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 <[email protected]> > To: election-methods <[email protected]>, > electionsciencefoundation <[email protected]> > Subject: [EM] MCA on electowiki > Message-ID: > <[email protected]> > 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§ion=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§ion=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
