Re: [EM] Burlington dumps IRV; Immunity from Majority Complaints (IMC) criterion
Dear Steve Eppley, the following criterion has been discussed several times in the Election Methods mailing list: Suppose a majority of the voters prefers candidate A to candidate B. Then candidate B must not be elected, unless there is a sequence of candidates from candidate B to candidate A where each candidate beats the next candidate with a majority that is at least as strong as the majority of candidate A against candidate B. The above criterion was called e.g. beatpath criterion or immunity from binary arguments. The above criterion is satisfied e.g. by the Schulze method. Your immunity from majority complaints criterion has the following problems: (1) To guarantee that only the ranked pairs method satisfies this criterion, you added the requirement that each candidate of this sequence must be ranked ahead the next candidate of this sequence according to the social ordering. (2) To guarantee that only the ranked pairs method with winning votes satisfies this criterion, you added the requirement that the strength of a pairwise comparison must be measured by the number of voters who prefer the winning candidate to the losing candidate of this pairwise comparison. These additional requirements are not justified by the original motivation for this criterion: Suppose a majority rank x over y but x does not finish ahead of y (in the election's order of finish). They may complain that x should have finished ahead of y, using majority rule as their argument. (...) So it is desirable to be able to turn their own majority rule argument against them. (3) Your criterion presumes that the purpose of an election method is to create a social ordering. However, most readers will argue that the purpose of an election method is to find a winner and not to create a social ordering. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] calculating the N matrix in Schulze STV
Hallo,
N[{a,b,c},d] = 169 or Ñ[{a,b,c}, {a,b,d}] = 169 means
that W=169 is the largest value such that the electorate
can be divided into 4 disjoint parts T1,T2,T3,T4 such that
(1) Every voter in T1 prefers candidate a to candidate d;
and T1 consists of at least W voters.
(2) Every voter in T2 prefers candidate b to candidate d;
and T2 consists of at least W voters.
(3) Every voter in T3 prefers candidate c to candidate d;
and T3 consists of at least W voters.
Here is the example of page 38:
Group 1: 60 voters a b c d e
Group 2: 45 voters a c e b d
Group 3: 30 voters a d b e c
Group 4: 15 voters a e d c b
Group 5: 12 voters b a e d c
Group 6: 48 voters b c d e a
Group 7: 39 voters b d a c e
Group 8: 21 voters b e c a d
Group 9: 27 voters c a d b e
Group 10: 9 voters c b a e d
Group 11: 51 voters c d e a b
Group 12: 33 voters c e b d a
Group 13: 42 voters d a c e b
Group 14: 18 voters d b e c a
Group 15: 6 voters d c b a e
Group 16: 54 voters d e a b c
Group 17: 57 voters e a b c d
Group 18: 36 voters e b d a c
Group 19: 24 voters e c a d b
Group 20: 3 voters e d c b a
T1, T2, and T3 can be chosen as follows:
T1
Group 1: 60 voters a b c d e
Group 2: 1 voter a c e b d (one of the 45 voters of group 2)
Group 3: 30 voters a d b e c
Group 4: 15 voters a e d c b
Group 5: 12 voters b a e d c
Group 9: 27 voters c a d b e
Group 19: 24 voters e c a d b
T2
Group 2: 44 voters a c e b d (44 of the 45 voters of group 2)
Group 7: 39 voters b d a c e
Group 8: 17 voters b e c a d (17 of the 21 voters of group 8)
Group 12: 33 voters c e b d a
Group 18: 36 voters e b d a c
T3
Group 6: 48 voters b c d e a
Group 8: 4 voters b e c a d (4 of the 21 voters of group 8)
Group 10: 9 voters c b a e d
Group 11: 51 voters c d e a b
Group 17: 57 voters e a b c d
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] calculating the N matrix in Schulze STV
Hallo, the precise algorithm is described in the file calcul02.pdf of this zip file: http://m-schulze.webhop.net/schulze3.zip Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Alternative for Germany uses Schulze Method
Hallo, the Alternative for Germany, a political party with about 8500 eligible members, adopted the Schulze method for all internal elections. See: https://www.alternativefuer.de/pdf/Beschlossene_Bundessatzung.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Associated Student Government at Northwestern University uses Schulze Method
Hallo, on 19 April 2013, the Associated Student Government at Northwestern University used the Schulze method to choose its President. With 3471 cast ballots, this was the largest Schulze election ever. See: https://asg.northwestern.edu/news/2013/04/announcing-2013-asg-executive-elections-results Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Herve Moulin's proof not really a proof
Dear Nicholas, you wrote (13 June 2012): Actually, on a weird second thought, wouldn't a method that refused to identify a winner in a three-way tie (Condorcet paradox) be compatible with both? In Woodall's terminology, the output of an election method is a probability distribution on the set of candidates. He defines the participation criterion as follows: Suppose a set of voters is added where each voter strictly prefers every candidate of set _A_ to every other candidate. Then the probability that the winner is chosen from set _A_ must not decrease. In my paper (http://m-schulze.webhop.net/schulze1.pdf), the output of an election method is a set of winners _W_ rather than a single winner. In (4.7.16) -- (4.7.17), I define the participation criterion as follows: Suppose a set of voters is added where each voter strictly prefers every candidate of set _A_ to every other candidate. Suppose the intersection of _A_ and _W_ was non-empty, then the intersection of _A_ and _W_ must be non-empty afterwards. Suppose _W_ was a subset of _A_, then _W_ must be a subset of _A_ afterwards. It is easy to see that Moulin's proof also works when Woodall's or my definition of the participation criterion is used. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Herve Moulin's proof not really a proof
Dear Nicholas, just tell me who wins in the mentioned 7 situations and I will tell you where your method violates the participation criterion or the Condorcet criterion: http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-February/019497.html Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Herve Moulin's proof not really a proof
Dear Nicholas, who is elected by your method in these 7 situations?: http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-February/019497.html Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] How would Condorcet himself have solved his paradox?
