[EM] MCA on electowiki (re Later-no-help and Favorite Betrayal criteria)
http://wiki.electorama.com/wiki/Majority_Choice_Approval#Criteria_compliance The Later-no-help criterion /wiki/Later-no-help_criterion and the Favorite Betrayal criterion /wiki/Favorite_Betrayal_criterion are satisfied by MCA-P They are also met by MCA-A, MCA-M and MCA-S. I consider it desirable that methods should have Later-no-Harm and Later-no-Help in at least approximate probabilistic balance. These methods all (badly) fail Later-no-Harm, so meeting LNHelp contributes to the strong truncation incentive. They're also satisfied by MCA-AR if MCA-P is used to pick the two finalists That method does not meet the Favourite Betrayal criterion. 25: A 24: AC 02: BA 22: B 25: CB 02: C=B (sincere is CB) No candidates' TR (or P) score reaches the majority threshold of 51 and all their Approval scores exceed it, so a resolution method is needed. Of the candidates that reached a majority score, I gather the method selects the two with the highest TR scores for a runoff. TR scores: A49,B26,C27. The method selects A and C for the runoff, which A wins 51-27. If the 2 C=B voters vote sincerely CB the result is the same. But if they change to BC the TR scores change to A49, B26, C25 and the method then selects A and B for the runoff which B wins 51-49, a result those two voters prefer. 25: A 24: AC 02: BA 22: B 25: CB 02: BC (was C=B, sincere is CB) Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] MCA on electowiki
Jameson Quinn wrote (18 Oct 2010): 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 Now quoting from the referred-to Electowiki page: Majority Choice Approval (MCA) is a class of rated voting systems which attempt to find majority support for some candidate. It is closely related to Bucklin Voting, which refers to ranked systems using similar rules. In fact, some people consider MCA a subclass of Bucklin, calling it ER-Bucklin http://wiki.electorama.com/wiki/ER-Bucklin (for Equal-Ratings-[allowed] Bucklin). Who are these people? As I understand it, ER-Bucklin is a method that uses ranked ballots that allow equal-ranking whereas MCA is a method that uses 3-slot ratings ballots (but could be extended to more than 3 rating slots). 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/Absolute_majority of voters, that candidate wins. If not, approvals are added to preferences, and again if there is only one candidate with a majority they win. 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 (most votes above lowest possible rating) Until I read this, the only versions of MCA that I was aware of were this one and another that differs only by using a hybrid FPP-Approval ballot that restricts voters to indicating one candidate as most preferred plus they can approve as many candidates as they like. (The latter version was an early suggestion that seem to quickly fall out of favour). MCA-P: Most preferred candidate (most votes at highest possible rating) I've heard of this, as a 3-slot method with a different name. The strategic incentive for voters to not use any rating-slot other than the top one is even higher than it is with MCA-A. A note on terminology Majority Choice Approval was first used to refer to a specific form, which would be 3-level MCA-AR in the nomenclature above (specifically, 3-MCA-AR-M). Later, a voting system naming poll http://betterpolls.com/v/1189 chose this term as a more-accessible replacement for ER-Bucklin in general. As I previously implied, this is news to me. How exactly does this mysterious 3-MCA-AR-M method work? Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] MCA on electowiki
Jameson Quinn wrote (18 Oct 2010): 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 Criteria compliances 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). It is well known that in general run-off methods fail mono-raise (aka Monotonicity), and these methods are no exception. 22: A 23: AC 24: B 27: CB 02: DC 06: E (104 ballots) TR scores: A45, B24, C27, D2, E6. Approval scores: A45, B51, C52, D2, E6. I am assuming that 3-slot ballots are used, and since no candidate has either a Top Ratings or Approval score that reaches the majority threshold the runoff will be between the TR winner A and the Approval winner C. A wins that runoff 45-29, but if the 2 DC ballots change to DA the Approval winner changes to B and now A loses that runoff 47-49. 22: A 23: AC 24: B 27: CB 02: DA (was DC) 06: E (104 ballots) TR scores: A45, B24, C27, D2, E6. Approval scores: A47, B51, C50, D2, E6. Also I would quibble that methods that use ballots that don't allow voters to express a full ranking of the candidates really properly meet Majority for Soild Coalitions, but instead just meet a restricted form of it (which is nonetheless very valuable). And I'm surprised that a MCA advocate doesn't mention the Favourite Betrayal criterion. Of course the suggested runoff variants of MCA also fail that. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] MCA on electowiki
