden email]>
Sent: Wednesday, July 3, 2019 12:45 AM To: [hidden email] Subject: Best Single-Winner Method: RR vs. MJ+ From: steve bosworth <[hidden email]>
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
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Hi Steve, Your proposed MJ+ is just Bucklin; that is, Bucklin-ratings, with equal ratings allowed. Are you saying that you no longer consider it necessary to break ties according to B&L's method, by dropping median ballots? Again, my objective for single winner elections is to find a strategically robust method that will almost always find the candidate whose variance from the voters is minimized. That is, the sum of all sentiment distances, squared, over all ballots, will be minimized by the winner.In 2D geometry, the variance minimizing point in a figure is also the average location. Majority Judgment, I find, sometimes does this, but often captures the candidate who maximizes total support above the median score. This tends to choose the largest factional winner more often than it finds the centroid candidate. Unfortunately, in a political election, one can't really measure absolute distance from each candidate to each voter. So many of our methods are attempts to infer sentiment distance from the voter's relative ratings or rankings. Seemingly, finding a candidate with the highest total score should choose the variance minimizing candidate, but what if some fraction of voters strategically exaggerate their preferences? B&L claim that the median is the best way to avoid those votes, but maybe there is another way. What if, instead of finding the total of all ballots, for each candidate, you drop the highest and lowest voting ballots for a candidate, and take the entire ballot in the middle slot? This is called Trimmed Mean voting, and it has some nice properties. I would also recommend that you look at Warren Smith's analysis of median rating methods: https://rangevoting.org/MedianVrange.html On Tue, Jul 2, 2019 at 5:59 PM steve bosworth <[hidden email]> wrote:
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