Dear Ted, I interpret Condorcet as follows: (1) Condorcet mistakenly believed that, when you successively lock the strongest pairwise defeats, then you get a linear ordering of the candidates before locking a defeat creates a directed cycle. (2) Condorcet mistakenly believed that, when you successively eliminate the weakest pairwise defeat that is in a directed cycle until there are no directed cycles anymore, then the remaining pairwise defeats always define a unique linear ordering of the candidates. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Question about Schulze beatpath method
Hallo, I rewrote section 5 (Tie-Breaking) of my paper, so that it is now more in accordance with the other parts of my paper: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] E-Petition for the Schulze Method
Hallo, here is an e-petition for the Schulze method: http://epetitions.direct.gov.uk/petitions/31387 Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Question about Schulze beatpath method
Hallo, in example 3 of my paper, the weakest link of the strongest path from candidate A to candidate C is the same link as the weakest link in the strongest path from candidate C to candidate A: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] finding the beat path winner with just one pass through the ranked pairs
Dear Ross, the runtime to calculate the strongest path from every candidate to every other candidate is O(C^3). However, the runtime to sort O(C^2) pairwise defeats is already O(C^4). So you cannot get a faster algorithm by sorting the pairwise defeats. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] ranked pair method that resolves beath path ties.
Dear Ross Hyman, you wrote (28 Nov 2011): One way of retaining monotonicity, I think, is to replace the Sets with objects that record the number of times that a A has beaten B. I guess that this tie-breaking strategy will violate independence of clones. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] ranked pair method that resolves beath path ties.
Dear Ross Hyman, you wrote (28 Nov 2011): One way of retaining monotonicity, I think, is to replace the Sets with objects that record the number of times that a A has beaten B. Suppose A-C-B is the strongest path from candidate A to candidate B. Suppose B-A is the strongest path from candidate B to candidate A. Suppose candidate C is replaced by clones C(1),...,C(n). Then the number of times A beats B is multiplied. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] ranked pair method that resolves beath path ties.
Dear Ross Hyman, you wrote (27 Nov 2011): A and B are both winners. A is in B's set and B is in A's set. So A is deleted from B's set and B is deleted from A's set. A(W): A(W), C(L), D(L) B(W): B(W), C(L), D(L) C(L): A(W), B(W), C(L), D(L) D(L): A(W), B(W), C(L), D(L) affirm A B A(W):A(W), C(L), D(L) B(L): A(W), B(L), C(L), D(L) C(L): A(W), B(L), C(L), D(L) D(L): A(W), B(L), C(L), D(L) B was reclassified as a Loser since A(W) is in its set. When I understand your proposal correctly, then you are basically saying that, when contradicting beatpaths have the same strength, then they are cancelling each other out and the next strongest beatpath decides. I believe that your proposal can lead to a violation of monotonicity. Let's say that there is one beatpath from candidate X to candidate Y of strength z and two beatpaths from candidate Y to candidate X of strength z. Then these beatpaths cancel each other out. However, if one of the two beatpaths from candidate Y to candidate X is weakened, then this beatpath decides that candidate Y is ranked ahead of candidate X in the collective ranking. (This is problematic especially when the weakened beatpath was the direct comparison Y vs. X.) By the way: In my paper, I also recommend that the ranked pairs method should be used to resolve situations where the Schulze winner is not unique. However, the precise formulation is important. See section 5 stage 3 of my paper: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Kevin's other posting on votes-only criteria vs preference criteria.
Hallo, Mike Ossipoff wrote (18 Nov 2011): Not many methods meet SDSC. ABucklin and MDD,ABucklin do. But difficultly-attainable criteria are useful for describing advantages offered by only a few methods. Also the Schulze method meets SDSC. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Markus: Re: Beatpath as a proposal in the U.S.
