[EM] Condorcet Enhancement

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[EM] Condorcet Enhancement

Forest Simmons
There are various ways to enhance a given method to make it Condorcet compliant:

1.  One can elect the ballot CW if there is one, and otherwise fall back on the given method.

2. One can apply the given method to the Smith set.

3. One can use the given method winner as the starting point in a seamless process that leads to a member of the Smith Set (or better).

Here is such a process:

First, create a directed graph whose vertices are the candidate names as follows:

For each covered candidate X, draw an arrow to that candidate Y (among those that cover X) which is ranked or rated strictly below X on the fewest number of ballots.

To enhance the winner A of any method, start at candidate A and follow the arrows as far as possible in the directed graph.  The enhanced winner W' is the one at the end of the directed path.

This W' covers W, but is itself uncovered (a member of the Landau Set), and so also a member of Smith.

If the original method elects monotonically, then so does the enhanced method.

If the original method satisfies the FBC or in any case lacks vulnerability to compromise, then the enhanced method gives little incentive for burying Favorite because when there is an arrow from Favorite to Y, candidate Y is already the natural compromise candidate for the supporters of Favorite, the one that is rated strictly below Favorite on the fewest ballots among those that cover Favorite.

Suggestions:

A.  Enhanced Approval.
B.  Enhanced Majority Judgment
C.  Enhanced Random Ballot
D.  Enhanced Asset Voting (different possible versions)
E.   Enhanced Chiastic Approval

Other versions?

If method M is Chicken Resistant, does it follow that the Enhanced version of Method M also Chicken Resistant?

Other thoughts?

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Re: [EM] Condorcet Enhancement

Magosányi Árpád
I would add Modified D21 to the list.
D21 is genially simplifies the ballot for human use compared to preferential voting. The voters give (partial) preferences, which can be evaluated using Condorcet. (I have found at least one inconsistency and one factual error about the evaluation method in the D21 paper. While I think the method is actually better than Majority (not a big feat in itself), that undermines the claims of the paper significantly.)

What does "Chicken Resistant" mean? Google failed to give me any relevant results.

On 5/20/19 12:10 AM, Forest Simmons wrote:
There are various ways to enhance a given method to make it Condorcet compliant:

1.  One can elect the ballot CW if there is one, and otherwise fall back on the given method.

2. One can apply the given method to the Smith set.

3. One can use the given method winner as the starting point in a seamless process that leads to a member of the Smith Set (or better).

Here is such a process:

First, create a directed graph whose vertices are the candidate names as follows:

For each covered candidate X, draw an arrow to that candidate Y (among those that cover X) which is ranked or rated strictly below X on the fewest number of ballots.

To enhance the winner A of any method, start at candidate A and follow the arrows as far as possible in the directed graph.  The enhanced winner W' is the one at the end of the directed path.

This W' covers W, but is itself uncovered (a member of the Landau Set), and so also a member of Smith.

If the original method elects monotonically, then so does the enhanced method.

If the original method satisfies the FBC or in any case lacks vulnerability to compromise, then the enhanced method gives little incentive for burying Favorite because when there is an arrow from Favorite to Y, candidate Y is already the natural compromise candidate for the supporters of Favorite, the one that is rated strictly below Favorite on the fewest ballots among those that cover Favorite.

Suggestions:

A.  Enhanced Approval.
B.  Enhanced Majority Judgment
C.  Enhanced Random Ballot
D.  Enhanced Asset Voting (different possible versions)
E.   Enhanced Chiastic Approval

Other versions?

If method M is Chicken Resistant, does it follow that the Enhanced version of Method M also Chicken Resistant?

Other thoughts?