Kathy Dopp wrote: The mathematical definition of increasing monotonicity says when I increase the independent variable, the dependent variable likewise increases (for voting, when I increase votes for a candidate, that candidate's chance of winning increases.) Or the mathematical definition of nondecreasing monotonicity says, when I increase the independent variable, the dependent variable never decreases (for voting when I increase votes for a candidate, the candidate's chances of winning never decreases.) I would say by any standard normal mathematical definition of monotonicity, if a voting method fails the Participation Criterion you linked to, it also fails to be monotonic. Adding votes or increasing ranking for a candidate, should not cause that candidate to lose whereas he otherwise might have won. To me, that is just another way of stating nonmonotonicity. Using Woodall's terms, the full name of what we usually call monotonicity on this mailing list is mono-raise. That is: monotonicity regarding raising (ranking higher) a candidate. There are many other forms of monotonicity: for instance, mono-add-top (adding a vote that ranks a candidate first shouldn't make the candidate lose), mono-append (adding a candidate to a truncated ballot should not make that candidate lose), and so on. See http://www.votingmatters.org.uk/ISSUE3/P5.HTM for the full list. Any of these might be called monotonicity criteria, since they involve situations where ballots are added or altered in a way that is seemingly favorable for the new candidate, and the method fails the criterion if the candidate loses. As for Participation, Woodall says: There is also the following property, which is not strictly a form of monotonicity but is very close to it. (...) Participation. The addition of a further ballot should not, for any positive whole number k, reduce the probability that at least one candidate is elected out of the first k candidates listed on that ballot. . It is, unfortunately, a very strict criterion. Only voting methods that consist of point systems with point system tiebreakers (not necessarily the same tiebreakers) can fulfill it. A point system is one where you give the first candidate on a ballot x points, the second y points, the third z points, etc. DAC/DSC is in this sense a series of point systems, each breaking ties of the last. In summing up: what we call monotonicity is just one form of monotonicity, that is true; and it is unfortunate but also true that most complex systems fail Participation. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] MCA on electowiki
In case you're wondering about a real example of MCA-P failing participation (and, in fact, mono-add-top), here it is. Situation before: 1 vote: AB 1 vote: CB 1 vote: DB 1 vote: E 1 vote: F 1 vote: A No majorities, so, since it's MCA-*P*, the highest *P*reference wins; that's A. (Exactly 50% isn't a majority. If it were, you could just add one G vote to the example.) Now, add another AB vote. A still isn't preferred by a majority (only 3/7), but B now has a majority approval (4/7). So B wins. Two points about this example: it took a lot of candidates, carefully balanced; and the participation-violating final AB vote was unstrategically extending approval. Simple strategy says that if you prefer one frontrunner, you shouldn't approve the other one; so the voters must not have known the true frontrunners. Yes, it's still unfortunate. But I'd bet that if you model how frequently in any given random elections model some voters would have reason to regret their participation, it would be somewhere well under 5%, probably under 2%; and any foreknowledge and strategy would tend to reduce that number even further. JQ 2010/10/19 Kristofer Munsterhjelm km-el...@broadpark.no Kathy Dopp wrote: The mathematical definition of increasing monotonicity says when I increase the independent variable, the dependent variable likewise increases (for voting, when I increase votes for a candidate, that candidate's chance of winning increases.) Or the mathematical definition of nondecreasing monotonicity says, when I increase the independent variable, the dependent variable never decreases (for voting when I increase votes for a candidate, the candidate's chances of winning never decreases.) I would say by any standard normal mathematical definition of monotonicity, if a voting method fails the Participation Criterion you linked to, it also fails to be monotonic. Adding votes or increasing ranking for a candidate, should not cause that candidate to lose whereas he otherwise might have won. To me, that is just another way of stating nonmonotonicity. Using Woodall's terms, the full name of what we usually call monotonicity on this mailing list is mono-raise. That is: monotonicity regarding raising (ranking higher) a candidate. There are