Hallo, Mike Ossipoff wrote (19 Nov 2011): Beatpath isn't a choice for a proposal in the U.S. The Schulze method is analyzed here: http://m-schulze.webhop.net/schulze1.pdf The Schulze method satisfies anonymity, neutrality, homogeneity, resolvability, Pareto, reversal symmetry, mono-raise, mono-add-plump, Condorcet, Smith, Schwartz, independence of clones, and independence of Smith-dominated alternatives. It satisfies Woodall's CDTT criterion, Woodall's plurality criterion, Ossipoff's SFC, and Ossipoff's SDSC. The Schulze method has been published several times in scientific journals and in scientific books. The Schulze method is currently used by more than 50 organizations with more than 70,000 members in total. Of all Condorcet methods, that are currently discussed, the Schulze method is that method that has the best chances of getting adopted. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] question about Schulze example (A,B,M1,M2)
Hallo, as long as the used tie-breaking strategy guarantees that M1 is ranked ahead of M2, I see no problem. See section 5 of my paper: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] question about Schulze example (A,B,M1,M2)
Hallo, Not quite what I'm looking for. That section describes a non-deterministic method for generating a complete linear order. Well, although this tie-breaking strategy is _formulated_ as a random tie-breaker, it is almost always decisive. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Voting reform statement; a clearer and more inspiring, version
Hallo, I wrote (24 Aug 2011): In my opinion, the Voting Reform Statement endorses too many alternative election methods. Opponents will argue that this long list demonstrates that even we don't have a clue which election method should be adopted. Jameson Quinn wrote (24 Aug 2011): Is that worse than what happens if we can't agree? Well, one of the most frequently used arguments against Condorcet methods is that there are too many Condorcet methods and that there is no agreement on the best one. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Wikimedia's Board of Trustees elections, 2011
Hallo, Wikimedia has now published details of the latest Board of Trustees elections: http://meta.wikimedia.org/wiki/Board_elections/2011/Results/en There was a circular tie for positions 7 to 9. Cain beat Richardson 861:818. Richardson beat Lorente 838:832. Lorente beat Cain 789:784. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Eric Maskin promotes the Black method
Hallo, Eric Maskin, a Nobel laureate, is currently very active in promoting the Black method. The Black method says: If there is a Condorcet winner, then the Condorcet winner should win; if there is no Condorcet winner, then the Borda winner should win. See e.g.: 1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268 8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww Maskin argues as follows: If election method X is the best possible election method in domain X and if election method Y is the best possible election method in domain Y and if domain X and domain Y are disjoint and if domain X and domain Y together cover all possible situations, then the best possible election method is to use election method X in domain X and election method Y in domain Y. Maskin argues: domain X = situations with a Condorcet winner; election method X = any Condorcet method; domain Y = situations without a Condorcet winner; election method Y = Borda method. *** That method, that uses election method X in domain X and election method Y in domain Y, will be called election method Z. *** Maskin's argumentation doesn't work because of the following reason: Whether an election method is good or bad depends on which criteria it satisfies. Most criteria say how the result should change when the profile changes. Now it can happen that the original profile and the new profile are in different domains. This means that, to satisfy some criterion, election method X for domain X and election method Y for domain Y must not be chosen independent from each other. Example: The participation criterion says that adding some ballots, that rank candidate A above candidate B, must not change the winner from candidate A to candidate B. Election method X satisfies the participation criterion in domain X. Reason: If candidate A was the winner in the original profile and if the original profile was in domain X, then this means that candidate A was the Condorcet winner and, therefore, that candidate A pairwise beat candidate B. If candidate B is the winner in the new profile and if the new profile is in domain X, then this means that candidate B is the Condorcet winner and, therefore, that candidate B pairwise beats candidate A. If candidate A pairwise beat candidate B in the original profile and if candidate B pairwise beats candidate A in the new profile, then this means that the added ballots rank candidate B above candidate A. Election method Y satisfies the participation criterion in domain Y, because the Borda method satisfies the participation criterion in general. However, election method Z doesn't satisfy the participation criterion since the Condorcet criterion and the participation criterion are incompatible. In short: Even if election method X satisfies criterion A in domain X and election method Y satisfies criterion A in domain Y, it doesn't mean that election method Z satisfies criterion A. Therefore, Maskin's argumentation doesn't work. *** I also question the claim that the Borda method is the best possible election method in situations without a Condorcet winner. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Continuous bias
Hallo, currently, there is the tradition to give 12, 10, 8 points always to its political/ethnic/geographic neighbours. I recommend that a Condorcet method should be used to reduce the effects of this voting behaviour. As Condorcet methods put less emphasis on first preferences, the above voting behaviour would be nivellated over all countries. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Pirate Party of Berlin adopts the Schulze method
