<div dir="ltr"><div dir="ltr">I wonder if what we really want is to take pairwise differences in scores, then calculate the median difference for each pair of candidates. That might give you a system that behaves like Condorcet but still accounts for intensity of preferences. (Is that a thing?)<br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Mar 11, 2024 at 4:01 PM Closed Limelike Curves <<a href="mailto:closed.limelike.curves@gmail.com" target="_blank">closed.limelike.curves@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="ltr"><div dir="auto">When I say "only one ballot," I mean only one ballot with <i>arbitrarily</i> many against. In other words, a candidate can be supported by 99.99...% of voters but still lose.</div><div dir="auto"><br></div><div dir="auto"><a href="https://en.wikipedia.org/wiki/Highest_median_voting_rules#Archimedean_property" target="_blank">Example is on Wikipedia</a>.</div></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Mar 11, 2024 at 1:20 PM steve bosworth <<a href="mailto:stevebosworth@hotmail.com" target="_blank">stevebosworth@hotmail.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">
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<span style="font-size:11pt;font-family:Calibri,Helvetica,sans-serif">Today's Topics:<br>
Re: Electing Cabinets, starting by using MJ to elect a provisional prime minister<br>
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Message: 1<br>
Date: Sun, 10 Mar 2024 23:54:34 -0700<br>
From: Closed Limelike Curves <<a href="mailto:closed.limelike.curves@gmail.com" style="font-family:Calibri,Helvetica,sans-serif" target="_blank">closed.limelike.curves@gmail.com</a>><br>
To: steve bosworth <<a href="mailto:stevebosworth@hotmail.com" style="font-family:Calibri,Helvetica,sans-serif" target="_blank">stevebosworth@hotmail.com</a></span></div>
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<span style="font-size:11pt;font-family:Calibri,Helvetica,sans-serif">In response to my suggestion that MJ be used to election a provisional prime minister,</span></div>
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<span style="font-size:11pt;font-family:Calibri,Helvetica,sans-serif">Limelike Currves wrote:I<br>
"I think a Condorcet method would be most likely to do that (since it<br>
maximizes the chances that the elected candidate will have majority<br>
support). Majority Judgment can actually do arbitrarily badly at this--a<br>
candidate can win even if only one voter supports them. (It lacks the<br>
Archimedean property.)"</span></div>
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<span style="font-size:11pt;font-family:Calibri,Helvetica,sans-serif">Please define the Archimediean property? Aim I mistaken to think</span></div>
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<span style="font-size:11pt;font-family:Calibri,Helvetica,sans-serif">that every voting system (including Condorcet and MJ) could elect a candidate if only one voter expressed their support for one of the candidates?</span></div>
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<div><span style="font-family:Calibri,Helvetica,sans-serif;font-size:11pt;color:rgb(0,0,0)">At the same time, MJ's grades are more expressive than Condorcet's preferences. Grades allow each voter more informatively to express
their different judgments about the suitability for office of as many of the candidates they want.</span></div>
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<span style="font-size:11pt;font-family:Calibri,Helvetica,sans-serif">Also, I think it is MJ that maximizes the chances for the winner to be elected by a majority of all the ballots cast. This majority is discovered by comparing all the grades given to all the candidates by all the ballots cast.
The one candidate who is found to continue to have received the highest median grade is supported by this majority.</span></div>
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<span style="font-size:11pt;font-family:Calibri,Helvetica,sans-serif">What do you think?</span></div>
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<span style="font-size:11pt;font-family:Calibri,Helvetica,sans-serif">Stephen</span></div>
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On Sat, Mar 9, 2024 at 12:52?PM steve bosworth <<a href="mailto:stevebosworth@hotmail.com" style="font-family:Calibri,Helvetica,sans-serif" target="_blank">stevebosworth@hotmail.com</a>><br>
wrote:<br>
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> Today's Topics:<br>
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> 1. Re: Electing Cabinets/Executive Committees ? starting with MJ<br>
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> 3/9/2024<br>
> From: <a href="mailto:stevebosworth@hotmail.com" style="font-family:Calibri,Helvetica,sans-serif" target="_blank">stevebosworth@hotmail.com</a><br>
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> What do you think of using Majority Judgment to elect the provisional<br>
> prime minister.<br>
> As a result, this winner would have received the largest number of highest<br>
> grades regarding their suitability for this office? This number would also<br>
> be a majority of all the votes in the elected parliament. Such a winner<br>
> would seem to be the one most likely to be able to negotiate the formation<br>
> of a unified cabinet that would receive the needed majority vote of<br>
> confidence.<br>
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