[EM] Election-Methods Digest, Vol 236, Issue 18

[Closed Limelike Curves]

When I say "only one ballot," I mean only one ballot with *arbitrarily*
many against. In other words, a candidate can be supported by 99.99...% of
voters but still lose.

Example is on Wikipedia
<https://en.wikipedia.org/wiki/Highest_median_voting_rules#Archimedean_property>
.

On Mon, Mar 11, 2024 at 1:20 PM steve bosworth <stevebosworth at hotmail.com>
wrote:

>
> Today's Topics:
>    Re: Electing Cabinets, starting by using MJ to elect a provisional
> prime minister
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Sun, 10 Mar 2024 23:54:34 -0700
> From: Closed Limelike Curves <closed.limelike.curves at gmail.com>
> To: steve bosworth <stevebosworth at hotmail.com
> In response to my suggestion that MJ be used to election a provisional
> prime minister,
> Limelike Currves wrote:I
> "I think a Condorcet method would be most likely to do that (since it
> maximizes the chances that the elected candidate will have majority
> support). Majority Judgment can actually do arbitrarily badly at this--a
> candidate can win even if only one voter supports them. (It lacks the
> Archimedean property.)"
>
> Please define the Archimediean property? Aim I mistaken to think
> that every voting system (including Condorcet and MJ) could elect a
> candidate if only one voter expressed their support for one of the
> candidates?
>
> 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.
>
> 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.
> What do you think?
> Stephen
>
> On Sat, Mar 9, 2024 at 12:52?PM steve bosworth <stevebosworth at hotmail.com>
> wrote:
>
> >
> > Today's Topics:
> >
> >    1. Re: Electing Cabinets/Executive Committees ? starting with MJ
> >
> > 3/9/2024
> > From: stevebosworth at hotmail.com
> >
> > What do you think of using Majority Judgment to elect the provisional
> > prime minister.
> > As a result, this winner would have received the largest number of
> highest
> > grades regarding their suitability for this office?  This number would
> also
> > be a majority of all the votes in the elected parliament. Such a winner
> > would seem to be the one most likely to be able to negotiate the
> formation
> > of a unified cabinet that would receive the needed majority vote of
> > confidence.
>
> ----
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