Re: [EM] Three rounds
On Mon, Nov 10, 2008 at 4:05 PM, Juho Laatu <[EMAIL PROTECTED]> wrote: > One could e.g. force supporters of the "eliminated" candidates to approve > more than one candidate (at least one of the "remaining" candidates) (instead > of just bullet voting their second preference). On possible way to terminate > the algorithm would be to stop when someone has reached >50% approval level. > > Also in "non-instant" runoffs one could e.g. force the voters to approve at > least one on the "remaining" candidates. (One could eliminate more than one > candidate at different rounds.) That is kinda like Bucklin, though without the approval threshold changing in each round for all voters. The process could be 1) Each candidate is designated a strong candidate 2) Each ballot is considered to approve the highest ranked strong candidate and all candidates ranked higher. 3) If the most approved candidate has > 50%, then that candidate is elected. 4) Re-designated the least approved strong candidate a weak candidate and goto 2). It still suffers from centre squeeze effects, though. For example 45: A>B>C 9: B>A>C 46: C>B>A Round 1 A: 45 B: 9 C: 46 no winner, B designated 'weak' Round 2 A: 54 B: 9 C: 41 A wins. The method has potential strategic truncation incentives. If B voters bullet voted for B, the result would have been Round 2 A: 46 B: 9 C: 41 C designated 'weak' Round 3 A: 46 B: 55 C: 41 B wins Ofc, the other voters can use counter strategies. It might be worth adding a rule that if all candidates on a ballot are weak, the ballot counts as approving everyone. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
How do your thoughts compare with Condorcet as a competitor? It: Normally is defined as not doing runoffs. Has no problem with voters offering whatever quantity of ranks they choose, including doing bullet voting. DWK On Mon, 10 Nov 2008 16:05:16 + (GMT) Juho Laatu wrote: FYI. Finland used to have three rounds in the presidential elections. Since 1994 a typical direct two round method has been used. Before that (in most elections) the voters first elected 300 (or 301) electors who then voted in three rounds (two candidates at the last round). Reasons behind moving to the direct two round system included assumed general popularity of a direct election, some problems with heavy trading and planning of votes by the electors, possibility of black horses and other voting patterns that are not based on the citizens' votes. Maybe three rounds / three election days in a direct election would have been too expensive and too tiring. - - - - - One somewhat related method: I sometimes played with the idea that in IRV one would not totally eliminate the least popular (first place) candidates but would use some softer means and would allow the "eliminated" candidates to win later if they turn out to be the favourites of many voters (after their first preference candidates have lost all chances to win). One could e.g. force supporters of the "eliminated" candidates to approve more than one candidate (at least one of the "remaining" candidates) (instead of just bullet voting their second preference). On possible way to terminate the algorithm would be to stop when someone has reached >50% approval level. Also in "non-instant" runoffs one could e.g. force the voters to approve at least one on the "remaining" candidates. (One could eliminate more than one candidate at different rounds.) Juho -- [EMAIL PROTECTED]people.clarityconnect.com/webpages3/davek Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026 Do to no one what you would not want done to you. If you want peace, work for justice. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
FYI. Finland used to have three rounds in the presidential elections. Since 1994 a typical direct two round method has been used. Before that (in most elections) the voters first elected 300 (or 301) electors who then voted in three rounds (two candidates at the last round). Reasons behind moving to the direct two round system included assumed general popularity of a direct election, some problems with heavy trading and planning of votes by the electors, possibility of black horses and other voting patterns that are not based on the citizens' votes. Maybe three rounds / three election days in a direct election would have been too expensive and too tiring. - - - - - One somewhat related method: I sometimes played with the idea that in IRV one would not totally eliminate the least popular (first place) candidates but would use some softer means and would allow the "eliminated" candidates to win later if they turn out to be the favourites of many voters (after their first preference candidates have lost all chances to win). One could e.g. force supporters of the "eliminated" candidates to approve more than one candidate (at least one of the "remaining" candidates) (instead of just bullet voting their second preference). On possible way to terminate the algorithm would be to stop when someone has reached >50% approval level. Also in "non-instant" runoffs one could e.g. force the voters to approve at least one on the "remaining" candidates. (One could eliminate more than one candidate at different rounds.) Juho --- On Mon, 10/11/08, Raph Frank <[EMAIL PROTECTED]> wrote: > From: Raph Frank <[EMAIL PROTECTED]> > Subject: Re: [EM] New MN court affidavits by those defending non-Monotonic > voting methods & IRV/STV > To: "Abd ul-Rahman Lomax" <[EMAIL PROTECTED]> > Cc: [EMAIL PROTECTED], "EM" > Date: Monday, 10 November, 2008, 2:30 PM > On Sun, Nov 9, 2008 at 1:16 AM, Abd ul-Rahman Lomax > <[EMAIL PROTECTED]> wrote: > > Top Two Runoff has an obvious problem, if the first > round is simple > > vote-for-one. Sometimes a compromise candidate fails > to make it into the > > runoff. This is really the same problem as IRV, but > the problem doesn't > > exist -- or is ameliorated -- under some election > rules. In particular, > > Robert's Rules, for runoff elections, does not > allow ballot restriction. > > As a compromise to repeating the balloting until the > deadlock is > resolved, what about the following rules > > Round 1 > > - All candidates on the ballot > - If a candidate gets a majority, he is elected and no > further rounds held > > Round 2 > > - All candidates on the ballot > - The top 2 from round 1 appear first on the ballot and are > marked as top-2 > - If a candidate gets a majority, he is elected and round 3 > is not held > > Round 3 > > - One of the top 2 from round 1 is on the ballot > -- (the one who received the most votes in round 2) > > - The plurality winner of round 2 is on the ballot > -- (excluding the above candidate) > > - Candidate with the most votes wins > > This gives the voters 2 chances to pick a majority winner > before going > to run-off. > > In a 'normal' top-2 situation, the top 2 will also > be the top 2 in > round 2 and they will be the 2 candidates for round 3. In > fact, it > would likely result in round 2 being the last round as one > of them > would get a majority. > > Election-Methods mailing list - see > http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
--- On Mon, 10/11/08, Raph Frank <[EMAIL PROTECTED]> wrote: > From: Raph Frank <[EMAIL PROTECTED]> > Subject: Re: [EM] Three rounds > To: [EMAIL PROTECTED] > Cc: election-methods@lists.electorama.com > Date: Monday, 10 November, 2008, 7:59 PM > On Mon, Nov 10, 2008 at 4:05 PM, Juho Laatu > <[EMAIL PROTECTED]> wrote: > > One could e.g. force supporters of the > "eliminated" candidates to approve more than one > candidate (at least one of the "remaining" > candidates) (instead of just bullet voting their second > preference). On possible way to terminate the algorithm > would be to stop when someone has reached >50% approval > level. > > > > Also in "non-instant" runoffs one could e.g. > force the voters to approve at least one on the > "remaining" candidates. (One could eliminate more > than one candidate at different rounds.) > > That is kinda like Bucklin, though without the approval > threshold > changing in each round for all voters. > > The process could be > > 1) Each candidate is designated a strong candidate > 2) Each ballot is considered to approve the highest ranked > strong > candidate and all candidates ranked higher. > 3) If the most approved candidate has > 50%, then that > candidate is elected. > 4) Re-designated the least approved strong candidate a weak > candidate > and goto 2). Yes, could go this way. > > It still suffers from centre squeeze effects, though. > > For example > > 45: A>B>C > 9: B>A>C > 46: C>B>A > > Round 1 > > A: 45 > B: 9 > C: 46 > > no winner, B designated 'weak' > > Round 2 > > A: 54 > B: 9 > C: 41 > > A wins. How about continuing and allowing the C supporters to compromise and approve also B. (Just didn't use the 50% termination rule this time.) After this round B would win and there would be no more interest to compromise (all voters already either approve the to be winner or would approve it as a compromise). > > The method has potential strategic truncation incentives. > > If B voters bullet voted for B, the result would have been > > Round 2 > > A: 46 > B: 9 > C: 41 > > C designated 'weak' > > Round 3 > > A: 46 > B: 55 > C: 41 > > B wins > > Ofc, the other voters can use counter strategies. > > It might be worth adding a rule that if all candidates on > a ballot > are weak, the ballot counts as approving everyone. Yes, short ballots like "B" would be seen as "B>A=C". The unlisted A and C candidates are at shared last position. B supporters are not allowed to refuse to compromise after B is declared "weak", so they have to approve both A and C. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
The sequential elimination processes tends to introduce additional problems. Most Condorcet methods don't have this problem. Condorcet may have some other problems that the sequential elimination based approach may avoid, but especially in large public elections with independent voter decision making and without too accurate knowledge about the behaviour of other voters the performance of Condorcet methods is very good. (Just checking how one could eliminate some of the problems of sequential elimination (e.g. by using approval and avoid losing the "eliminated" candidates).) Juho --- On Mon, 10/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: > From: Dave Ketchum <[EMAIL PROTECTED]> > Subject: Re: [EM] Three rounds > To: [EMAIL PROTECTED] > Cc: election-methods@lists.electorama.com > Date: Monday, 10 November, 2008, 8:10 PM > How do your thoughts compare with Condorcet as a competitor? > It: > Normally is defined as not doing runoffs. > Has no problem with voters offering whatever quantity > of ranks they choose, including doing bullet voting. > > DWK > > On Mon, 10 Nov 2008 16:05:16 + (GMT) Juho Laatu wrote: > > FYI. Finland used to have three rounds in the > presidential elections. Since 1994 a typical direct two > round method has been used. Before that (in most elections) > the voters first elected 300 (or 301) electors who then > voted in three rounds (two candidates at the last round). > > > > Reasons behind moving to the direct two round system > included assumed general popularity of a direct election, > some problems with heavy trading and planning of votes by > the electors, possibility of black horses and other voting > patterns that are not based on the citizens' votes. > Maybe three rounds / three election days in a direct > election would have been too expensive and too tiring. > > > > - - - - - > > > > One somewhat related method: > > > > I sometimes played with the idea that in IRV one would > not totally eliminate the least popular (first place) > candidates but would use some softer means and would allow > the "eliminated" candidates to win later if they > turn out to be the favourites of many voters (after their > first preference candidates have lost all chances to win). > > > > One could e.g. force supporters of the > "eliminated" candidates to approve more than one > candidate (at least one of the "remaining" > candidates) (instead of just bullet voting their second > preference). On possible way to terminate the algorithm > would be to stop when someone has reached >50% approval > level. > > > > Also in "non-instant" runoffs one could e.g. > force the voters to approve at least one on the > "remaining" candidates. (One could eliminate more > than one candidate at different rounds.) > > > > Juho > -- [EMAIL PROTECTED] > people.clarityconnect.com/webpages3/davek > Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 > 607-687-5026 >Do to no one what you would not want done to > you. > If you want peace, work for justice. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
