[EM] MCA on electowiki

Mon Oct 18 16:06:14 PDT 2010

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).

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
>
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