[EM] Electing Cabinets, starting by using MJ: Election-Methods Digest, Vol 236, Issue 18

[steve bosworth]

Today's Topics:
   Re: Electing Cabinets, starting by using MJ to elect a provisional prime minister
Stephen: The following responds to the two responses from Limelike.curves also copied below, in addition to a copy of my first suggestions, bellow.

Thank you Limelike for the Wikipedia link to the following example and information:

"Highest median rules violate the Archimedean property<https://en.wikipedia.org/wiki/Archimedean_property> (a much weaker form of the majority criterion<https://en.wikipedia.org/wiki/Majority_criterion>). As shown below, it is possible for Alice<https://en.wikipedia.org/wiki/Alice_and_Bob> to defeat Bob<https://en.wikipedia.org/wiki/Alice_and_Bob> in an election, even if only one voter thinks Bob is better than Alice, and a very large number of voters (up to 100% of them) give Alice a higher rating.

Ballots (Bolded medians)

# ballots

Alice

Bob

Charlie

Many<https://en.wikipedia.org/wiki/Arbitrarily_large>

100/100

52/100

0/100

1

50/100

51/100

1/100

Many<https://en.wikipedia.org/wiki/Arbitrarily_large>

49/100

0/100

100/100

In this election, Bob has the highest median score (51) and defeats Alice, even though every voter except for one (perhaps Bob himself) thinks Alice is a better candidate. This is true no matter how many voters there are. As a result, even a single voter's weak preferences can override the strong preferences of the rest of the electorate.

The above example restricted to candidates Alice and Bob also serves as an example of highest median rules failing the majority criterion<https://en.wikipedia.org/wiki/Majority_criterion>, although highest medians can pass the majority criterion with normalized ballots (i.e. ballots scaled to use the whole 0-100 range). However, normalization still cannot recover the Archimedean criterion.”

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Correct me if I’m mistaken: Belinski’s way of breaking ties avoids the use of the infinitesimals as addressed by the Archimedean property<https://en.wikipedia.org/wiki/Archimedean_property> as presented in Wikipedia.

At the same time, Belinski’s use of adding and subtracting whole numbers, alone, to discover the median winner makes it much easier for ordinary votes to understand the MJ count than to understand the details of any Condorcet count. Also, Belinski’s grades are much more expressive than Condorcet’s preferences. In addition, MJ allows voter to give the same grade to more than one candidate.

Secondly, we seem to understand the majority criterion<https://en.wikipedia.org/wiki/Majority_criterion> differently. Initially, both Alice and Bob (and each candidate) received the same total number of grades (see below). Ordering all the grades received by each candidate from highest to lowest, we initially discover that Alice and Bob have the same median grade. In order to break this tie using Belinski’s method, one grade having the same value as this median grade is temporarily removed from each of their lists of grades repeatedly until one of them is seen to have the highest median grade. This will be Bob in this example. Bob’s majority is determined by a higher median grade than received by Alice, and that is why he is elected. One voter judged him to be more suitable for office.

At the same time, I accept that it would be hard objectively to claim that either Bob or Alice would be most suitable for the office. I also accept that Alice has a higher average. At the same time, I agree with Belinski’s wider argument that averaging all the grades is less informative for an active democracy because averaging is more likely to prompt voters not to vote honestly -- to exaggerate their grades: perhaps, only to give Excellent to the one or several candidates they judge only to be Acceptable, and then, indiscriminately to Reject the rest.

To the extent that such less than truthful voting occurs, both the public and any analysts are deprived of the much richer data-base and education that Belinski’s MJ count otherwise enables its post-election reports to supply. Carefully analyzed, these reports would enable commentators to report on the comprehensive snapshot of the number and intensity of support that every candidate seems to have received, and similarly, the number and intensity with which many of the contentious issues in the relevant society are being supported or opposed. This information would seem to help strength any democracy.

What do you think?

Stephen

________________________________
From: steve bosworth <stevebosworth at hotmail.com>
Sent: Monday, March 11, 2024 1:13 PM
To: election-methods at lists.electorama.com <election-methods at lists.electorama.com>
Subject: Re: Election-Methods Digest, Vol 236, Issue 18


Today's Topics:
   Re: Electing Cabinets, starting by using MJ to elect a provisional prime minister
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
> > On 03/11/2024 11:22 PM EDT Closed Limelike Curves <
> closed.limelike.curves at gmail.com> wrote:
> >
> > 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?)
> >
> Do you actually think that in a competitive partisan political election
> where voters have a stake in the outcome, want to prevail politically, and
> vote by secret ballot that they would mark their ballots honestly about
> intensity of preference?
>
> "My system is only intended for honest men." Jean-Charles de Borda
>
> r b-j . _ . _ . _ . _ rbj at audioimagination.com
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
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.)"

Stephen: 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:

> 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.


________________________________
From: steve bosworth <stevebosworth at hotmail.com>
Sent: Monday, March 11, 2024 1:13 PM
To: election-methods at lists.electorama.com <election-methods at lists.electorama.com>
Subject: Re: Election-Methods Digest, Vol 236, Issue 18

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.)"
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Stephen: 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
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


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