If I understand you 'sequential elimination' is IRV and not Condorcet. DWK On Tue, 11 Nov 2008 00:01:36 + (GMT) Juho Laatu wrote: The sequential elimination processes tends to introduce additional problems. Most Condorcet methods don't have this problem. Condorcet may have some other problems that the sequential elimination based approach may avoid, but especially in large public elections with independent voter decision making and without too accurate knowledge about the behaviour of other voters the performance of Condorcet methods is very good. (Just checking how one could eliminate some of the problems of sequential elimination (e.g. by using approval and avoid losing the "eliminated" candidates).) Juho --- On Mon, 10/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: From: Dave Ketchum <[EMAIL PROTECTED]> Subject: Re: [EM] Three rounds To: [EMAIL PROTECTED] Cc: election-methods@lists.electorama.com Date: Monday, 10 November, 2008, 8:10 PM How do your thoughts compare with Condorcet as a competitor? It: Normally is defined as not doing runoffs. Has no problem with voters offering whatever quantity of ranks they choose, including doing bullet voting. DWK On Mon, 10 Nov 2008 16:05:16 + (GMT) Juho Laatu wrote: FYI. Finland used to have three rounds in the presidential elections. Since 1994 a typical direct two round method has been used. Before that (in most elections) the voters first elected 300 (or 301) electors who then voted in three rounds (two candidates at the last round). Reasons behind moving to the direct two round system included assumed general popularity of a direct election, some problems with heavy trading and planning of votes by the electors, possibility of black horses and other voting patterns that are not based on the citizens' votes. Maybe three rounds / three election days in a direct election would have been too expensive and too tiring. - - - - - One somewhat related method: I sometimes played with the idea that in IRV one would not totally eliminate the least popular (first place) candidates but would use some softer means and would allow the "eliminated" candidates to win later if they turn out to be the favourites of many voters (after their first preference candidates have lost all chances to win). One could e.g. force supporters of the "eliminated" candidates to approve more than one candidate (at least one of the "remaining" candidates) (instead of just bullet voting their second preference). On possible way to terminate the algorithm would be to stop when someone has reached >50% approval level. Also in "non-instant" runoffs one could e.g. force the voters to approve at least one on the "remaining" candidates. (One could eliminate more than one candidate at different rounds.) Juho -- [EMAIL PROTECTED]people.clarityconnect.com/webpages3/davek Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026 Do to no one what you would not want done to you. If you want peace, work for justice. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Yes, IRV is a good example. Most Condorcet methods do the comparisons/evaluation just once (when all the candidates are in the same situation). Juho --- On Tue, 11/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: > From: Dave Ketchum <[EMAIL PROTECTED]> > Subject: Re: [EM] Three rounds > To: [EMAIL PROTECTED] > Cc: election-methods@lists.electorama.com > Date: Tuesday, 11 November, 2008, 2:47 AM > If I understand you 'sequential elimination' is IRV > and not Condorcet. > > DWK > > On Tue, 11 Nov 2008 00:01:36 + (GMT) Juho Laatu wrote: > > The sequential elimination processes tends to > introduce additional problems. Most Condorcet methods > don't have this problem. > > > > Condorcet may have some other problems that the > sequential elimination based approach may avoid, but > especially in large public elections with independent voter > decision making and without too accurate knowledge about the > behaviour of other voters the performance of Condorcet > methods is very good. > > > > (Just checking how one could eliminate some of the > problems of sequential elimination (e.g. by using approval > and avoid losing the "eliminated" candidates).) > > > > Juho > > > > > > --- On Mon, 10/11/08, Dave Ketchum > <[EMAIL PROTECTED]> wrote: > > > > > >>From: Dave Ketchum <[EMAIL PROTECTED]> > >>Subject: Re: [EM] Three rounds > >>To: [EMAIL PROTECTED] > >>Cc: election-methods@lists.electorama.com > >>Date: Monday, 10 November, 2008, 8:10 PM > >>How do your thoughts compare with Condorcet as a > competitor? > >> It: > >> Normally is defined as not doing runoffs. > >> Has no problem with voters offering whatever > quantity > >>of ranks they choose, including doing bullet > voting. > >> > >>DWK > >> > >>On Mon, 10 Nov 2008 16:05:16 + (GMT) Juho Laatu > wrote: > >> > >>>FYI. Finland used to have three rounds in the > >> > >>presidential elections. Since 1994 a typical direct > two > >>round method has been used. Before that (in most > elections) > >>the voters first elected 300 (or 301) electors who > then > >>voted in three rounds (two candidates at the last > round). > >> > >>>Reasons behind moving to the direct two round > system > >> > >>included assumed general popularity of a direct > election, > >>some problems with heavy trading and planning of > votes by > >>the electors, possibility of black horses and other > voting > >>patterns that are not based on the citizens' > votes. > >>Maybe three rounds / three election days in a > direct > >>election would have been too expensive and too > tiring. > >> > >>>- - - - - > >>> > >>>One somewhat related method: > >>> > >>>I sometimes played with the idea that in IRV > one would > >> > >>not totally eliminate the least popular (first > place) > >>candidates but would use some softer means and > would allow > >>the "eliminated" candidates to win later > if they > >>turn out to be the favourites of many voters (after > their > >>first preference candidates have lost all chances > to win). > >> > >>>One could e.g. force supporters of the > >> > >>"eliminated" candidates to approve more > than one > >>candidate (at least one of the > "remaining" > >>candidates) (instead of just bullet voting their > second > >>preference). On possible way to terminate the > algorithm > >>would be to stop when someone has reached >50% > approval > >>level. > >> > >>>Also in "non-instant" runoffs one > could e.g. > >> > >>force the voters to approve at least one on the > >>"remaining" candidates. (One could > eliminate more > >>than one candidate at different rounds.) > >> > >>>Juho > -- > [EMAIL PROTECTED] > people.clarityconnect.com/webpages3/davek > Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 > 607-687-5026 > Do to no one what you would not want done to > you. > If you want peace, work for justice. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Not clear to me what you meant. While ballots are almost identical, such that Condorcet can accept what voters have done by IRV rules, their processing is entirely different. IRV is interested in first choices. If it decides that A is a loser it must go back to the ballots that ranked A top and reclassify them by next rank of each. Condorcet is interested in which candidate is best liked. For this it needs an NxN array summing all the ballots. If it is convenient to count the ballots in multiple locations this is fine - create an NxN array at each location and sum them together in one final location for analysis. DWK On Tue, 11 Nov 2008 06:39:53 + (GMT) Juho Laatu wrote: Yes, IRV is a good example. Most Condorcet methods do the comparisons/evaluation just once (when all the candidates are in the same situation). Juho --- On Tue, 11/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: From: Dave Ketchum <[EMAIL PROTECTED]> Subject: Re: [EM] Three rounds To: [EMAIL PROTECTED] Cc: election-methods@lists.electorama.com Date: Tuesday, 11 November, 2008, 2:47 AM If I understand you 'sequential elimination' is IRV and not Condorcet. DWK On Tue, 11 Nov 2008 00:01:36 + (GMT) Juho Laatu wrote: The sequential elimination processes tends to introduce additional problems. Most Condorcet methods don't have this problem. Condorcet may have some other problems that the sequential elimination based approach may avoid, but especially in large public elections with independent voter decision making and without too accurate knowledge about the behaviour of other voters the performance of Condorcet methods is very good. (Just checking how one could eliminate some of the problems of sequential elimination (e.g. by using approval and avoid losing the "eliminated" candidates).) Juho --- On Mon, 10/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: From: Dave Ketchum <[EMAIL PROTECTED]> Subject: Re: [EM] Three rounds To: [EMAIL PROTECTED] Cc: election-methods@lists.electorama.com Date: Monday, 10 November, 2008, 8:10 PM How do your thoughts compare with Condorcet as a competitor? It: Normally is defined as not doing runoffs. Has no problem with voters offering whatever quantity of ranks they choose, including doing bullet voting. DWK On Mon, 10 Nov 2008 16:05:16 + (GMT) Juho Laatu wrote: FYI. Finland used to have three rounds in the presidential elections. Since 1994 a typical direct two round method has been used. Before that (in most elections) the voters first elected 300 (or 301) electors who then voted in three rounds (two candidates at the last round). Reasons behind moving to the direct two round system included assumed general popularity of a direct election, some problems with heavy trading and planning of votes by the electors, possibility of black horses and other voting patterns that are not based on the citizens' votes. Maybe three rounds / three election days in a direct election would have been too expensive and too tiring. - - - - - One somewhat related method: I sometimes played with the idea that in IRV one would not totally eliminate the least popular (first place) candidates but would use some softer means and would allow the "eliminated" candidates to win later if they turn out to be the favourites of many voters (after their first preference candidates have lost all chances to win). One could e.g. force supporters of the "eliminated" candidates to approve more than one candidate (at least one of the "remaining" candidates) (instead of just bullet voting their second preference). On possible way to terminate the algorithm would be to stop when someone has reached >50% approval level. Also in "non-instant" runoffs one could e.g. force the voters to approve at least one on the "remaining" candidates. (One could eliminate more than one candidate at different rounds.) Juho -- [EMAIL PROTECTED]people.clarityconnect.com/webpages3/davek Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026 Do to no one what you would not want done to you. If you want peace, work for justice. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Raph Frank wrote: On Mon, Nov 10, 2008 at 4:05 PM, Juho Laatu <[EMAIL PROTECTED]> wrote: One could e.g. force supporters of the "eliminated" candidates to approve more than one candidate (at least one of the "remaining" candidates) (instead of just bullet voting their second preference). On possible way to terminate the algorithm would be to stop when someone has reached >50% approval level. Also in "non-instant" runoffs one could e.g. force the voters to approve at least one on the "remaining" candidates. (One could eliminate more than one candidate at different rounds.) That is kinda like Bucklin, though without the approval threshold changing in each round for all voters. If you're going to have an advanced runoff method, why not do something explicitly more Condorcetian? Perhaps something like: Determine the Schwartz set. If it is singular, the candidate wins, otherwise: the two highest ranked members of the Schwartz set, according to some Condorcet rule, advance to the runoff. Another option would be to use D'Hondt without lists, based on a good Condorcet method, to elect the two candidates for the runoff. But that's too complex, I think. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