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Re: [EM] Condorcet Enhancement

Abd ul-Rahman Lomax
In reply to this post by Forest Simmons

Condorcet compliance is valuable if it is based on *persistent preference.* I.e,. if a Condorcet winner as expressed on the ballots survives to the next phase, then the method can be Condorcet compliant, even if later voter decisions choose someone else. Problem is when we have a large candidate set, that "Condorcet winner" may be approved for election by only a minority, and it could even be a small minority. Most voting systems analysis completely neglects ballot placement, and, as well, the problem that Dodgson identified, most voters not having enough information to rank many candidates.

Majority approval of an election is a basic democratic requirement, necessary in NGOs, generally, but badly neglected in public elections. IRV produces a fake majority by ballot exclusion, too often. I've suggested using a Score ballot, defining a scoring level as "approved for election in place of an additional poll" -- probably midrange -- and then considering these rules:

1. The primary cannot complete with an election unless the winner is approved by a majority.

2. If a Condorcet winner exists, this candidate must not be eliminated from the next round (and write-in votes should always be allowed; doing otherwise creates fake majorities).

3. Likewise a Range winner cannot be eliminated.

Whether or not a Condorect winner loses if there is a different Approval winner is an issue of balance. Yes, the voters will have approved a different winner -- and the voters should have the power to disregard their own preference in order to complete an election. But it is possible that this is based on misinformation about the true possible voting. So maybe a conflict here would require a second election. I have no strong position on this. This issue is resolved by Asset.

4.  It is possible that Asset could always find a winner even with only one round general election. In this case, the preferences to be considered are the preferences of the chosen electors. They may use many, many rounds, in their process, and single-winner, a majority of electoral votes would be required. I prefer, instead, though, electing an Assembly and the Assembly elects officers (i.e., what single-winner elections are used for) or makes other Yes/No decisions, which may be amended and iterated many, many times, by being a deliberative body with immediate voting.

Without Asset, my sense is that using an advanced voting system, such as the hybrids proposed, unless candidacies multiply because of improved systems, will produce a majority-approved result usually in the first round, and failure in a second round would be very rare, and the failure might be by such a narrow social utility margin that little harm is done by electing the "wrong" candidate. We only toss a coin with exact vote equality, but from a social utility point of view, not a great deal of harm is done by electing a candidate with 49.9% of the vote. Or a third round could be required, how important is it?

Problematic systems will elect a minority-approved candidate under much more harmful conditions than that!

However, this is also what I expect. An advanced system will show the true support for minority candidates, and this will encourage the multiplication of candidacies, which then runs into the problem that Asset was designed to address. All roads lead to Asset, and what amazes me is that Asset is simply very basic democracy, simply representative instead of direct.

What we have called "representative" democracy does not represent the voters, but districts, leading to a horrible mess that nobody thinks can be fixed.

On 5/19/2019 7:10 PM, Forest Simmons wrote:
There are various ways to enhance a given method to make it Condorcet compliant:

1.  One can elect the ballot CW if there is one, and otherwise fall back on the given method.

2. One can apply the given method to the Smith set.

3. One can use the given method winner as the starting point in a seamless process that leads to a member of the Smith Set (or better).

Here is such a process:

First, create a directed graph whose vertices are the candidate names as follows:

For each covered candidate X, draw an arrow to that candidate Y (among those that cover X) which is ranked or rated strictly below X on the fewest number of ballots.

To enhance the winner A of any method, start at candidate A and follow the arrows as far as possible in the directed graph.  The enhanced winner W' is the one at the end of the directed path.

This W' covers W, but is itself uncovered (a member of the Landau Set), and so also a member of Smith.

If the original method elects monotonically, then so does the enhanced method.

If the original method satisfies the FBC or in any case lacks vulnerability to compromise, then the enhanced method gives little incentive for burying Favorite because when there is an arrow from Favorite to Y, candidate Y is already the natural compromise candidate for the supporters of Favorite, the one that is rated strictly below Favorite on the fewest ballots among those that cover Favorite.

Suggestions:

A.  Enhanced Approval.
B.  Enhanced Majority Judgment
C.  Enhanced Random Ballot
D.  Enhanced Asset Voting (different possible versions)
E.   Enhanced Chiastic Approval

Other versions?