Hallo, Robert Bristow-Johnson wrote (1 March 2011): that said, i can't figure out from the website who wins according to the Schulze algorithm. I wrote (1 March 2011): magalski beats baum 48:39. baum beats mayer 48:46. mayer beats magalski 48:47. The bylaws say that the strength of a pairwise defeat is measured by the absolute number of votes for the winner of this pairwise defeat. So each defeat has a strength of 48. Therefore, there is a tie between magalski, baum, and mayer. There was a runoff (for the first to the third place of the party list) on 19 March 2011. This runoff was held using approval voting. magalski: 42 votes baum: 42 votes mayer: 27 votes As there was a tie between magalski and baum, the winner (baum) was chosen by lot. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] electing a variable number of seats
Dear Charlie, I recommend that you should use a method to create a proportional ranking. A proportional ranking is a complete ranking of all candidates such that, for every possible number M, the first M candidates of this ranking represent the electorate in a manner as proportional as possible. Proportional ranking methods are sometimes used to create a party list for proportional representation by party lists. Here, the different parties don't know in advance how many seats they will get. Proportional ranking methods have been proposed e.g. here: 1. Colin Rosenstiel, Producing a Party List using STV, Voting Matters, issue 9, May 1998, http://www.votingmatters.org.uk/ISSUE9/P4.HTM 2. Joseph Otten, a. Ordered List Selection, Voting Matters, issue 9, May 1998, http://www.votingmatters.org.uk/ISSUE9/P5.HTM b. Ordered List Selection - revisited, Voting Matters, issue 12, November 2000, http://www.votingmatters.org.uk/ISSUE12/P1.HTM 3. Markus Schulze, a. Free Riding and Vote Management under Proportional Representation by the Single Transferable Vote, http://m-schulze.webhop.net/schulze2.pdf b. Implementing the Schulze STV Method, http://m-schulze.webhop.net/schulze3.zip Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] An interesting real election
Dear Andrew, you wrote (31 January 2011): Notice that if someone now votes 2 1 6, the Schulze method picks 1 over 2, which is the opposite of what the new voter wanted. Well, the Condorcet criterion and the participation criterion are incompatible with each other. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] An interesting real election
Hallo, over a long period of time, the Simpson-Kramer method was considered to be the best Condorcet method because this method minimizes the number of overruled voters. However, the Simpson-Kramer method has recently been criticized e.g. for violating the Smith criterion, reversal symmetry, and independence of clones. Therefore, my aim was to find a method that satisfies the Smith criterion, reversal symmetry, and independence of clones and that chooses the Simpson-Kramer winner wherever possible. In your example, candidate #2 is the Simpson-Kramer winner. Therefore, candidate #2 should be elected. See section 1 of my paper: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] a Borda-Condorcet relation
Hallo, if you don't want to read the paper by Dasgupta and Maskin, you can see Maskin's lecture here: http://research.microsoft.com/apps/video/default.aspx?id=143268 Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] a Borda-Condorcet relation
Hallo, What they call majority rule is Condorcet, and what they propose is Black. Actually, they propose Copeland/Borda. See the footnote on page 13: http://www.econ.cam.ac.uk/faculty/dasgupta/MajRuVot.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Schulze Method
Hallo, I have uploaded a new version of my paper A New Monotonic, Clone-Independent, ...: http://m-schulze.webhop.net/schulze1.pdf I have shortened my paper from 167 pages to 64 pages. The new version is simpler and more stringent than the old version (because, in the new version, I use one and only one heuristic for the Schulze method). The proofs are simpler because I moved the random ballot tie-breaker from section 2 to section 5. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] it's been pretty quiet around here...
Hallo, I believe that the main reason, why Condorcet methods never played a role in political reality, is that the Condorcet supporters could never agree on a concrete method. In consequence, the Condorcet opponents simply replied: The Condorcet method has a problem. There may not be a Condorcet winner. See e.g.: http://www.publications.parliament.uk/pa/cm21/cmselect/cmproced/40/40ap04.htm http://www.lwvmn.org/LWVMNAlternativeVotingStudyReport.pdf http://www.lwvor.org/documents/ElectionMethods2008.pdf Therefore, in my opinion, you should always promote a concrete Condorcet method. And you should treat the Condorcet criterion as one criterion among many criteria. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Proportional election method needed for the Czech Green party - Council elections
Dear Peter Zbornik, you wrote (9 May 2010): In your paper schulze3.pdf, there are some instances, where the Schulze proportional ranking fails to produce an unambiguous ordering (see for instance the result for data set A10). Why do there ambiguities occur and how would you recommend them to be resolved in a deterministic manner without resorting to random number generation etc? In 5 instances (A10, A12, A23, A33, A67), the Schulze proportional ranking is not unique. This is caused by the small numbers of voters and the large numbers of candidates. For example, in instance A10 (83 voters, 19 candidates), there are two possible Schulze proportional rankings: NAPMQFGRSLIBDJKEHOC and NMPQAFGRSLIBDJKEHOC. You wrote (9 May 2010): Does Schulze-STV allow for truncated ballots? I.e. when there are 5 candidates, does Schulze-STV allow me to only rank two of them on my ballot? I recommend proportional completion. This is explained in section 5.3 of http://m-schulze.webhop.net/schulze2.pdf and in the file calcul01.pdf of http://m-schulze.webhop.net/schulze3.zip You wrote (9 May 2010): I am also curious to know, if you think it would be difficult for you to implement a program, which would handle the green council elections in an optimal proportional manner, i.e. methods, which would only impose the required ranking. It would be simple to incorporate all the requested specifications. Send me an input file with explanations. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Proportional election method needed for the Czech Green party - Council elections
Dear Peter Zbornik,
the fact, that the Schulze single-winner election method
satisfies the majority criterion, is a direct consequence
of the fact that every pairwise victory is stronger than
every pairwise defeat.