On Mon, Nov 10, 2008 at 11:59 PM, Juho Laatu <[EMAIL PROTECTED]> wrote: > --- On Mon, 10/11/08, Raph Frank <[EMAIL PROTECTED]> wrote: > >> From: Raph Frank <[EMAIL PROTECTED]> >> Subject: Re: [EM] Three rounds >> To: [EMAIL PROTECTED] >> Cc: election-methods@lists.electorama.com >> Date: Monday, 10 November, 2008, 7:59 PM >> On Mon, Nov 10, 2008 at 4:05 PM, Juho Laatu >> <[EMAIL PROTECTED]> wrote: >> > One could e.g. force supporters of the >> "eliminated" candidates to approve more than one >> candidate (at least one of the "remaining" >> candidates) (instead of just bullet voting their second >> preference). On possible way to terminate the algorithm >> would be to stop when someone has reached >50% approval >> level. >> > >> > Also in "non-instant" runoffs one could e.g. >> force the voters to approve at least one on the >> "remaining" candidates. (One could eliminate more >> than one candidate at different rounds.) >> >> That is kinda like Bucklin, though without the approval >> threshold >> changing in each round for all voters. >> >> The process could be >> >> 1) Each candidate is designated a strong candidate >> 2) Each ballot is considered to approve the highest ranked >> strong >> candidate and all candidates ranked higher. >> 3) If the most approved candidate has > 50%, then that >> candidate is elected. >> 4) Re-designated the least approved strong candidate a weak >> candidate >> and goto 2). > > Yes, could go this way. > >> >> It still suffers from centre squeeze effects, though. >> >> For example >> >> 45: A>B>C >> 9: B>A>C >> 46: C>B>A >> >> Round 1 >> >> A: 45 >> B: 9 >> C: 46 >> >> no winner, B designated 'weak' >> >> Round 2 >> >> A: 54 >> B: 9 >> C: 41 >> >> A wins. > > How about continuing and allowing the C supporters to compromise and approve > also B. (Just didn't use the 50% termination rule this time.) After this > round B would win and there would be no more interest to compromise (all > voters already either approve the to be winner or would approve it as a > compromise). If you just keep keep declaring candidates as 'weak' until all candidates are weak, then it is basically approval voting. Once someone passes 50%, that candidate is declared as the potential winner. All ballots are then considered to also approve candidates that they prefer to the potential winner. So, 45: A>B>C Approves A (as highest strong candidate) 9: B>A>C Approves A (as highest strong candidate) Approves B (as weak candidate) 46: C>B>A Approves C (as highest strong) Approves B (as preferred to potential winner) A: 54 B: 55 C: 46 Ofc, it might just be easier to just pick the condorcet winner :), though I am not sure that the above method would always elect the condorcet winner. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
I just referred to the basic property of IRV that it makes final irreversible decisions (eliminates candidates) before even reading the later preferences in each ballot. (Some really strong compromise candidates may be eliminated early. And on the other hand also candidates with not much first place support may be elected.) Juho --- On Tue, 11/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: > From: Dave Ketchum <[EMAIL PROTECTED]> > Subject: Re: [EM] Three rounds > To: [EMAIL PROTECTED] > Cc: election-methods@lists.electorama.com > Date: Tuesday, 11 November, 2008, 6:43 PM > Not clear to me what you meant. > > While ballots are almost identical, such that Condorcet can > accept what > voters have done by IRV rules, their processing is entirely > different. > > IRV is interested in first choices. If it decides that A > is a loser it > must go back to the ballots that ranked A top and > reclassify them by next > rank of each. > > Condorcet is interested in which candidate is best liked. > For this it > needs an NxN array summing all the ballots. If it is > convenient to count > the ballots in multiple locations this is fine - create an > NxN array at > each location and sum them together in one final location > for analysis. > > DWK > > On Tue, 11 Nov 2008 06:39:53 + (GMT) Juho Laatu wrote: > > Yes, IRV is a good example. Most Condorcet methods do > the comparisons/evaluation just once (when all the > candidates are in the same situation). > > > > Juho > > > > > > > > > > --- On Tue, 11/11/08, Dave Ketchum > <[EMAIL PROTECTED]> wrote: > > > > > >>From: Dave Ketchum <[EMAIL PROTECTED]> > >>Subject: Re: [EM] Three rounds > >>To: [EMAIL PROTECTED] > >>Cc: election-methods@lists.electorama.com > >>Date: Tuesday, 11 November, 2008, 2:47 AM > > > > > >>If I understand you 'sequential > elimination' is IRV > >>and not Condorcet. > >> > >>DWK > >> > >>On Tue, 11 Nov 2008 00:01:36 + (GMT) Juho Laatu > wrote: > >> > >>>The sequential elimination processes tends to > >> > >>introduce additional problems. Most Condorcet > methods > >>don't have this problem. > >> > >>>Condorcet may have some other problems that the > >> > >>sequential elimination based approach may avoid, > but > >>especially in large public elections with > independent voter > >>decision making and without too accurate knowledge > about the > >>behaviour of other voters the performance of > Condorcet > >>methods is very good. > >> > >>>(Just checking how one could eliminate some of > the > >> > >>problems of sequential elimination (e.g. by using > approval > >>and avoid losing the "eliminated" > candidates).) > >> > >>>Juho > >>> > >>> > >>>--- On Mon, 10/11/08, Dave Ketchum > >> > >><[EMAIL PROTECTED]> wrote: > >> > >>> > >>>>From: Dave Ketchum > <[EMAIL PROTECTED]> > >>>>Subject: Re: [EM] Three rounds > >>>>To: [EMAIL PROTECTED] > >>>>Cc: election-methods@lists.electorama.com > >>>>Date: Monday, 10 November, 2008, 8:10 PM > >>>>How do your thoughts compare with Condorcet > as a > >>> > >>competitor? > >> > >>>>It: > >>>>Normally is defined as not doing > runoffs. > >>>>Has no problem with voters offering > whatever > >>> > >>quantity > >> > >>>>of ranks they choose, including doing > bullet > >>> > >>voting. > >> > >>>>DWK > >>>> > >>>>On Mon, 10 Nov 2008 16:05:16 + (GMT) > Juho Laatu > >>> > >>wrote: > >> > >>>>>FYI. Finland used to have three rounds > in the > >>>> > >>>>presidential elections. Since 1994 a > typical direct > >>> > >>two > >> > >>>>round method has been used. Before that (in > most > >>> > >>elections) > >> > >>>>the voters first elected 300 (or 301) > electors who > >>> > >>then > >> > >>>>voted in three rounds (two candidates at > the last > >>> > >>round). > >> > >>>>>Reasons behind moving to
Re: [EM] Three rounds
Is Schwartz set specifically "Condorcetian"? Also methods like minmax could be said to be strongly "Condorcetian" (although they do not necessarily elect from the Schwartz/Smith sets). Also party lists could be used. One approach to breaking cycles and identifying clone sets would be to not to count the votes of fellow party members against the candidates (not before all candidates of the competing parties/branches have been eliminated). How did you use D'Hondt without parties? Sorry about making only "opposite proposals" :-). Schwartz and partyless approaches may be ok too. And use of some sequential approach to break a Condorcet cycle as well. Juho --- On Tue, 11/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > From: Kristofer Munsterhjelm <[EMAIL PROTECTED]> > Subject: Re: [EM] Three rounds > To: "Raph Frank" <[EMAIL PROTECTED]> > Cc: [EMAIL PROTECTED], election-methods@lists.electorama.com > Date: Tuesday, 11 November, 2008, 8:50 PM > Raph Frank wrote: > > On Mon, Nov 10, 2008 at 4:05 PM, Juho Laatu > <[EMAIL PROTECTED]> wrote: > >> One could e.g. force supporters of the > "eliminated" candidates to approve more than one > candidate (at least one of the "remaining" > candidates) (instead of just bullet voting their second > preference). On possible way to terminate the algorithm > would be to stop when someone has reached >50% approval > level. > >> > >> Also in "non-instant" runoffs one could > e.g. force the voters to approve at least one on the > "remaining" candidates. (One could eliminate more > than one candidate at different rounds.) > > > > That is kinda like Bucklin, though without the > approval threshold > > changing in each round for all voters. > > > If you're going to have an advanced runoff method, why > not do something explicitly more Condorcetian? Perhaps > something like: > > Determine the Schwartz set. If it is singular, the > candidate wins, > otherwise: the two highest ranked members of the Schwartz > set, according to some Condorcet rule, advance to the > runoff. > > Another option would be to use D'Hondt without lists, > based on a good Condorcet method, to elect the two > candidates for the runoff. But that's too complex, I > think. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Right, the method is not Condorcet compliant. 