If method M is Chicken Resistant, does it follow that the Enhanced version of Method M also Chicken Resistant?

Other thoughts?

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Re: [EM] Condorcet Enhancement

Forest Simmons
In reply to this post by Forest Simmons
By Chicken Resistant I mean satisfying the Chicken Dilemma Criterion.  See


Since I posted this Condorcet Enhancement technique, while working on the proof of monotonicity I realized that more is required of the base method than mere monotonicity.  Satisfaction of the FBC by the base method is sufficient to preserve monotonicity in the enhanced method. Otherwise, the attempted proof breaks down because raising the enhanced winner W' relative to the other candidates could change the base method winner from W to some W'' not in the set of candidates that flow into W' in the directed graph.  If the method satisfies the Favorite Betrayal Criterion, then raising W' in the base method leaves the new base winner in the set {W, W'} which is contained in the set of vertices that drain into W', since candidate W' is by definition the final destination of W in the flow of the digraph.

So enhanced MMPO (MinMaxPairwiseOpposition), enhanced Equal Rank Whole  and rated versions of Bucklin (including Majority Judgment), enhanced Borda, enhanced Plurality, enhanced Range (including enhanced approval), enhanced Random Ballot, and some versions of enhanced asset voting, will all be monotone from start to finish. 

When using cardinal ratings (i.e. grades, scores, or range style ballots) we can improve upon the directed graph as follows:

If X is covered, draw an arrow from X to the candidate Y (from among those that cover X) that incurs the least total disappointment in the transition from X to Y.

The disappointment incurred on a given ballot is zero if Y is rated above X on that ballot, otherwise it is the difference in the rating of X and the rating of Y on that ballot.

The total disappointment is the sum over all ballots of the ballot disappointments.

If we use the resulting digraph in our Condorcet enhancement, we produce a Condorcet method that respects the expressed ratings of the voters beyond the utility contribution from the base method. In other words when the enhancement phase is based on mere rankings, some of the utility flavor of the base phase may be lost.

On Mon, May 20, 2019 at 10:43 AM <[hidden email]> wrote:
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Today's Topics:

   1. Condorcet Enhancement (Forest Simmons)
   2. Re: Condorcet Enhancement (Magos?nyi ?rp?d)
   3. Re: Condorcet Enhancement (Abd ul-Rahman Lomax)


----------------------------------------------------------------------

Message: 1
Date: Sun, 19 May 2019 16:10:17 -0700
From: Forest Simmons <[hidden email]>
To: EM <[hidden email]>
Subject: [EM] Condorcet Enhancement
Message-ID:
        <CAP29oncLAXha=7kX2iQexe8oSNCkOSti4Z+1BOOrPvnfhuem=[hidden email]>
Content-Type: text/plain; charset="utf-8"

There are various ways to enhance a given method to make it Condorcet
compliant:

1.  One can elect the ballot CW if there is one, and otherwise fall back on
the given method.

2. One can apply the given method to the Smith set.

3. One can use the given method winner as the starting point in a seamless
process that leads to a member of the Smith Set (or better).

Here is such a process:

First, create a directed graph whose vertices are the candidate names as
follows:

For each covered candidate X, draw an arrow to that candidate Y (among
those that cover X) which is ranked or rated strictly below X on the fewest
number of ballots.

To enhance the winner A of any method, start at candidate A and follow the
arrows as far as possible in the directed graph.  The enhanced winner W' is
the one at the end of the directed path.

This W' covers W, but is itself uncovered (a member of the Landau Set), and
so also a member of Smith.

If the original method elects monotonically, then so does the enhanced
method.

If the original method satisfies the FBC or in any case lacks vulnerability
to compromise, then the enhanced method gives little incentive for burying
Favorite because when there is an arrow from Favorite to Y, candidate Y is
already the natural compromise candidate for the supporters of Favorite,
the one that is rated strictly below Favorite on the fewest ballots among
those that cover Favorite.

