Re: [EM] 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@gmail.com
To: steve bosworth <stevebosworth@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@hotmail.com
wrote:
Today's Topics:
1. Re: Electing Cabinets/Executive Committees ? starting with MJ
3/9/2024
From: stevebosworth@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.
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@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@gmail.com
To: steve bosworth <stevebosworth@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@hotmail.com
wrote:
Today's Topics:
1. Re: Electing Cabinets/Executive Committees ? starting with MJ
3/9/2024
From: stevebosworth@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.
Election-Methods mailing list - see https://electorama.com/em for list
info
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?)
On Mon, Mar 11, 2024 at 4:01 PM Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
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@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@gmail.com
To: steve bosworth <stevebosworth@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@hotmail.com
wrote:
Today's Topics:
1. Re: Electing Cabinets/Executive Committees ? starting with MJ
3/9/2024
From: stevebosworth@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.
Election-Methods mailing list - see https://electorama.com/em for list
info
On 03/11/2024 11:22 PM EDT Closed Limelike Curves closed.limelike.curves@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@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
I think that somewhere between 0% and 100% of voters would do this.
Empirically, about 8% of US voters are honest and vote 3rd party, even if
we assume nobody likes either major party candidate. With less extreme
pressure, that number would probably be higher.
On Mon, Mar 11, 2024 at 10:07 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
On 03/11/2024 11:22 PM EDT Closed Limelike Curves <
closed.limelike.curves@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@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Election-Methods mailing list - see https://electorama.com/em for list
info
The question is about whether voters might be tempted to exaggerate the intensity of their preference (on a Score ballot), so as to have more effect in their vote.
On 03/12/2024 1:14 AM EDT Closed Limelike Curves closed.limelike.curves@gmail.com wrote:
I think that somewhere between 0% and 100% of voters would do this. Empirically, about 8% of US voters are honest and vote 3rd party, even if we assume nobody likes either major party candidate. With less extreme pressure, that number would probably be higher.
On Mon, Mar 11, 2024 at 10:07 PM robert bristow-johnson rbj@audioimagination.com wrote:
On 03/11/2024 11:22 PM EDT Closed Limelike Curves closed.limelike.curves@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@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Election-Methods mailing list - see https://electorama.com/em for list info
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Oh, definitely. Most of them will, probably. But probably not all; and if
all of them do it, every cardinal system collapses back into approval,
which is fine anyways.
On Mon, Mar 11, 2024 at 10:17 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
The question is about whether voters might be tempted to exaggerate the
intensity of their preference (on a Score ballot), so as to have more
effect in their vote.
On 03/12/2024 1:14 AM EDT Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
I think that somewhere between 0% and 100% of voters would do this.
Empirically, about 8% of US voters are honest and vote 3rd party, even if
we assume nobody likes either major party candidate. With less extreme
pressure, that number would probably be higher.
On Mon, Mar 11, 2024 at 10:07 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
On 03/11/2024 11:22 PM EDT Closed Limelike Curves <
closed.limelike.curves@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@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Election-Methods mailing list - see https://electorama.com/em for
list info
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
On Mon, Mar 11, 2024 at 22:25 Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
Oh, definitely. Most of them will, probably. But probably not all; and if
all of them do it, every cardinal system collapses back into approval,
which is fine anyways.
Yes.
On Mon, Mar 11, 2024 at 10:17 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
The question is about whether voters might be tempted to exaggerate the
intensity of their preference (on a Score ballot), so as to have more
effect in their vote.
On 03/12/2024 1:14 AM EDT Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
I think that somewhere between 0% and 100% of voters would do this.
Empirically, about 8% of US voters are honest and vote 3rd party, even if
we assume nobody likes either major party candidate. With less extreme
pressure, that number would probably be higher.
On Mon, Mar 11, 2024 at 10:07 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
On 03/11/2024 11:22 PM EDT Closed Limelike Curves <
closed.limelike.curves@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@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Election-Methods mailing list - see https://electorama.com/em for
list info
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Election-Methods mailing list - see https://electorama.com/em for list
info
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 propertyhttps://en.wikipedia.org/wiki/Archimedean_property (a much weaker form of the majority criterionhttps://en.wikipedia.org/wiki/Majority_criterion). As shown below, it is possible for Alicehttps://en.wikipedia.org/wiki/Alice_and_Bob to defeat Bobhttps://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
Manyhttps://en.wikipedia.org/wiki/Arbitrarily_large
100/100
52/100
0/100
1
50/100
51/100
1/100
Manyhttps://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 criterionhttps://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 propertyhttps://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 criterionhttps://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@hotmail.com
Sent: Monday, March 11, 2024 1:13 PM
To: election-methods@lists.electorama.com election-methods@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@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@audioimagination.com
Date: Sun, 10 Mar 2024 23:54:34 -0700
From: Closed Limelike Curves closed.limelike.curves@gmail.com
To: steve bosworth <stevebosworth@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@hotmail.com
wrote:
3/9/2024
From: stevebosworth@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@hotmail.com
Sent: Monday, March 11, 2024 1:13 PM
To: election-methods@lists.electorama.com election-methods@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@gmail.com
To: steve bosworth <stevebosworth@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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