40 A>B>C 25 B>A>C 35 C>B>A B supporters must compromise first and approve also A. Next C supporters must approve also B (maybe approving additionally only B at this round is enough although B is a weak candidate now). A wins although B is the Condorcet winner. (The rule that I used was something like "those voters whose most approved candidate among those candidates that they approve is least approved must approve one more candidate (or multiple if ranked equal) except if that would mean approving the most approved candidate".) Juho --- On Tue, 11/11/08, Raph Frank <[EMAIL PROTECTED]> wrote: > From: Raph Frank <[EMAIL PROTECTED]> > Subject: Re: [EM] Three rounds > To: [EMAIL PROTECTED] > Cc: election-methods@lists.electorama.com > Date: Tuesday, 11 November, 2008, 1:21 PM > On Mon, Nov 10, 2008 at 11:59 PM, Juho Laatu > <[EMAIL PROTECTED]> wrote: > > --- On Mon, 10/11/08, Raph Frank > <[EMAIL PROTECTED]> wrote: > > > >> From: Raph Frank <[EMAIL PROTECTED]> > >> Subject: Re: [EM] Three rounds > >> To: [EMAIL PROTECTED] > >> Cc: election-methods@lists.electorama.com > >> Date: Monday, 10 November, 2008, 7:59 PM > >> On Mon, Nov 10, 2008 at 4:05 PM, Juho Laatu > >> <[EMAIL PROTECTED]> wrote: > >> > One could e.g. force supporters of the > >> "eliminated" candidates to approve more > than one > >> candidate (at least one of the > "remaining" > >> candidates) (instead of just bullet voting their > second > >> preference). On possible way to terminate the > algorithm > >> would be to stop when someone has reached >50% > approval > >> level. > >> > > >> > Also in "non-instant" runoffs one > could e.g. > >> force the voters to approve at least one on the > >> "remaining" candidates. (One could > eliminate more > >> than one candidate at different rounds.) > >> > >> That is kinda like Bucklin, though without the > approval > >> threshold > >> changing in each round for all voters. > >> > >> The process could be > >> > >> 1) Each candidate is designated a strong candidate > >> 2) Each ballot is considered to approve the > highest ranked > >> strong > >> candidate and all candidates ranked higher. > >> 3) If the most approved candidate has > 50%, > then that > >> candidate is elected. > >> 4) Re-designated the least approved strong > candidate a weak > >> candidate > >> and goto 2). > > > > Yes, could go this way. > > > >> > >> It still suffers from centre squeeze effects, > though. > >> > >> For example > >> > >> 45: A>B>C > >> 9: B>A>C > >> 46: C>B>A > >> > >> Round 1 > >> > >> A: 45 > >> B: 9 > >> C: 46 > >> > >> no winner, B designated 'weak' > >> > >> Round 2 > >> > >> A: 54 > >> B: 9 > >> C: 41 > >> > >> A wins. > > > > How about continuing and allowing the C supporters to > compromise and approve also B. (Just didn't use the 50% > termination rule this time.) After this round B would win > and there would be no more interest to compromise (all > voters already either approve the to be winner or would > approve it as a compromise). > > If you just keep keep declaring candidates as > 'weak' until all > candidates are weak, then it is basically approval voting. > > Once someone passes 50%, that candidate is declared as the > potential > winner. All ballots are then considered to also approve > candidates > that they prefer to the potential winner. > > So, > > 45: A>B>C > Approves A (as highest strong candidate) > > 9: B>A>C > Approves A (as highest strong candidate) > Approves B (as weak candidate) > > 46: C>B>A > Approves C (as highest strong) > Approves B (as preferred to potential winner) > > A: 54 > B: 55 > C: 46 > > Ofc, it might just be easier to just pick the condorcet > winner :), > though I am not sure that the above method would always > elect the > condorcet winner. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
On Tue, 11 Nov 2008 22:18:55 + (GMT) Juho Laatu wrote: I just referred to the basic property of IRV that it makes final irreversible decisions (eliminates candidates) before even reading the later preferences in each ballot. Agreed. (Some really strong compromise candidates may be eliminated early. And on the other hand also candidates with not much first place support may be elected.) True that well liked candidates can lose if short on first place votes. Possible, though difficult, to win with only a few first place votes - they must have more than the least as each least gets discarded. DWK Juho --- On Tue, 11/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: From: Dave Ketchum <[EMAIL PROTECTED]> Subject: Re: [EM] Three rounds To: [EMAIL PROTECTED] Cc: election-methods@lists.electorama.com Date: Tuesday, 11 November, 2008, 6:43 PM Not clear to me what you meant. While ballots are almost identical, such that Condorcet can accept what voters have done by IRV rules, their processing is entirely different. IRV is interested in first choices. If it decides that A is a loser it must go back to the ballots that ranked A top and reclassify them by next rank of each. Condorcet is interested in which candidate is best liked. For this it needs an NxN array summing all the ballots. If it is convenient to count the ballots in multiple locations this is fine - create an NxN array at each location and sum them together in one final location for analysis. DWK On Tue, 11 Nov 2008 06:39:53 + (GMT) Juho Laatu wrote: Yes, IRV is a good example. Most Condorcet methods do the comparisons/evaluation just once (when all the candidates are in the same situation). Juho --- On Tue, 11/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: From: Dave Ketchum <[EMAIL PROTECTED]> Subject: Re: [EM] Three rounds To: [EMAIL PROTECTED] Cc: election-methods@lists.electorama.com Date: Tuesday, 11 November, 2008, 2:47 AM If I understand you 'sequential elimination' is IRV and not Condorcet. DWK On Tue, 11 Nov 2008 00:01:36 + (GMT) Juho Laatu wrote: The sequential elimination processes tends to introduce additional problems. Most Condorcet methods don't have this problem. Condorcet may have some other problems that the sequential elimination based approach may avoid, but especially in large public elections with independent voter decision making and without too accurate knowledge about the behaviour of other voters the performance of Condorcet methods is very good. (Just checking how one could eliminate some of the problems of sequential elimination (e.g. by using approval and avoid losing the "eliminated" candidates).) Juho --- On Mon, 10/11/08, Dave Ketchum <[EMAIL PROTECTED]> wrote: From: Dave Ketchum <[EMAIL PROTECTED]> Subject: Re: [EM] Three rounds To: [EMAIL PROTECTED] Cc: election-methods@lists.electorama.com Date: Monday, 10 November, 2008, 8:10 PM How do your thoughts compare with Condorcet as a competitor? It: Normally is defined as not doing runoffs. Has no problem with voters offering whatever quantity of ranks they choose, including doing bullet voting. DWK On Mon, 10 Nov 2008 16:05:16 + (GMT) Juho Laatu wrote: FYI. Finland used to have three rounds in the presidential elections. Since 1994 a typical direct two round method has been used. Before that (in most elections) the voters first elected 300 (or 301) electors who then voted in three rounds (two candidates at the last round). Reasons behind moving to the direct two round system included assumed general popularity of a direct election, some problems with heavy trading and planning of votes by the electors, possibility of black horses and other voting patterns that are not based on the citizens' votes. Maybe three rounds / three election days in a direct election would have been too expensive and too tiring. - - - - - One somewhat related method: I sometimes played with the idea that in IRV one would not totally eliminate the least popular (first place) candidates but would use some softer means and would allow the "eliminated" candidates to win later if they turn out to be the favourites of many voters (after their first preference candidates have lost all chances to win). One could e.g. force supporters of the "eliminated" candidates to approve more than one candidate (at least one of the "remaining" candidates) (instead of just bullet voting their second preference). On possible way to terminate the algorithm would be to stop when someone has reached 50% approval level. Also in "non-instant" runoff
Re: [EM] Three rounds
Juho Laatu wrote: Is Schwartz set specifically "Condorcetian"? Also methods like minmax could be said to be strongly "Condorcetian" (although they do not necessarily elect from the Schwartz/Smith sets). Schwartz is Condorcet-like because a CW will always be in the Schwartz set, and Smith (and Schwartz) is a reasonable extension of the Condorcet criterion (from "a candidate who is preferred to all others should win" to "of a group where the group is preferred to all outside the group, a group member should win"). Minmax is Condorcet yet not Schwartz, but anything that's Schwartz is also Condorcet. Also party lists could be used. One approach to breaking cycles and identifying clone sets would be to not to count the votes of fellow party members against the candidates (not before all candidates of the competing parties/branches have been eliminated). How did you use D'Hondt without parties? I used the Condorcet idea. First iteration: elect as for a single winner (this includes the legitimate single winner so that a runoff never hurts him). Second iteration: count ballots as usual, but all preferences below the winner of the first iteration count half. So, for instance, A > B > C > D with B as first iteration winner counts C > D as 0.5 victory of C over D. Then generate a social ordering based on the new matrix, eliminate the winner of the first iteration from that ordering, and pick whoever won as the winner of the second iteration. The winners from each iteration go to the runoff. The full method is given somewhere in the archive, just search for "D'Hondt without lists"; but for runoffs, there are just two iterations, so it's as simple as this (I think; it's late and so I may have made an error). If you're going to use party list, I don't see much point in a runoff. Either it'll be multiwinner, in which case a runoff doesn't make much sense, or it'll be single-winner, in which case you can just use the equivalent single-winner method. For ordinary party list, that method would be Plurality; instead of voting for a party, vote for the party's designated "appointee". Sorry about making only "opposite proposals" :-). Schwartz and partyless approaches may be ok too. And use of some sequential approach to break a Condorcet cycle as well. What kind of sequential approaches were you thinking of? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
--- On Wed, 12/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > From: Kristofer Munsterhjelm <[EMAIL PROTECTED]> > Subject: Re: [EM] Three rounds > To: [EMAIL PROTECTED] > Cc: election-methods@lists.electorama.com > Date: Wednesday, 12 November, 2008, 3:01 AM > Juho Laatu wrote: > > Is Schwartz set specifically "Condorcetian"? > Also methods like minmax > > could be said to be strongly "Condorcetian" > (although they do not > > necessarily elect from the Schwartz/Smith sets). > > Schwartz is Condorcet-like because a CW will always be in > the Schwartz set, and Smith (and Schwartz) is a reasonable > extension of the Condorcet criterion (from "a candidate > who is preferred to all others should win" to "of > a group where the group is preferred to all outside the > group, a group member should win"). Minmax is Condorcet > yet not Schwartz, but anything that's Schwartz is also > Condorcet. Clones of members of the Smith set (I'll ignore ties in this mail) are in the Smith set but Smith set members need not be clones. The Smith set is thus not a (unified) group of clones (but just a group of candidates that happen to best all the others in a pairwise comparison). There are also other potential "reasonable extensions" of the Condorcet criterion. One interesting question is if it is more important for the elected candidate to have weak opposition or to have a narrow opposition. (Beatpaths may be considered a "winner evaluation criterion" too - although their meaning in real life situations is not clear - maybe they are used just to identify clones in some approximate way rather than describe the value of the to be winner.) One basic example. 