Similarly, the fact, that the Schulze proportional ranking
method satisfies the proportionality criterion for the
top-down approach, is a direct consequence of the fact
that every link H[A(1),...,A(n-1),x,y] from an outcome
{A(1),...,A(n-1),x} in agreement with the proportionality
criterion to an outcome {A(1),...,A(n-1),y} in disagreement
with the proportionality criterion has a strength of more
than N/(n+1) and that every link H[A(1),...,A(n-1),y,x]
from an outcome {A(1),...,A(n-1),y} in disagreement
with the proportionality criterion to an outcome
{A(1),...,A(n-1),x} in agreement with the proportionality
criterion has a strength of less than N/(n+1). This means
that every path from an outcome in agreement with the
proportionality criterion to an outcome in disagreement
with the proportionality criterion has a strength of
more than N/(n+1) and that every path from an outcome
in disagreement with the proportionality criterion to an
outcome in agreement with the proportionality criterion
has a strength of less than N/(n+1). This means that every
outcome in agreement with the proportionality criterion
disqualifies every outcome in disagreement with the
proportionality criterion.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Fwd: Proportionality proof of Schulze proportional ranking
Dear Warren,
for the top-down approach to create a party list,
I would define proportionality as follows:
Suppose place 1 to (n-1) have already been
filled. Suppose A(i) (with i = 1,...,(n-1))
is the candidate of place i.
Suppose we want to fill the n-th place.
Suppose it is possible to find a candidate B
such that the set {A(1),...,A(n-1),B} satisfies
Droop proportionality for n seats.
Then the n-th seat goes to a candidate B
such that the set {A(1),...,A(n-1),B} satisfies
Droop proportionality for n seats.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Proportional election method needed for the Czech Green party - Council elections
Dear Peter Zbornik,
in the scientific literature, candidates, who
have not yet been elected, are sometimes called
hopeful.
***
The Schulze proportional ranking method can be
described as follows:
Suppose place 1 to (n-1) have already been
filled. Suppose A(i) (with i = 1,...,(n-1))
is the candidate of place i.
Suppose we want to fill the n-th place.
Suppose x,y are two hopeful candidates. Then
H[A(1),...,A(n-1),x,y] is the largest possible
value such that the electorate can be divided
into n+1 disjoint parts T(1),...,T(n+1) such that
1. For all i := 1,...,n: |T(i)| = H[A(1),...,A(n-1),x,y].
2. For all i := 1,...,(n-1): Every voter in T(i)
prefers candidate A(i) to candidate y.
3. Every voter in T(n) prefers candidate x
to candidate y.
Apply the Schulze single-winner election method
to the matrix d[x,y] := H[A(1),...,A(n-1),x,y].
The winner gets the n-th place.
***
The best way to understand the Schulze proportional
ranking method is to investigate the properties of
H[A(1),...,A(n-1),x,y]. For example:
a. Suppose x and y are the only hopeful candidates.
Suppose N is the number of voters.
Suppose Droop proportionality for n seats requires
that x must be elected and that y must not be
elected, then we get H[A(1),...,A(n-1),x,y] N/(n+1)
and H[A(1),...,A(n-1),y,x] N/(n+1), and, therefore,
H[A(1),...,A(n-1),x,y] H[A(1),...,A(n-1),y,x].
This guarantees that the Schulze proportional
ranking method satisfies the proportionality
criterion for the top-down approach to create
party lists.
b. Adding or removing another hopeful candidate z
does not change H[A(1),...,A(n-1),x,y].
c. H[A(1),...,A(n-1),x,y] is monotonic. That means:
Ranking candidate x higher cannot decrease
H[A(1),...,A(n-1),x,y]. Ranking candidate x
lower cannot increase H[A(1),...,A(n-1),x,y].
Ranking candidate y higher cannot increase
H[A(1),...,A(n-1),x,y]. Ranking candidate y
lower cannot decrease H[A(1),...,A(n-1),x,y].
d. H[A(1),...,A(n-1),x,y] depends only on which
candidates of {A(1),...,A(n-1),x} the individual
voter prefers to candidate y, but it does not
depend on the order in which this voter prefers
these candidates to candidate y.
This guarantees that my method is not needlessly
vulnerable to Hylland free riding. In my paper
(http://m-schulze.webhop.net/schulze2.pdf), I argue
that other STV methods are needlessly vulnerable to
Hylland free riding, because the result depends on
the order in which the individual voter prefers
strong winners. In my paper, I argue that voters,
who understand STV well, know that it is a useful
strategy to give candidates, who are certain of
election, an insincerely low ranking. I argue
that, therefore, the order in which the individual
voter prefers strong winners doesn't contain any
information about the opinion of this voter, but
only information about how clever this voter is in
identifying strong winners. Therefore, the result
should not depend on the order in which the
individual voter prefers strong winners.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Proportional election method needed for the Czech Green party - Council elections
Dear Peter Zbornik,
I wrote (6 May 2010):
The Schulze proportional ranking method can be
described as follows:
Suppose place 1 to (n-1) have already been
filled. Suppose A(i) (with i = 1,...,(n-1))
is the candidate of place i.
Suppose we want to fill the n-th place.
Suppose x,y are two hopeful candidates. Then
H[A(1),...,A(n-1),x,y] is the largest possible
value such that the electorate can be divided
into n+1 disjoint parts T(1),...,T(n+1) such that
1. For all i := 1,...,n: |T(i)| = H[A(1),...,A(n-1),x,y].
2. For all i := 1,...,(n-1): Every voter in T(i)
prefers candidate A(i) to candidate y.
3. Every voter in T(n) prefers candidate x
to candidate y.
Apply the Schulze single-winner election method
to the matrix d[x,y] := H[A(1),...,A(n-1),x,y].
