[EM] Condorcet Enhancement

Mon May 20 13:02:14 PDT 2019

By Chicken Resistant I mean satisfying the Chicken Dilemma Criterion.  See

https://electowiki.org/wiki/Chicken_Dilemma_Criterion

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 <
election-methods-request at lists.electorama.com> wrote:

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> Today's Topics:
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>    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 <fsimmons at pcc.edu>
> To: EM <election-methods at lists.electorama.com>
> Subject: [EM] Condorcet Enhancement
> Message-ID:
>         <CAP29oncLAXha=7kX2iQexe8oSNCkOSti4Z+1BOOrPvnfhuem=
> Q at mail.gmail.com>
> 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 <m4gw4s at gmail.com>
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] Condorcet Enhancement
> Message-ID: <4b2ad187-9ef4-fc8d-788e-2d6a8c266c30 at gmail.com>
> 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 <abd at lomaxdesign.com>
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] Condorcet Enhancement
> Message-ID: <ffcc4b4d-3d57-b295-1e90-53f3224abcad at lomaxdesign.com>
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>
> 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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