17: A>B>D>C 16: A>D>B>C 17: B>C>D>A 16: B>D>C>A 17: C>A>D>B 16: C>D>A>B A, B and C are in a strong loop. A, B and C form the Smith set but they are not clones. Each of them is beaten badly by another member of the loop. D loses to all the Smith set members, but only with a very narrow margin. One could say that D is the most acceptable choice, and that electing the candidate with weakest opposition (against any single one of the other candidates) is a natural extension of the Condorcet criterion. (D is the Condorcet loser but it is also very close to being the Condorcet winner. The visual impression of "being below the top three" positions D somewhere deep down at the bottom of the picture and at the end of the preference list, but obviously such 2D visualization does not describe the cyclic relations in the best way.) > > > Also party lists could be used. One approach to > breaking cycles and > > identifying clone sets would be to not to count the > votes of fellow > > party members against the candidates (not before all > candidates of > > the competing parties/branches have been eliminated). > How did you use > > D'Hondt without parties? > > I used the Condorcet idea. First iteration: elect as for a > single winner (this includes the legitimate single winner so > that a runoff never hurts him). Second iteration: count > ballots as usual, but all preferences below the winner of > the first iteration count half. So, for instance, > > A > B > C > D > with B as first iteration winner > counts C > D as 0.5 victory of C over D. > > Then generate a social ordering based on the new matrix, > eliminate the winner of the first iteration from that > ordering, and pick whoever won as the winner of the second > iteration. The winners from each iteration go to the runoff. > > The full method is given somewhere in the archive, just > search for "D'Hondt without lists"; but for > runoffs, there are just two iterations, so it's as > simple as this (I think; it's late and so I may have > made an error). > > If you're going to use party list, I don't see much > point in a runoff. Either it'll be multiwinner, in which > case a runoff doesn't make much sense, or it'll be > single-winner, in which case you can just use the equivalent > single-winner method. For ordinary party list, that method > would be Plurality; instead of voting for a party, vote for > the party's designated "appointee". I was thinking of single winner elections only. The party lists could be more interesting when breaking Condorcet cycles. But in a runoff one could first vote between parties and only then between candidates of the winning party. I'm not sure that this is very useful, but this way one could e.g. reduce the risk of the best compromise candidate of a party being eliminated too early. For example 40: A1>A2>B>C 08: A2&g
Re: [EM] Three rounds
Juho Laatu wrote: --- On Wed, 12/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: Schwartz is Condorcet-like because a CW will always be in the Schwartz set, and Smith (and Schwartz) is a reasonable extension of the Condorcet criterion (from "a candidate who is preferred to all others should win" to "of a group where the group is preferred to all outside the group, a group member should win"). Minmax is Condorcet yet not Schwartz, but anything that's Schwartz is also Condorcet. Clones of members of the Smith set (I'll ignore ties in this mail) are in the Smith set but Smith set members need not be clones. The Smith set is thus not a (unified) group of clones (but just a group of candidates that happen to best all the others in a pairwise comparison). There are also other potential "reasonable extensions" of the Condorcet criterion. One interesting question is if it is more important for the elected candidate to have weak opposition or to have a narrow opposition. (Beatpaths may be considered a "winner evaluation criterion" too - although their meaning in real life situations is not clear - maybe they are used just to identify clones in some approximate way rather than describe the value of the to be winner.) One basic example. 17: A>B>D>C 16: A>D>B>C 17: B>C>D>A 16: B>D>C>A 17: C>A>D>B 16: C>D>A>B A, B and C are in a strong loop. A, B and C form the Smith set but they are not clones. Each of them is beaten badly by another member of the loop. D loses to all the Smith set members, but only with a very narrow margin. One could say that D is the most acceptable choice, and that electing the candidate with weakest opposition (against any single one of the other candidates) is a natural extension of the Condorcet criterion. (D is the Condorcet loser but it is also very close to being the Condorcet winner. The visual impression of "being below the top three" positions D somewhere deep down at the bottom of the picture and at the end of the preference list, but obviously such 2D visualization does not describe the cyclic relations in the best way.) I think that in order to get anywhere on this path, we would have to know what it is we actually want from a runoff. There are two reasons why you might have a runoff: the honest, that voters can discuss which of the two candidates are better without having to consider the others, and the strategic, arising from that in a runoff that has only two candidates, the optimum strategy is honesty (if we consider the runoff one election, not half an election). I'm going to skip past the strategic reason for now, but I'll note that earlier I mentioned some ideas regarding that, with two election methods being run in parallel (one resistant to strategy and one vulnerable), the winner of each going to the runoff; this could even work if one method is vulnerable to a different strategy than the other. For honesty, then, we have to know which are the two best candidates. This sounds like a proportional representation problem with a "council" of two; however, such methods cannot be invulnerable to cloning, since the Droop proportionality criterion and clone independence contradict each other (by http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM , "clone-no-harm"). Also, if we want to retain the properties of the first-round election system, and that election system is Condorcet, then one of the candidates in the runoff must be the CW (when it exists). I would go further and say that there's no need for a runoff if there's a CW, but others may disagree. In any event, if the first round method is Smith or Schwartz, or more generally picks from a well defined subset of the candidates, then one of the candidates of the second round must be from that set as well. The former destroys any chance of passing the DPC, since Droop proportionality is incompatible with Condorcet (by example given in the Voting Matters article linked to above). It seems difficult to consider a consistent way of picking the other candidate, given this. Consider opinions on a line, where the centrist at 0.5 is the CW, and assume that runoffs will be held even when there's a CW. Then where should you put the other candidate? Not to the right, because that would be biased against the left-leaning voters. Not to the left, because that would be biased against the right-leaning voters. So it must be another centrist, a clone. But what choice is that? However, that may work only as an argument against "runoffs should be held even when there's a Condorcet winner". To my knowledge, on a political line and with honest voters that prefer candidates closer to them to those farther away, there'll always be a Condorcet winner. That means we'll have to consider opinion spaces in greater than one dimension. Call the candidate that's retained from the first round to pass criteria, the retained candidate. Perhaps we could then say that if the retained candidate is
Re: [EM] Three rounds
On Thu, Nov 13, 2008 at 2:39 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > For honesty, then, we have to know which are the two best candidates. This > sounds like a proportional representation problem with a "council" of two; > however, such methods cannot be invulnerable to cloning, since the Droop > proportionality criterion and clone independence contradict each other (by > http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM , "clone-no-harm"). I disagree, a PR method is not what you want here. If the best candidate is cloned, then both clones should be picked as the top-2. This will not happen with PR. In the linear policy case, the best candidate is at the 50% mark. PR will likely elect candidates at the 33% and 67% marks. Neither of those candidates is optimal. In fact, I think that picking one of the 2 would be give roughly the same result as the plurality system. > Also, if we want to retain the properties of the first-round election > system, and that election system is Condorcet, then one of the candidates in > the runoff must be the CW (when it exists). I would go further and say that > there's no need for a runoff if there's a CW, but others may disagree. In a condorcet election, the top 2 candidates would be at the 50% mark in the 1d policy space. The runoff would held the voters decide from 2 pretty good candidates. > The former > destroys any chance of passing the DPC, since Droop proportionality is > incompatible with Condorcet (by example given in the Voting Matters article > linked to above). I don't see why you want them picked by a PR method, the idea shouldn't be to pick 2 candidates who each represent half of the community, it should be to pick 2 that represent the whole community, > Then where should you put the other candidate? Not to the right, because > that would be biased against the left-leaning voters. Not to the left, > because that would be biased against the right-leaning voters. So it must be > another centrist, a clone. But what choice is that? It is a choice. First, there are more than 1 dimension in politics and second, even if there wasn't it allows the voters pick the most capable of the 2 candidates who both have similar policy views. > Call the candidate that's retained from the first round to pass criteria, > the retained candidate. Perhaps we could then say that if the retained > candidate is off-center in n-space, then the right thing would be to pick > the viable candidate closest to its antipode (reversed coordinates) as the > other candidate. But what's a viable candidate? You could deweight the votes that voted for the first winner. This would shift the winning point away from the centre. >> 40: A1>A2>B>C >> 08: A2>A1>B>C >> 07: A2>B>A1>C >> 25: B>A2>C>A1 >> 20: C>B>A2>A1 >> A2 would be eliminated first in IRV but here A1 and A2 form a party >> (with 55 first preference votes) and therefore C will be eliminated >> first, B next, and then A2 will win. > > This seems to be more of a problem with IRV, and so I'd say that a better > solution would be to switch to another voting system rather than try to > patch it up with party lists. Also, the A2>B>A1 voters cannot be considered members of the A party. This highlights a problem with the party list system, it assumes voters are rock solid supporters of their first choice's party. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
