On Mon, Oct 18, 2010 at 7:06 PM, Jameson Quinn <[email protected]> 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 <[email protected]> >> >> 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 > > -- 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
