[EM] MCA on electowiki

[Kathy Dopp]

On Mon, Oct 18, 2010 at 7:06 PM, Jameson Quinn <jameson.quinn at gmail.com> wrote:
> Because by simply voting (participation), you change the threshold needed
> for an absolute majority, and thus for certain kinds of wins. You cannot do
> this by changing your vote (monotonicity).

But  Statement of Participation Criterion that you linked to says:

Adding one or more ballots that vote X over Y should never change the
winner from X to Y.

so failing the criteria means adding more votes having X > Y would
change the winner from X to Y.  i.e. failing monotonicity.

Kathy

>
> 2010/10/18 Kathy Dopp <kathy.dopp at gmail.com>
>>
>> James,
>>
>> Why is failure of the "participation criteria" not equivalent to
>> failure of monotonicity?
>>
>> Thanks.
>> Kathy
>>
>> > Date: Mon, 18 Oct 2010 14:26:06 -0500
>> > From: Jameson Quinn <jameson.quinn at gmail.com>
>> > To: election-methods <election-methods at electorama.com>,
>> >        electionsciencefoundation <electionscience at googlegroups.com>
>> > Subject: [EM] MCA on electowiki
>> > Message-ID:
>> >        <AANLkTimGdVNrtAZ9VHn2jqJbAd2wXO7vYHz_NhxUSTR8 at mail.gmail.com>
>> > Content-Type: text/plain; charset="iso-8859-1"
>> >
>> > I edited Electowiki to essentially replace the Bucklin-ER article with a
>> > new, expanded MCA article. In this article, I define 6 MCA variants. I
>> > find
>> > that as a class, they do surprisingly well on criteria compliance.
>> > Please
>> > check my work:
>> >
>> >
>> > http://wiki.electorama.com/wiki/Majority_Choice_Approval#Criteria_compliance
>> >
>> >
>> > <http://wiki.electorama.com/wiki/Majority_Choice_Approval#Criteria_compliance>I
>> > also put a mention of the pre-Napoleonic use of Bucklin in Geneva on the
>> > Bucklin page.
>> >
>> > Here's a copy of the definitions and compliances for MCA:
>> >
>> > How does it work?
>> >
>> > Voters rate candidates into a fixed number of rating classes. There are
>> > commonly 3, 4, 5, or even 100 possible rating levels. The following
>> > discussion assumes 3 ratings, called "preferred", "approved", and
>> > "unapproved".
>> >
>> > If one and only one candidate is preferred by an absolute
>> >
>> > majority<http://wiki.electorama.com/wiki/index.php?title=Absolute_majority&action=edit&redlink=1>
>> > of
>> > voters, that candidate wins. If not, the same happens if there is only
>> > one
>> > candidate approved by a majority.
>> >
>> > If the election is still unresolved, one of two things must be true.
>> > Either
>> > multiple candidates attain a majority at the same rating level, or there
>> > are
>> > no candidates with an absolute majority at any level. In either case,
>> > there
>> > are different ways to resolve between the possible winners - that is, in
>> > the
>> > former case, between those candidates with a majority, or in the latter
>> > case, between all candidates.
>> >
>> > The possible resolution methods include:
>> >
>> >   - MCA-A: Most approved candidate
>> >
>> >
>> >   - MCA-P: Most preferred candidate
>> >
>> >
>> >   - MCA-M: Candidate with the highest score at the rating level where an
>> >   absolute majority first appears, or MCA-A if there are no majorities.
>> >
>> >
>> >   - MCA-S: Range or Score winner, using (in the case of 3 ranking
>> > levels) 2
>> >   points for preference and 1 point for approval.
>> >
>> >
>> >   - MCA-R: Runoff - One or two of the methods above is used to pick two
>> >   "finalists", who are then measured against each other using one of the
>> >   following methods:
>> >
>> >
>> >   -
>> >      - MCA-IR: Instant runoff (Condorcet-style, using ballots): Ballots
>> > are
>> >      recounted for whichever one of the finalists they rate higher.
>> > Ballots which
>> >      rate both candidates at the same level are counted for neither.
>> >
>> >
>> >   -
>> >      - MCA-AR: Actual runoff: Voters return to the polls to choose one
>> > of
>> >      the finalists. This has the advantage that one candidate is
>> > guaranteed to
>> >      receive the absolute majority of the valid votes in the last
>> > round of voting
>> >      of the system as a whole.
>> >
>> >
>> > [edit<http://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approval&action=edit&section=2>
>> > ]A note on the term MCA
>> >
>> > "Majority Choice Approval" was at first used to refer to a specific form
>> > of
>> > MCA, which would be 3-level MCA-AR in the nomenclature above. Later, a
>> > voting system naming poll <http://betterpolls.com/v/1189> chose it as a
>> > more-accessible replacement term for ER-Bucklin in general.
>> >
>> >  [edit<http://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approval&action=edit&section=3>