--- On Thu, 13/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > I think that in order to get anywhere on this path, we > would have to know what it is we actually want from a > runoff. First I want to note that I don't want to promote runoffs, just to study them. > There are two reasons why you might have a runoff: > the honest, that voters can discuss which of the two > candidates are better without having to consider the others, Sometimes it may be possible to achieve the same effect my publishing polls before the election. > But what's a viable candidate? Is > it viable if in Smith (or mutual majority, or whatnot)? Mutual majority makes more sense than Smith. In the given example A, B and C formed a strongly looped Smith set, and D was a Condorcet loser (but not by mutual majority) that was almost a Condorcet winner. In this situation also D could be a viable candidate for the last runoff round. > > The party lists could be more interesting when > breaking Condorcet > > cycles. But in a runoff one could first vote between > parties and only > > then between candidates of the winning party. I'm > not sure that this is > > very useful, but this way one could e.g. reduce the > risk of the best > > compromise candidate of a party being eliminated too > early. > > > > For example > > 40: A1>A2>B>C > > 08: A2>A1>B>C > > 07: A2>B>A1>C > > 25: B>A2>C>A1 > > 20: C>B>A2>A1 > > A2 would be eliminated first in IRV but here A1 and A2 > form a party > > (with 55 first preference votes) and therefore C will > be eliminated > > first, B next, and then A2 will win. > > This seems to be more of a problem with IRV, and so I'd > say that a better solution would be to switch to another > voting system rather than try to patch it up with party > lists. Yes, this is a problem of IRV. Yes, there may be better methods than the IRV based ones. Use of parties may provide some limited benefits, but they add complexity too. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
--- On Thu, 13/11/08, Raph Frank <[EMAIL PROTECTED]> wrote: > On Thu, Nov 13, 2008 at 2:39 PM, Kristofer Munsterhjelm > <[EMAIL PROTECTED]> wrote: > > For honesty, then, we have to know which are the two > best candidates. This > > sounds like a proportional representation problem with > a "council" of two; > > however, such methods cannot be invulnerable to > cloning, since the Droop > > proportionality criterion and clone independence > contradict each other (by > > http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM , > "clone-no-harm"). > > I disagree, a PR method is not what you want here. If the > best > candidate is cloned, then both clones should be picked as > the top-2. I agree that the targets of proportional methods and single winner methods are different. The best single winner may not be included in the best set of proportional representatives. > PR will likely elect > candidates at the > 33% and 67% marks. Neither of those candidates is optimal. > > In fact, I think that picking one of the 2 would be give > roughly the > same result as the plurality system. One could also claim that in a typical two-party system the two main candidates often are roughly at the 45% and 55% marks. > >> 40: A1>A2>B>C > >> 08: A2>A1>B>C > >> 07: A2>B>A1>C > >> 25: B>A2>C>A1 > >> 20: C>B>A2>A1 > >> A2 would be eliminated first in IRV but here A1 > and A2 form a party > >> (with 55 first preference votes) and therefore C > will be eliminated > >> first, B next, and then A2 will win. > > > > This seems to be more of a problem with IRV, and so > I'd say that a better > > solution would be to switch to another voting system > rather than try to > > patch it up with party lists. > > Also, the A2>B>A1 voters cannot be considered members > of the A party. > This highlights a problem with the party list system, it > assumes > voters are rock solid supporters of their first > choice's party. This party list based method actually allowed the party supporters not to be rock solid supporters of the party. Those 7 A2>B>A1 voters were able to indicate that they preferred B to A1. And their favourite still won. Those voters may still be considered to be members of the A party. It is quite natural that members that are close to the border of the party like some of the candidates of the nearby B party better than the candidates of the very other end of the A party. These voters may still accept the alliance of A1 and A2 although they might be even happier if A2 and B (and maybe A1) would establish a new party together. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
On Thu, Nov 13, 2008 at 10:11 PM, Juho Laatu <[EMAIL PROTECTED]> wrote: > This party list based method actually allowed the party supporters not to be > rock solid supporters of the party. Those 7 A2>B>A1 voters were able to > indicate that they preferred B to A1. And their favourite still won. Hmm, it is IRV except but it uses a different elimination order. A candidate from the smallest party is eliminated first (and presumably the candidate from the party with the fewest votes if the party has more than 1 vote). I assume that the party totals are re-calculated after each elimination? That means that the largest party doesn't automatically win (as their candidates would be eliminated last) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
--- On Fri, 14/11/08, Raph Frank <[EMAIL PROTECTED]> wrote: > From: Raph Frank <[EMAIL PROTECTED]> > Subject: Re: [EM] Three rounds > To: [EMAIL PROTECTED] > Cc: election-methods@lists.electorama.com > Date: Friday, 14 November, 2008, 12:26 AM > On Thu, Nov 13, 2008 at 10:11 PM, Juho Laatu > <[EMAIL PROTECTED]> wrote: > > This party list based method actually allowed the > party supporters not to be rock solid supporters of the > party. Those 7 A2>B>A1 voters were able to indicate > that they preferred B to A1. And their favourite still won. > > Hmm, it is IRV except but it uses a different elimination > order. A > candidate from the smallest party is eliminated first (and > presumably > the candidate from the party with the fewest votes if the > party has > more than 1 vote). > > I assume that the party totals are re-calculated after each > elimination? That means that the largest party doesn't > automatically > win (as their candidates would be eliminated last) Yes, that was my assumption in this method. After C was eliminated those votes supported B. But that meant only 45 votes for B, which was this time not enough against the 55 votes of the A party. The A party candidates were just like one combined "A1+A2" candidate in a regular IRV election until that candidate won. After that there was a second race between the candidates of the A party. This approach clearly encourages formation of parties or other groupings/coalitions. If all candidates are either under a left wing or right wing coalition the bigger of those coalitions will win. (Hierarchies of groupings/parties/coalitions are possible too.) This approach also encourages parties to nominate more than one candidate, as in the example where the A party won thanks to nominating a good compromise candidate (A2, that had less first place popularity than A1) that appealed also to the A2>B>A1 voters that would have voted for B (making B the winner) if A2 would not have been available. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Raph Frank wrote: On Thu, Nov 13, 2008 at 2:39 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: For honesty, then, we have to know which are the two best candidates. This sounds like a proportional representation problem with a "council" of two; however, such methods cannot be invulnerable to cloning, since the Droop proportionality criterion and clone independence contradict each other (by http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM , "clone-no-harm"). I disagree, a PR method is not what you want here. If the best candidate is cloned, then both clones should be picked as the top-2. This will not happen with PR. In the linear policy case, the best candidate is at the 50% mark. PR will likely elect candidates at the 33% and 67% marks. Neither of those candidates is optimal. In fact, I think that picking one of the 2 would be give roughly the same result as the plurality system. I might have been too vague. What I meant was that it sounds like a proportional representation problem at first, but then (as I show afterwards), turns out not to be so, since we can't satisfy the DPC (which PR methods should have) and the various good single-winner criteria at the same time. It might seem like a PR problem since one would intuitively think that the runoff candidates should in concert cover as much of the opinion space as possible. Also, if we want to retain the properties of the first-round election system, and that election system is Condorcet, then one of the candidates in the runoff must be the CW (when it exists). I would go further and say that there's no need for a runoff if there's a CW, but others may disagree. In a condorcet election, the top 2 candidates would be at the 50% mark in the 1d policy space. The runoff would held the voters decide from 2 pretty good candidates. This does mean that a party can crowd out its competitors by running two candidates of the exact same position. On the other hand, that may be what you want, since one could reason that this brings a competition of quality to the center position, where the two best centrists would be picked for the runoff. That doesn't give the people much to discuss between the first and second rounds, though, since the candidates' position would be identical. In any case, if that's what you want, then picking the candidates for a runoff should be easy. First round, use a method like Schulze to get a social ordering. Pick the first and second place candidates on that social ordering for the second round. The former destroys any chance of passing the DPC, since Droop proportionality is incompatible with Condorcet (by example given in the Voting Matters article linked to above). I don't see why you want them picked by a PR method, the idea shouldn't be to pick 2 candidates who each represent half of the community, it should be to pick 2 that represent the whole community, It's a reasonable first guess to imagine using a PR method, but it doesn't work. See above. Call the candidate that's retained from the first round to pass criteria, the retained candidate. Perhaps we could then say that if the retained candidate is off-center in n-space, then the right thing would be to pick the viable candidate closest to its antipode (reversed coordinates) as the other candidate. But what's a viable candidate? You could deweight the votes that voted for the first winner. This would shift the winning point away from the centre. That's what D'Hondt without lists does; or rather, it deweights those preferences that are lower than the winner of the first round, since the voters already "got what they wanted" on a higher preference. (Of course, I would use Sainte-Laguë instead of D'Hondt, but that's an implementation detail.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
On Fri, Nov 14, 2008 at 8:56 AM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > This does mean that a party can crowd out its competitors by running two > candidates of the exact same position. On the other hand, that may be what > you want, since one could reason that this brings a competition of quality > to the center position, where the two best centrists would be picked for the > runoff. That doesn't give the people much to discuss between the first and > second rounds, though, since the candidates' position would be identical. Their positions would likely be similar but not identical, especially in a multi dimensional political space. The campaign would come down to questions of capability as a representative and small policy differences. One possible issue would be a small turnout at the second round. This might encourage them to appeal to extremists. > First round, use a method like Schulze to get a > social ordering. Pick the first and second place candidates on that social > ordering for the second round. Right, that is what I was thinking. With any condorcet method, you could just say pick the winner and then pick the winner excluding the first winner, but I think most condorcet completion methods generate a complete ordering. Another option would be to pick the 2 most approved candidates for the 2nd round. > It's a reasonable first guess to imagine using a PR method, but it doesn't > work. See above. Yeah, we agree. > That's what D'Hondt without lists does; or rather, it deweights those > preferences that are lower than the winner of the first round, since the > voters already "got what they wanted" on a higher preference. (Of course, I > would use Sainte-Laguë instead of D'Hondt, but that's an implementation > detail.) Interesting. The process is that you vote for your top choice that is still in the running but it is deweighted by the number of higher choices who have already been elected? A vote of A>B>C would vote for C if A and B were elected at a weight of 1/5 strength (assuming Sainte-Lague)? How are eliminations handled? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