The winner gets the n-th place.
You wrote (6 May 2010):
The example below is intriguing. But I am afraid I fail
to understand this formulation of Schulze's proportional
ranking. I would be grateful if M. Schulze or someone
else, could give an example, which could help me get it.
Specifically, I didn't understand what H[A(1),...,A(n-1),x,y]
is. Is it a function, H[A(1),...,A(n-1),x,y]=
min(cardinality of T(i), 0=i=n+1 plus other criteria)?,
I didn't get the properties of T(n+1). Why are there n+1
partitions of the electorate and not only n?
H[A(1),...,A(n-1),x,y] is a real number. My mail above is
supposed to be a definition for H[A(1),...,A(n-1),x,y].
There are n+1 partitions because there can also be
some voters who prefer candidate y to every candidate
in {A(1),...,A(n-1),x}. The voters in T(n+1) are those
who prefer candidate y to every candidate in
{A(1),...,A(n-1),x}.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] The rise and fall of Bucklin voting in the United States
Hallo, here is that paper where Condorcet proposes the Bucklin method: http://archive.numdam.org/ARCHIVE/MSH/MSH_1990__111_/MSH_1990__111__7_0/MSH_1990__111__7_0.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] VoteFair representation ranking recommended for Czech Green Party
Dear Richard Fobes, you wrote (4 May 2010): The book does not refer to the independence of irrelevant alternatives criteria, so where did you get the idea that it claims to satisfy that criteria? For example, on page 256 you claim: When VoteFair ranking is used, adding or withdrawing non-winning candidates cannot increase or decrease the chances of a particular candidate winning. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Proportional election method needed for the Czech Green party - Council elections
Dear Raph Frank, you wrote (3 May 2010): For the rest of the council, I think electing them using Schulze-STV with the restriction that only results where the President and VP are members are allowed would give better proportionality. If I understand Peter Zbornik correctly, then he wants a ranking of the members of the council, so that it is clear who the 2nd vice president, the 3rd vice president, the 4th vice president, etc., is. Therefore, I recommend a proportional ranking method for the election of the council. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] VoteFair representation ranking recommended for Czech Green Party
Dear Richard Fobes, you wrote (2 May 2010): Once again Markus Schulze is trying to discredit the Condorcet-Kemeny method. If I really wanted to discredit this method, then I would mention ... ... that this method violates independence of clones. ... that this method has a prohibitive runtime so that it is illusory that VoteFair representation ranking could ever be used e.g. to fill 7 seats out of 30 candidates. ... that, although this method has been proposed more than 30 years ago, it has never been used by a larger organization. ... that many of the claims in your book are ridiculous; for example, your claim that this method was strategyproof and satisfied independence of irrelevant alternatives. * You wrote (2 May 2010): This is ironic because his method -- which he calls the Schulze method, and which would more meaningfully be called the Condorcet-Schulze method -- produces the same results as the Condorcet-Kemeny method in most cases. I call my method Schulze method and not Condorcet- Schulze method, because I consider the Condorcet criterion to be only one criterion among many criteria. * I wrote (29 April 2010): Does the San Francisco Bay Area Curling Club still use the Kemeny-Young method? If not, why did it abolish the Kemeny-Young method? You wrote (2 May 2010): This club continues to use VoteFair ranking, a subset of which is the Condorcet-Kemeny method. In 2009, the announcement said: We will be using the VoteFair system. In this system, you rank all the candidates in order of preference and the most preferred candidates will get the office. You will rank *all* the candidates in order of preference. In 2010, the announcement said: The two nominees with the most votes will hold office for two years, the nominee with the third highest level of votes will hold office for one year. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] VoteFair representation ranking recommended for Czech Green Party
Hallo, VoteFair representation ranking is described in chapter 15 of this book: http://www.solutionscreative.com/download/EndingHiddenUnfairnessInElections_OntarioVersion.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Uncovered set methods (Re: How close can we get to the IIAC)
Hallo, is Jobst Heitzig's river method identical to Blake Cretney's goldfish method? Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] MinMax(AWP) and Participation
Hallo, the Young method calculates for each candidate A the minimum number of ballots that have to be removed so that candidate A doesn't lose any of its pairwise comparisons. The Young method chooses that candidate for whom this number is the smallest. Also the Young method satisfies mono-add-top, mono-remove-bottom, and Condorcet. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Participation
Hallo, Bucklin violates mono-add-top. See: http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012752.html Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Uncovered set methods (Re: How close can we get to the IIAC)
Dear Forest, you wrote (20 April 2010): 1. It elects the same member of a clone set as the method would when restricted to the clone set. Well, how do you define clones? In the approval voting paradigm, the term clones implies that all candidates have the same approval score. So when you apply UncAAO to a clone set, then all candidates of its uncovered set are tied. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] How close can we get to the IIAC