many other forms of monotonicity: for instance, mono-add-top (adding a vote that ranks a candidate first shouldn't make the candidate lose), mono-append (adding a candidate to a truncated ballot should not make that candidate lose), and so on. See http://www.votingmatters.org.uk/ISSUE3/P5.HTM for the full list. Any of these might be called monotonicity criteria, since they involve situations where ballots are added or altered in a way that is seemingly favorable for the new candidate, and the method fails the criterion if the candidate loses. As for Participation, Woodall says: There is also the following property, which is not strictly a form of monotonicity but is very close to it. (...) Participation. The addition of a further ballot should not, for any positive whole number k, reduce the probability that at least one candidate is elected out of the first k candidates listed on that ballot. . It is, unfortunately, a very strict criterion. Only voting methods that consist of point systems with point system tiebreakers (not necessarily the same tiebreakers) can fulfill it. A point system is one where you give the first candidate on a ballot x points, the second y points, the third z points, etc. DAC/DSC is in this sense a series of point systems, each breaking ties of the last. In summing up: what we call monotonicity is just one form of monotonicity, that is true; and it is unfortunate but also true that most complex systems fail Participation. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] MCA on electowiki
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_complianceI 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 majorityhttp://wiki.electorama.com/wiki/index.php?title=Absolute_majorityaction=editredlink=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. [edithttp://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approvalaction=editsection=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. [edithttp://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approvalaction=editsection=3 ] Criteria compliance All MCA variants satisfy the Plurality criterionhttp://wiki.electorama.com/wiki/Plurality_criterion, the Majority criterion for solid coalitionshttp://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 criterionhttp://wiki.electorama.com/wiki/Strong_Defensive_Strategy_criterion ). The Condorcet criterionhttp://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 alternativeshttp://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 ISDAhttp://wiki.electorama.com/wiki/ISDA by MCA-IR and MCA-AR, if ISDA-compliant Condorcet methods (ie, Schulzehttp://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 criterionhttp://wiki.electorama.com/wiki/Later-no-help_criterion and the Favorite Betrayal criterionhttp://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
Re: [EM] MCA on electowiki
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.qu...@gmail.com To: election-methods election-meth...@electorama.com, electionsciencefoundation electionscie...@googlegroups.com Subject: [EM] MCA on electowiki Message-ID: aanlktimgdvnrtaz9vhn2jqjbad2wxo7vyhz_nhxus...@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_complianceI 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 majorityhttp://wiki.electorama.com/wiki/index.php?title=Absolute_majorityaction=editredlink=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. [edithttp://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approvalaction=editsection=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. [edithttp://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approvalaction=editsection=3 ] Criteria compliance All MCA variants satisfy the Plurality criterionhttp://wiki.electorama.com/wiki/Plurality_criterion, the Majority criterion for solid coalitionshttp://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 criterionhttp://wiki.electorama.com/wiki/Strong_Defensive_Strategy_criterion ). The Condorcet criterionhttp://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 alternativeshttp://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 ISDAhttp://wiki.electorama.com/wiki/ISDA by MCA-IR and MCA-AR, if ISDA-compliant Condorcet methods (ie, Schulzehttp://wiki.electorama.com/wiki/Schulze) are used
Re: [EM] MCA on electowiki