--- On Fri, 14/11/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > Raph Frank wrote: > > In a condorcet election, the top 2 candidates would be > at the 50% mark > > in the 1d policy space. > > > > The runoff would held the voters decide from 2 pretty > good candidates. > > This does mean that a party can crowd out its competitors > by running two candidates of the exact same position. On the > other hand, that may be what you want, since one could > reason that this brings a competition of quality to the > center position, where the two best centrists would be > picked for the runoff. That doesn't give the people much > to discuss between the first and second rounds, though, > since the candidates' position would be identical. Since the party doesn't know beforehand what exactly is the winning formula/candidate they should name candidates that differ from each others and cover the whole expected potential winning area. If there is a final runoff between two leading candidates then one could nominate only identical twins as candidates to make sure that if one of the party candidates goes to the final runoff then also the other candidate will be from the same party. But it may be more efficient to spread one's (limited number of?) candidates in the opinion space more evenly and thereby try to guarantee that one has at least one candidate at the final round, and that one has a candidate close to the spot that represents the public opinion. Another theme is that all candidates of all parties should position themselves in the area that is expected to represent the public opinion. Of course within the limits of maintaining credibility. It may also be clever to seek areas that are not too densely populated by other candidates yet. The US presidential elections may serve as a good example. Obama will not say "I'm a Democrat, I want free abortion and high taxes". He should rather trust that he will get most of the Democrat votes anyway and focus on getting some Republican votes. In a 1d space (where Democrats cover 0%-50%) he may even present himself as being at the 55% mark. McCain on the other hand could present himself as a 45% mark candidate. In addition Obama and McCain of course have to convince also the 0%-25% and the 75%-100% voters respectively well enough so that they will vote and not stay at home. But it is better to do that without too much publicity. So, based on this discussion each party should first estimate the potential winning area, then populate that area well enough, and maybe also try to identify ideal spots within that territory (no competitors nearby at least on one side, can be reserved with one nice speech/slogan,...). If current candidates are D40%, D45%, R47%, D50% and R60% then an ideal spot for the last Republican candidate could be e.g. at 52%. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Raph Frank wrote: On Fri, Nov 14, 2008 at 8:56 AM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: This does mean that a party can crowd out its competitors by running two candidates of the exact same position. On the other hand, that may be what you want, since one could reason that this brings a competition of quality to the center position, where the two best centrists would be picked for the runoff. That doesn't give the people much to discuss between the first and second rounds, though, since the candidates' position would be identical. Their positions would likely be similar but not identical, especially in a multi dimensional political space. The campaign would come down to questions of capability as a representative and small policy differences. One possible issue would be a small turnout at the second round. This might encourage them to appeal to extremists. This, in turn, may cause the runoff to have Range-like effects. Say that the runoff is held with two centrists as the candidates. Then voters who feels the same way about both candidates may not bother to show up, even though they prefer one candidate to the other. If that effect is too prevalent, it could be confused for an apathetic populace. First round, use a method like Schulze to get a social ordering. Pick the first and second place candidates on that social ordering for the second round. Right, that is what I was thinking. With any condorcet method, you could just say pick the winner and then pick the winner excluding the first winner, but I think most condorcet completion methods generate a complete ordering. I mention a complete ordering since some methods may act differently if you eliminate the winner (particularly if they're nonmonotonic). Using the complete ordering seems more sensible in that case. Another option would be to pick the 2 most approved candidates for the 2nd round. Then you'd need an approval cutoff, or plain Approval. I think Approval would satisfy IIA if you use a constant strategy (compare all candidates to an objective standard and approve those better than that standard), but since the best Approval strategies are relative, there may still be a point in an Approval runoff. That's what D'Hondt without lists does; or rather, it deweights those preferences that are lower than the winner of the first round, since the voters already "got what they wanted" on a higher preference. (Of course, I would use Sainte-Laguë instead of D'Hondt, but that's an implementation detail.) Interesting. The process is that you vote for your top choice that is still in the running but it is deweighted by the number of higher choices who have already been elected? A vote of A>B>C would vote for C if A and B were elected at a weight of 1/5 strength (assuming Sainte-Lague)? How are eliminations handled? To paraphrase from the post (http://www.mail-archive.com/[EMAIL PROTECTED]/msg08230.html ), D'Hondt without lists has this rule: Downweight any preferences where both candidates compared are ranked below k elected candidates, by f(k). For D'Hondt, f(x) is 1/(x+1), or [1; 1/2; 1/3, ...], counting from 0. In the case of Sainte-Laguë, f(x) is 1/(2x + 1), or [1; 1/3; 1/5, ...]. So in your A>B>C case, B>C would have weight 1/3. If you had A>B>C>D, then C>D would have weight 1/5. Eliminations are handled by removing already elected candidates from the ordering. For instance, if A's elected and the result for the second round is A > B > C > D, A is removed to make B > C > D, and B is elected. This limits IIA oddness. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
On Fri, Nov 14, 2008 at 3:51 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > To paraphrase from the post > (http://www.mail-archive.com/[EMAIL PROTECTED]/msg08230.html > ), D'Hondt without lists has this rule: > Ahh, I see, you keep electing the condorcet winner but the decreasing weight for lower preferences means that a ballot that has had its top choice elected has less effect. I assume it meets the Droop rule? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Raph Frank wrote: On Fri, Nov 14, 2008 at 3:51 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: To paraphrase from the post (http://www.mail-archive.com/[EMAIL PROTECTED]/msg08230.html ), D'Hondt without lists has this rule: Ahh, I see, you keep electing the condorcet winner but the decreasing weight for lower preferences means that a ballot that has had its top choice elected has less effect. I assume it meets the Droop rule? If you mean the Droop proportionality criterion: no, it doesn't. Since no reweighting is done in the first round, it elects the Condorcet winner then, and that's incompatible with the DPC. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Raph Frank wrote: If you mean the Droop proportionality criterion: no, it doesn't. Since no reweighting is done in the first round, it elects the Condorcet winner then, and that's incompatible with the DPC. What about running the process for double the number of steps as there are seats. If there are 5 seats, then the first 4 rounds would be 'setup' rounds. Assuming the winners in each round is A, B, C ..., then the election would proceed as Setup stage Round 1: A Round 2: AB Round 3: ABC Round 4: ABCD Election stage Round 5: E elected: ABCDE Round 6: A eliminated and then F elected: Winners: BCDEF Round 7: B eliminated and then G elected Winners: CDEFG Round 8: C eliminated and then H elected Winners: DEFGH Round 9: D eliminated and then I elected Winners: EFGHI Note: a candidate may be referred to by more than 1 letter. A candidate might be eliminated in round 6 but then re-elected in round 8, so that candidate is both A and H. I wonder if it can be shown that if there is at least one solid coalition with a) a Droop quota and b) none of them elected, then they one of them is guaranteed to get elected for the final. If that was true, then each of the winners in rounds 5-9 would meet the criteron. Effectively, if a candidate who is part of a solid coalition is eliminated, he would be reelected immediately, or replaced by another candidate who also meets the criteron. I don't think so. Though I haven't investigated this method, I'm thinking that since it uses a divisor method (Sainte-Laguë), there would be instances where it breaks quota, just like ordinary Sainte-Laguë breaks quota, since quota (no candidate or party should need more than a quota worth of votes to get a seat, or get a seat with less than a quota's worth) is incompatible with the two criteria Sainte-Laguë meets (population pair and house monotonicity). On the other hand, quota violations are very rare in ordinary Sainte-Laguë/Webster, so it might not matter. Yet it does seem to matter when we port divisor methods directly to single-winner methods (e.g RRV), as quota methods outperform them in my simulations. Perhaps there's a multiwinner analog of the Condorcet criterion. If so, we would have a base on which to construct a method instead of having to guess blindly. Perhaps something like "if the method, when electing k winners, returns the set X, and there is a way of partitioning the ballots into k piles so that each pile has a CW, and each CW is in X, then the method passes this criterion". Or, is there something that is to the Droop proportionality criterion as the Smith criterion is to mutual majority? None of this is really applicable to the runoff (since we don't want DPC there), but since we were discussing methods that do meet the DPC, my mind wanders :-) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