Hallo, Here's a method I proposed a while back that is monotone, clone free, always elects a candidate from the uncovered set, and is independent from candidates that beat the winner, i.e. if a candidate that pairwise beats the winner is removed, the winner still wins: 1. List the candidates in order of decreasing approval. 2. If the approval winner A is uncovered, then A wins. 3. Otherwise, let C1 be the first candidate is the list that covers A. If C1 is uncovered, then C1 wins. 4. Else let C2 be the first candidate in the list that covers C1. If C2 is uncovered, then C2 wins. etc. Situation 1: Suppose the order of decreasing approval is CDAB. A beats B B beats C C beats D D beats A A beats C B beats D uncovered set: A, B, D. The winner is D. * Situation 2: Suppose some voters rank D higher so that D beats B. Suppose the order of decreasing approval is still CDAB. A beats B B beats C C beats D D beats A A beats C D beats B uncovered set: A, C, D. Now, the winner is C. So, monotonicity is violated. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] How close can we get to the IIAC
Hallo, Here's a method I proposed a while back that is monotone, clone free, always elects a candidate from the uncovered set, and is independent from candidates that beat the winner, i.e. if a candidate that pairwise beats the winner is removed, the winner still wins: 1. List the candidates in order of decreasing approval. 2. If the approval winner A is uncovered, then A wins. 3. Otherwise, let C1 be the first candidate is the list that covers A. If C1 is uncovered, then C1 wins. 4. Else let C2 be the first candidate in the list that covers C1. If C2 is uncovered, then C2 wins. etc. Situation 1: Suppose the order of decreasing approval is CDAB. A beats B B beats C C beats D D beats A A beats C B beats D uncovered set: A, B, D. The winner is D. Situation 3: B beats D. If B is removed, then the uncovered set is: A, C, D. So, if B is removed, then C wins. So, the proposed method doesn't satisfy this property: If a candidate that pairwise beats the winner is removed, the winner still wins. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Paper by Ron Rivest
Hallo, Kristofer Munsterhjelm wrote (16 April 2010): I'm curious now as to how often, say, Ranked Pairs would disagree with GT/GTD/GTS. Do you consider the GT agreement a worthwhile metric, i.e. that (absent criteria problems) methods closer to GT are better? I don't like probabilistic models, because I don't think that voters are random variables. However, I am impressed how often authors get to the conclusion that the Schulze method is the best method in random simulations. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Paper by Ron Rivest
Hallo, here is an interesting paper by Ron Rivest: http://people.csail.mit.edu/rivest/RivestShen-AnOptimalSingleWinnerPreferentialVotingSystemBasedOnGameTheory.pdf He gets to the conclusion that the Schulze method is nearly perfect (page 12). Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet How?
Hallo, Dave Ketchum (7 April 2010): For RP I see deleting the smallest margins from the list until what remains is not a cycle, but does identify a winner. Deleting the smallest margins from the list until what remains is not a cycle rather sounds like the Schulze method. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Papers on Schulze method
Hallo, Rosa Camps, Xavier Mora, and Laia Saumell have written several papers on the Schulze method: http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.2263v1.pdf http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.2190v1.pdf http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.2195v1.pdf http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.3931v1.pdf They discuss how the Schulze method could be generalized so that it generates continuous rates for the different alternatives. I don't consider this topic interesting. However, their papers are nevertheless interesting in so far as they recapitulate many of the proofs of my papers. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet How?
Dear Robert, Terry Bouricius is also a Burlington resident and is known in Burlington for being the primary promoter of IRV (i think that's right, ain't it Terry?). i didn't see him at the debate, but Rep. Mark Larson and someone from League of Women Voters were on the pro- IRV side and they didn't come fightin', in my opinion. and part of the problem is that *they* didn't really understand or acknowledge the cascade of anomalies that resulted when the IRV election fails to elect the Condorcet winner as it did in 2009. Here are some videos with Terry Bouricius: http://www.cctv.org/watch-tv/programs/instant-runoff-voting-debate http://www.cctv.org/watch-tv/programs/instant-runoff-voting-0 http://www.cctv.org/watch-tv/programs/leaguewmn-s-voters-instant-run-voting Terry's main argument against the adoption of Condorcet methods is that they aren't used in governmental elections (first video, 00:24:04 -- 00:25:36). Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet How?
Hallo, here are some interesting videos on IRV in Burlington: http://www.cctv.org/watch-tv/programs/instant-runoff-voting-interviews http://www.cctv.org/watch-tv/programs/irv-or-down-instant-runoff-voting-debate I have the impression that there was no reasonable debate on IRV. Most anti-IRV arguments were ridiculous or simply false. The anti-IRV campaign was a pure anti-Kiss campaign. in fact, if the election was decided with Condorcet rules (doesn't matter which, since there was no cycle), these same Republicans would have bitched all the more, since the Condorcet candidate had only 23% and came third in plurality. so the primary political motivation behind the repeal was not due to that the Condorcet winner was not elected. I agree that the Republicans would also have attacked Condorcet. But as Montroll was preferred to Wright with 56% against 44%, an anti-Condorcet/anti-Montroll campaign wouldn't have been successful. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet How?
Dear Robert, are you the questioner at 00:42:00 -- 00:44:25? Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet How?