Suggestions:

A.  Enhanced Approval.
B.  Enhanced Majority Judgment
C.  Enhanced Random Ballot
D.  Enhanced Asset Voting (different possible versions)
E.   Enhanced Chiastic Approval

Other versions?

If method M is Chicken Resistant, does it follow that the Enhanced version
of Method M also Chicken Resistant?

Other thoughts?
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Message: 2
Date: Mon, 20 May 2019 07:57:22 +0100
From: Magos?nyi ?rp?d <[hidden email]>
To: [hidden email]
Subject: Re: [EM] Condorcet Enhancement
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

I would add Modified D21 to the list.
D21 is genially simplifies the ballot for human use compared to
preferential voting. The voters give (partial) preferences, which can be
evaluated using Condorcet. (I have found at least one inconsistency and
one factual error about the evaluation method in the D21 paper. While I
think the method is actually better than Majority (not a big feat in
itself), that undermines the claims of the paper significantly.)

What does "Chicken Resistant" mean? Google failed to give me any
relevant results.

On 5/20/19 12:10 AM, Forest Simmons wrote:
> There are various ways to enhance a given method to make it Condorcet
> compliant:
>
> 1.? One can elect the ballot CW if there is one, and otherwise fall
> back on the given method.
>
> 2. One can apply the given method to the Smith set.
>
> 3. One can use the given method winner as the starting point in a
> seamless process that leads to a member of the Smith Set (or better).
>
> Here is such a process:
>
> First, create a directed graph whose vertices are the candidate names
> as follows:
>
> For each covered candidate X, draw an arrow to that candidate Y (among
> those that cover X) which is ranked or rated strictly below X on the
> fewest number of ballots.
>
> To enhance the winner A of any method, start at candidate A and follow
> the arrows as far as possible in the directed graph.? The enhanced
> winner W' is the one at the end of the directed path.
>
> This W' covers W, but is itself uncovered (a member of the Landau
> Set), and so also a member of Smith.
>
> If the original method elects monotonically, then so does the enhanced
> method.
>
> If the original method satisfies the FBC or in any case lacks
> vulnerability to compromise, then the enhanced method gives little
> incentive for burying Favorite because when there is an arrow from
> Favorite to Y, candidate Y is already the natural compromise candidate
> for the supporters of Favorite, the one that is rated strictly below
> Favorite on the fewest ballots among those that cover Favorite.
>
> Suggestions:
>
> A.? Enhanced Approval.
> B.? Enhanced Majority Judgment
> C.? Enhanced Random Ballot
> D.? Enhanced Asset Voting (different possible versions)
> E.?? Enhanced Chiastic Approval
>
> Other versions?
>
> If method M is Chicken Resistant, does it follow that the Enhanced
> version of Method M also Chicken Resistant?
>
> Other thoughts?
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info


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------------------------------

Message: 3
Date: Mon, 20 May 2019 13:42:02 -0400
From: Abd ul-Rahman Lomax <[hidden email]>
To: [hidden email]
Subject: Re: [EM] Condorcet Enhancement
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"; Format="flowed"

Condorcet compliance is valuable if it is based on *persistent
preference.* I.e,. if a Condorcet winner as expressed on the ballots
survives to the next phase, then the method can be Condorcet compliant,
even if later voter decisions choose someone else. Problem is when we
have a large candidate set, that "Condorcet winner" may be approved for
election by only a minority, and it could even be a small minority. Most
voting systems analysis completely neglects ballot placement, and, as
well, the problem that Dodgson identified, most voters not having enough
information to rank many candidates.