By the way, my first message mistakenly said MCA fails the Summability criterion; I meant the Consistency criterion. Here's the latest version of the criteria compliance, which is the same as before except for the above change and some editing and reformatting: [edithttp://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approvalaction=editsection=3 ]Criteria compliance All MCA variants satisfy the Plurality criterionhttp://wiki.electorama.com/wiki/Plurality_criterion, the Majority criterion for solid coalitionshttp://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 criterionhttp://wiki.electorama.com/wiki/Strong_Defensive_Strategy_criterion ). All of the methods are matrix-summablehttp://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=2http://wiki.electorama.com/wiki/Summability_criterion ; the others require only O(N) tallies, and are thus summable for k=1http://wiki.electorama.com/wiki/Summability_criterion . The Participation criterionhttp://wiki.electorama.com/wiki/Participation_criterion and its stronger cousin the Consistency criterionhttp://wiki.electorama.com/wiki/Consistency_criterion, as well as the Later-no-harm criterionhttp://wiki.electorama.com/wiki/Later-no-harm_criterion are not satisfied by any MCA variant, although MCA-P only fails Participation if the additional vote causes an approval majority. Other criteria are satisfied by some, but not all, MCA variants. To wit: - Clone Independencehttp://wiki.electorama.com/wiki/Strategic_nomination is satisfied by most MCA versions. In fact, even the stronger Independence of irrelevant alternativeshttp://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 ISDAhttp://wiki.electorama.com/wiki/ISDA by MCA-IR and MCA-AR, if ISDA-compliant Condorcet methods (ie, Schulzehttp://wiki.electorama.com/wiki/Schulze) are used to choose the two finalists. Using simpler methods (such as MCA itself) to decide the finalists, MCA-IR and MCA-AR are not strictly clone independent. - The Condorcet criterionhttp://wiki.electorama.com/wiki/Condorcet_criterion is satisfied by MCA-IR if the pairwise championhttp://wiki.electorama.com/wiki/Pairwise_champion (aka CW) is visible on the ballots and would beat at least one other candidate by an absolute majority. It is satisfied by MCA-AR if at least half the voters at least approve the PC in the first round of voting. These methods also satisfy the Strategy-Free criterionhttp://wiki.electorama.com/wiki/Strategy-Free_criterion if an SFC-compliant method such as Schulzehttp://wiki.electorama.com/wiki/Schulze is used to pick at least one of the finalists. All other MCA versions, however, fail the Condorcet and strategy-free criteria. - The Later-no-help criterionhttp://wiki.electorama.com/wiki/Later-no-help_criterion and the Favorite Betrayal criterionhttp://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. - MCA-AR satisfies the Guaranteed majority criterionhttp://wiki.electorama.com/wiki/Guaranteed_majority_criterion, a criterion which can only be satisfied by a multi-round (runoff-based) method. Thus, the MCA 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 criterionhttp://wiki.electorama.com/wiki/Universality_criterion), are able to seem to violate Arrow's Theoremhttp://wiki.electorama.com/wiki/Arrow%27s_Theorem by simultaneously satisfying monotonicity and independence of irrelevant alternativeshttp://wiki.electorama.com/wiki/Independence_of_irrelevant_alternatives (as well as of course sovereignty and non-dictatorship). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] MCA on electowiki
On Mon, Oct 18, 2010 at 7:06 PM, Jameson Quinn jameson.qu...@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.d...@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.qu...@gmail.com To: election-methods election-meth...@electorama.com, electionsciencefoundation electionscie...@googlegroups.com Subject: [EM] MCA on electowiki Message-ID: aanlktimgdvnrtaz9vhn2jqjbad2wxo7vyhz_nhxus...@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_complianceI 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 majorityhttp://wiki.electorama.com/wiki/index.php?title=Absolute_majorityaction=editredlink=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. [edithttp://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approvalaction=editsection=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. [edithttp://wiki.electorama.com/wiki/index.php?title=Majority_Choice_Approvalaction=editsection=3 ] Criteria compliance All MCA variants satisfy the Plurality criterionhttp://wiki.electorama.com/wiki/Plurality_criterion, the Majority criterion for solid coalitionshttp://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 criterionhttp://wiki.electorama.com/wiki/Strong_Defensive_Strategy_criterion ). The Condorcet criterionhttp://wiki.electorama.com/wiki/Condorcet_criterion
Re: [EM] MCA on electowiki
2010/10/18 Kathy Dopp kathy.d...@gmail.com On Mon, Oct 18, 2010 at 7:06 PM, Jameson Quinn jameson.qu...@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 This is not the definition of monotonicity. Monotonicity states that changing an existing vote from X≤Y to XY should not change the winner from X to Y. It says nothing about adding new XY votes. Clearly, the two ideas are related. However, MCA's failures of the Combined Monotonicity and Participation Criterion are limited to the rare participation-type failures, not the potentially more common monotonicity-type failures. (This goes for all stated versions of MCA) JQ Election-Methods mailing list - see http://electorama.com/em for list info