>> > ] Criteria compliance
>> >
>> > All MCA variants satisfy the Plurality
>> > criterion<http://wiki.electorama.com/wiki/Plurality_criterion>,
>> > the Majority criterion for solid
>> >
>> > coalitions<http://wiki.electorama.com/wiki/Majority_criterion_for_solid_coalitions>
>> > , Monotonicity <http://wiki.electorama.com/wiki/Monotonicity_criterion>
>> > (for
>> > MCA-AR, assuming first- and second- round votes are consistent), and
>> > Minimal
>> > Defense <http://wiki.electorama.com/wiki/Minimal_Defense_criterion>
>> > (which
>> > implies satisfaction of the Strong Defensive Strategy
>> >
>> > criterion<http://wiki.electorama.com/wiki/Strong_Defensive_Strategy_criterion>
>> > ).
>> >
>> > The Condorcet
>> > criterion<http://wiki.electorama.com/wiki/Condorcet_criterion> is
>> > satisfied by MCA-VR if the pairwise champion (PC, aka CW) is visible on
>> > the
>> > ballots. It is satisfied by MCA-AR if at least half the voters at least
>> > approve the PC in the first round. Other MCA versions fail this
>> > criterion.
>> >
>> > Clone Independence
>> > <http://wiki.electorama.com/wiki/Strategic_nomination> is
>> > satisfied by most MCA versions. In fact, even the stronger Independence
>> > of
>> > irrelevant
>> > alternatives<http://wiki.electorama.com/wiki/Independence_of_irrelevant_alternatives>
>> > is
>> > satisfied by MCA-A, MCA-P, MCA-M, and MCA-S. Clone independence is
>> > satisfied
>> > along with the weaker and related
>> > ISDA<http://wiki.electorama.com/wiki/ISDA> by
>> > MCA-IR and MCA-AR, if ISDA-compliant Condorcet methods (ie,
>> > Schulze<http://wiki.electorama.com/wiki/Schulze>)
>> > are used to choose the two "finalists". Using simpler methods to decide
>> > the
>> > finalists, MCA-IR and MCA-AR are not clone independent.
>> >
>> > The Later-no-help
>> > criterion<http://wiki.electorama.com/wiki/Later-no-help_criterion> and
>> > the Favorite Betrayal
>> > criterion<http://wiki.electorama.com/wiki/Favorite_Betrayal_criterion>
>> > are
>> > satisfied by MCA-P. They're also satisfied by MCA-AR if MCA-P is used to
>> > pick the two finalists.
>> >
>> > The Participation
>> > <http://wiki.electorama.com/wiki/Participation_criterion>
>> >  and Summability
>> > criterion<http://wiki.electorama.com/wiki/Summability_criterion> are
>> > not satisfied by any MCA variant, although MCA-P only fails
>> > Participation if
>> > the additional vote causes an approval majority.
>> >
>> > None of the methods satisfy
>> > Later-no-harm<http://wiki.electorama.com/wiki/Later-no-harm_criterion>
>> > .
>> >
>> > All of the methods are
>> > matrix-summable<http://wiki.electorama.com/wiki/Summability_criterion>
>> > for
>> > counting at the precinct level. Only MCA-IR actually requires a matrix
>> > (or,
>> > possibly two counting rounds), and is thus "summable for
>> > k=2<http://wiki.electorama.com/wiki/Summability_criterion>" ;
>> > the others require only O(N) tallies, and are thus "summable for
>> > k=1<http://wiki.electorama.com/wiki/Summability_criterion>
>> > ".
>> >
>> > Thus, the method which satisfies the most criteria is MCA-AR, using
>> > Schulze<http://wiki.electorama.com/wiki/Schulze> over
>> > the ballots to select one finalist and MCA-P to select the other. Also
>> > notable are MCA-M and MCA-P, which, as rated methods (and thus ones
>> > which
>> > fail Arrow's ranking-based Universality Criterion), are able to seem to
>> > "violate Arrow's Theorem
>> > <http://wiki.electorama.com/wiki/Arrow%27s_Theorem>"
>> > by simultaneously satisfying monotonicity and independence of irrelevant
>> >
>> > alternatives<http://wiki.electorama.com/wiki/Independence_of_irrelevant_alternatives>
>> > (as
>> > well as of course sovereignty and non-dictatorship).
>>
>>
>>
>> --
>>
>> Kathy Dopp
>> http://electionmathematics.org
>> Town of Colonie, NY 12304
>> "One of the best ways to keep any conversation civil is to support the
>> discussion with true facts."
>>
>> Fundamentals of Verifiable Elections
>> http://kathydopp.com/wordpress/?p=174
>>
>> Realities Mar Instant Runoff Voting
>>
>> http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf
>>
>> View some of my research on my SSRN Author page:
>> http://ssrn.com/author=1451051
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info
>
>



-- 

Kathy Dopp
http://electionmathematics.org
Town of Colonie, NY 12304
"One of the best ways to keep any conversation civil is to support the
discussion with true facts."

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

Realities Mar Instant Runoff Voting
http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

View some of my research on my SSRN Author page:
http://ssrn.com/author=1451051