Majority approval of an election is a basic democratic requirement,
necessary in NGOs, generally, but badly neglected in public elections.
IRV produces a fake majority by ballot exclusion, too often. I've
suggested using a Score ballot, defining a scoring level as "approved
for election in place of an additional poll" -- probably midrange -- and
then considering these rules:

1. The primary cannot complete with an election unless the winner is
approved by a majority.

2. If a Condorcet winner exists, this candidate must not be eliminated
from the next round (and write-in votes should always be allowed; doing
otherwise creates fake majorities).

3. Likewise a Range winner cannot be eliminated.

Whether or not a Condorect winner loses if there is a different Approval
winner is an issue of balance. Yes, the voters will have approved a
different winner -- and the voters should have the power to disregard
their own preference in order to complete an election. But it is
possible that this is based on misinformation about the true possible
voting. So maybe a conflict here would require a second election. I have
no strong position on this. This issue is resolved by Asset.

4.? It is possible that Asset could always find a winner even with only
one round general election. In this case, the preferences to be
considered are the preferences of the chosen electors. They may use
many, many rounds, in their process, and single-winner, a majority of
electoral votes would be required. I prefer, instead, though, electing
an Assembly and the Assembly elects officers (i.e., what single-winner
elections are used for) or makes other Yes/No decisions, which may be
amended and iterated many, many times, by being a deliberative body with
immediate voting.

Without Asset, my sense is that using an advanced voting system, such as
the hybrids proposed, unless candidacies multiply because of improved
systems, will produce a majority-approved result usually in the first
round, and failure in a second round would be very rare, and the failure
might be by such a narrow social utility margin that little harm is done
by electing the "wrong" candidate. We only toss a coin with exact vote
equality, but from a social utility point of view, not a great deal of
harm is done by electing a candidate with 49.9% of the vote. Or a third
round could be required, how important is it?

Problematic systems will elect a minority-approved candidate under much
more harmful conditions than that!

However, this is also what I expect. An advanced system will show the
true support for minority candidates, and this will encourage the
multiplication of candidacies, which then runs into the problem that
Asset was designed to address. All roads lead to Asset, and what amazes
me is that Asset is simply very basic democracy, simply representative
instead of direct.

What we have called "representative" democracy does not represent the
voters, but districts, leading to a horrible mess that nobody thinks can
be fixed.

On 5/19/2019 7:10 PM, Forest Simmons wrote:
> There are various ways to enhance a given method to make it Condorcet
> compliant:
>
> 1.? One can elect the ballot CW if there is one, and otherwise fall
> back on the given method.
>
> 2. One can apply the given method to the Smith set.
>
> 3. One can use the given method winner as the starting point in a
> seamless process that leads to a member of the Smith Set (or better).
>
> Here is such a process:
>
> First, create a directed graph whose vertices are the candidate names
> as follows:
>
> For each covered candidate X, draw an arrow to that candidate Y (among
> those that cover X) which is ranked or rated strictly below X on the
> fewest number of ballots.
>
> To enhance the winner A of any method, start at candidate A and follow
> the arrows as far as possible in the directed graph.? The enhanced
> winner W' is the one at the end of the directed path.
>
> This W' covers W, but is itself uncovered (a member of the Landau
> Set), and so also a member of Smith.
>
> If the original method elects monotonically, then so does the enhanced
> method.
>
> If the original method satisfies the FBC or in any case lacks
> vulnerability to compromise, then the enhanced method gives little
> incentive for burying Favorite because when there is an arrow from
> Favorite to Y, candidate Y is already the natural compromise candidate
> for the supporters of Favorite, the one that is rated strictly below
> Favorite on the fewest ballots among those that cover Favorite.
>
> Suggestions:
>
> A.? Enhanced Approval.
> B.? Enhanced Majority Judgment
> C.? Enhanced Random Ballot
> D.? Enhanced Asset Voting (different possible versions)
> E.?? Enhanced Chiastic Approval
>
> Other versions?
>
> If method M is Chicken Resistant, does it follow that the Enhanced
> version of Method M also Chicken Resistant?
>
> Other thoughts?
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info
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