On Sat, Nov 15, 2008 at 3:45 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > I don't think so. Though I haven't investigated this method, I'm thinking > that since it uses a divisor method (Sainte-Laguë), there would be instances > where it breaks quota, just like ordinary Sainte-Laguë breaks quota, since > quota (no candidate or party should need more than a quota worth of votes to > get a seat, or get a seat with less than a quota's worth) is incompatible > with the two criteria Sainte-Laguë meets (population pair and house > monotonicity). Well, I was thinking if the proposal was used with d'Hondt. > Perhaps something like "if the method, when electing k winners, > returns the set X, and there is a way of partitioning the ballots into k > piles so that each pile has a CW, and each CW is in X, then the method > passes this criterion". > Or, is there something that is to the Droop proportionality criterion as the > Smith criterion is to mutual majority? In the single winner case, Droop proportionality says that if a majority ranks a group of candidates above all other candidates, then one of those candidates will win. All methods that meet the condorcet criterion would also meet the Droop proportionality criteron. However, all single winner methods that meet the Droop proportionality criterion don't necessarily meet the condorcet criterion. IRV being an example that meets the Droop proportionality criterion but not meet the condorcet criterion. In that context, a multi-winner condorcet criterion would have to a stricter requirement than merely meeting the Droop criterion and any method that fails the Droop proportionality criterion would have to fail it. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Raph Frank wrote: On Sat, Nov 15, 2008 at 3:45 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: I don't think so. Though I haven't investigated this method, I'm thinking that since it uses a divisor method (Sainte-Laguë), there would be instances where it breaks quota, just like ordinary Sainte-Laguë breaks quota, since quota (no candidate or party should need more than a quota worth of votes to get a seat, or get a seat with less than a quota's worth) is incompatible with the two criteria Sainte-Laguë meets (population pair and house monotonicity). Well, I was thinking if the proposal was used with d'Hondt. D'Hondt is also a divisor method, and since divisor methods meet the two monotonicity criteria, they are all incompatible with quota. To my knowledge, only divisor methods meet both monotonicity criteria. I'm unsure as to whether that is true for divisor methods on sets, like Ossipoff's Cycle Webster method, but it doesn't seem to be the case for Cycle Webster, at least. Perhaps something like "if the method, when electing k winners, returns the set X, and there is a way of partitioning the ballots into k piles so that each pile has a CW, and each CW is in X, then the method passes this criterion". Or, is there something that is to the Droop proportionality criterion as the Smith criterion is to mutual majority? In the single winner case, Droop proportionality says that if a majority ranks a group of candidates above all other candidates, then one of those candidates will win. All methods that meet the condorcet criterion would also meet the Droop proportionality criteron. However, all single winner methods that meet the Droop proportionality criterion don't necessarily meet the condorcet criterion. IRV being an example that meets the Droop proportionality criterion but not meet the condorcet criterion. The single-winner criterion corresponding to the DPC is the mutual majority criterion. Any method that's Smith also passes mutual majority, and since Condorcet is just the case of the Smith set being a singleton, any Condorcet method passes the criterion when there's a CW. When there's not, a method may pass or fail; it passes if it's Smith, and it may either if it's not. Minmax and Black both fail mutual majority, to my knowledge. While I'm not familiar with which well known Condorcet methods, if any, that pass mutual majority while not being Smith, it's easy to make one: "CW if there is one, else IRV", for instance. In that context, a multi-winner condorcet criterion would have to a stricter requirement than merely meeting the Droop criterion and any method that fails the Droop proportionality criterion would have to fail it. It may pass it yet fail DPC if the multi-winner Condorcet "winner" (winner set?) is not present in all elections. If it elects the multiwinner Condorcet candidates (and in that case passes the DPC) when they exist, but fails DPC in all other cases, then it would fail DPC in general. But if it's like the Smith set, in that it's a subset of the Droop Proportionality set (mutual majority set in the case of single-winner), then what you say is true. If it's a subset of the DP set, then we know that it can't always be a proper subset. Otherwise, there would be cases where there are no eliminations in STV, so that any method that passes DPC must elect the entire set; if the subset was a proper subset, it would the fail the DPC, which is not desirable. But that's not so surprising, since it's also the case with Smith (regarding the mutual majority set); just produce ballots that all vote A > B > C and then a cycle among the other candidates. But what would this multi-winner Condorcet criterion be? That's the question. One may also ask whether it's a desirable criterion (like Condorcet), or if it's too strict (like Participation). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
On Sat, Nov 15, 2008 at 8:36 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > The single-winner criterion corresponding to the DPC is the mutual majority > criterion. Any method that's Smith also passes mutual majority, and since > Condorcet is just the case of the Smith set being a singleton, any Condorcet > method passes the criterion when there's a CW. Mutual majority looks the same as the Droop criterion, but for single winner cases. I wouldn't think much of a condorcet method that doesn't meet Smith, but the two criteria aren't the same. > But what would this multi-winner Condorcet criterion be? That's the > question. One may also ask whether it's a desirable criterion (like > Condorcet), or if it's too strict (like Participation). If the objective is to find a multi-winner equivalent of the condorcet criterion rather the Smith criterion, I am not so sure how useful that is. It would be a criterion that covers less cases than the Droop criterion. Maybe An outcome is not a valid outcome if there is any non-elected candidate who is preferred to all the winning candidates by a Droop quota of the voters. No invalid outcome may be used unless there are no valid outcomes. This would be similar to re-defining the condorcet criterion as A candidate shall be deemed an invalid winner if a majority prefer any other candidate to that candidate. An invalid candidate may not be declared the winner unless there are no valid candidates. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
Raph Frank wrote: On Sat, Nov 15, 2008 at 8:36 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: The single-winner criterion corresponding to the DPC is the mutual majority criterion. Any method that's Smith also passes mutual majority, and since Condorcet is just the case of the Smith set being a singleton, any Condorcet method passes the criterion when there's a CW. Mutual majority looks the same as the Droop criterion, but for single winner cases. I wouldn't think much of a condorcet method that doesn't meet Smith, but the two criteria aren't the same. Yes. Smith is a subset of mutual majority. The Condorcet winner is always in Smith, so when there's a CW, it's in the mutual majority set. But what would this multi-winner Condorcet criterion be? That's the question. One may also ask whether it's a desirable criterion (like Condorcet), or if it's too strict (like Participation). If the objective is to find a multi-winner equivalent of the condorcet criterion rather the Smith criterion, I am not so sure how useful that is. It would be a criterion that covers less cases than the Droop criterion. Maybe An outcome is not a valid outcome if there is any non-elected candidate who is preferred to all the winning candidates by a Droop quota of the voters. No invalid outcome may be used unless there are no valid outcomes. This would be similar to re-defining the condorcet criterion as A candidate shall be deemed an invalid winner if a majority prefer any other candidate to that candidate. An invalid candidate may not be declared the winner unless there are no valid candidates. That rule would admit more sets than the DPC. Call the candidates that a Droop quota supports above the others, "Droop CWs". Your criterion basically says "if you're picking k winners, and there are at least k Droop CWs, all the winners have to be Droop CWs; if there are less than k Droop CWs, those have to be included in the winning set". If there are Droop CWs, and also there's a subset that has to be included as the winners, then those winners will be Droop CWs (similar to how the Condorcet winner, when there is one, is in the Mutual Majority set). However, if there's a single winner CW for the election in question, that winner will also be a Droop CW. Similarly, if there's a candidate that x voters prefer to all others, where x is larger than the Droop quota, that candidate will also be a Droop CW. I guess that shouldn't surprise us; since Condorcet doesn't imply Mutual Majority, a multiwinner Condorcet criterion wouldn't imply the DPC either. However, the failure mode is different. Condorcet fails MM only when there's no CW (and the Condorcet criterion can't say which candidate you should elect); however, this fails even when there are Droop CWs (since we know Condorcet and the DPC is incompatible, and that a Condorcet winner must also be a Droop CW). So we may need a Smith set, and that set would have to be defined so that electing from it implies DPC. I have no idea how it would actually be defined, though. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Three rounds
On Mon, Nov 17, 2008 at 2:35 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > That rule would admit more sets than the DPC. Call the candidates that a > Droop quota supports above the others, "Droop CWs". Your criterion basically > says "if you're picking k winners, and there are at least k Droop CWs, all > the winners have to be Droop CWs; if there are less than k Droop CWs, those > have to be included in the winning set". I am not 100% sure that is equivalent to what I suggested, but seems reasonable. > I guess that shouldn't surprise us; since Condorcet doesn't imply Mutual > Majority, a multiwinner Condorcet criterion wouldn't imply the DPC either. > However, the failure mode is different. Condorcet fails MM only when there's > no CW (and the Condorcet criterion can't say which candidate you should > elect); however, this fails even when there are Droop CWs (since we know > Condorcet and the DPC is incompatible, and that a Condorcet winner must also > be a Droop CW). Well, it fails multi-winner condorcet when there isn't enough Droop CWs. The difference in the single winner case is that only a single winner is required. > So we may need a Smith set, and that set would have to be defined so that > electing from it implies DPC. I have no idea how it would actually be > defined, though. Maybe, base it on Copeland; A candidate shall be deemed to defeat an outcome if he is preferred to all winning candidates in the outcome by a Droop quota. The final outcome must be one of the outcomes which ties for fewest defeats. Election-Methods mailing list - see http://electorama.com/em for list info