Hallo, Kristofer Munsterhjelm wrote (21 March 2010): Schulze's advantage is that it's actually being used and that it provides good results (by the Minmax standard). Ranked Pairs's (or MAM's, rather) is that it's easy to explain. The question is: which of these qualities are more important, were we to encourage the use of a Condorcet method in real (governmental) elections? I claim that Burlington repealed IRV mainly because it chose a candidate with a strong worst defeat. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Book on Schulze method
Hallo, here is another book in favour of the Schulze method: Christoph Börgers, Mathematics of Social Choice: Voting, Compensation, and Division, SIAM, 2009 http://books.google.com/books?id=dccBaphP1G4Cpg=PA37#v=onepageq=f=false Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Pirate Party of Sweden adopts the Schulze method
Hallo, here are the preliminary results of the primaries: http://www.piratpartiet.se/nyheter/piratpartiets_primarval_ar_avslutat http://www.piratpartiet.se/nyheter/piratpartiet_presenterar_sin_riksdagsgrupp Only 1300 of the 50,000 eligible pirates participated at this election. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Pirate Party of Sweden adopts the Schulze method
Hallo, when I apply the Schulze method to the ballot data of the Pirate Party primaries, then I get the following ranking: 1. Rick Falkvinge 2. Anna Troberg 3. Gun Svensson 4. Anna Svensson 5. Stefan Flod 6. Carl Johan Rehbinder 7. Sandra Grosse 8. Hanna Donsberg 9. Johnny Olsson 10. Mikael Nilsson 11. Johanna Julen 12. Malin Littorin Ferm 13. Klara Tovhult 14. Marten Fjallstrom 15. Eva Wei 16. Rickard Olsson 17. Jan Lindgren 18. Gustav Nipe 19. Kalle Vedin 20. Bjorn Felten 21. Jacob Dexe 22. Klara Ellstrom Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Pirate Party of Sweden adopts the Schulze method
Hallo, in October 2009, the Pirate Party of Sweden adopted the Schulze method. See e.g.: http://forum.piratpartiet.se/FindPost174988.aspx http://forum.piratpartiet.se/FindPost176567.aspx http://forum.piratpartiet.se/FindPost191479.aspx The Schulze method is used in the internal elections (14 December 2009 to 17 January 2010) to fill the 82 list places for the upcoming Riksdag elections. There are 230 candidates and about 50,000 eligible voters: http://www.piratpartiet.se/primarvalskandidater Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Pirate Party of Sweden adopts the Schulze method
Hallo, the Schulze ranking will be used as defined in the Wikipedia article: http://en.wikipedia.org/wiki/Schulze_method I agree that it would have been better if a proportional ordering method had been used. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Score DSV
Dear Jameson Quinn, please explain why Score DSV satisfies monotonicity in the 4-candidate case when the Dutta set is used instead of the Smith set. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Explaining PR-STV
Hallo,
I would explain proportional representaion
by the single transferable vote as follows:
1) Each voter gets a complete list of all
candidates and ranks these candidates in
order of preference.
2) Suppose M is the number of seats and
V is the number of votes. If there is a
set of X candidates such that strictly more
than (Y*V)/(M+1) votes strictly prefer
each candidate of this set to each candidate
outside this set, then at least min{X,Y}
candidates of this set must be elected.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] 'Shulze (Votes For)' definition?
Dear Chris Benham, you wrote (14 Aug 2009): What I don't understand is the difference between winning votes (which I'm familiar with) and votes for, as they are both defined on page 13 of Markus Schulze's paper, pasted below. http://m-schulze.webhop.net/schulze1.pdf Kevin Venzke and Kristofer Munsterhjelm are correct. What I call votes for in my paper is usually called pairwise opposition in this mailing list. The difference is described at the end of section 2.2.2: So the only difference between the Schulze method with winning votes and the Schulze method with votes for (resp. between the Schulze method with losing votes and the Schulze method with votes against) is that the condition N[c(i),c(i+1)] N[c(i+1),c(i)] for all i = 1,...,(n-1) is dropped. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] National Popular Vote Condorcet
Hallo, this problem had already been mentioned here: http://article.gmane.org/gmane.politics.election-methods/10991 Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] information content, game theory, cooperation
Dear Árpád Magosányi, here are the proposed statutory rules for the Schulze method: http://m-schulze.webhop.net/propstat.pdf If I understand you correctly, then you want to define the Schulze method in an axiomatic manner in your proposal. I don't think that this is a good idea. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Schulze definition (was: information content, game theory, cooperation)
Hallo, here is another short, but complete definition of the Schulze method: http://en.wikipedia.org/wiki/User:MarkusSchulze/Schulze_method_(simple_version) * - tends to produce winners with weak worst pairwise defeats I usually define this desideratum using MinMax scores for sets of candidates: Suppose the MinMax score of a set X of candidates is the strength of the strongest pairwise win of a candidate A outside set X against a candidate B inside set X. Then the winner should always be a candidate of the set with minimum MinMax score. See also section 9 of my paper: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Schulze definition (was: information content, game theory, cooperation)
Hallo, here is another paper that confirms the observation, that the Schulze winner is almost always identical to the MinMax winner: http://dukespace.lib.duke.edu/dspace/bitstream/10161/1278/1/Wright_Barry.pdf See pages 67-70. In the 4-candidate case, the Schulze winner and the MinMax winner are identical with a probability of 99.7%. In the 5-candidate case, the Schulze winner and the MinMax winner are identical with a probability of 99.2%. In the 6-candidate case, the Schulze winner and the MinMax winner are identical with a probability of 99.1%. In the 7-candidate case, the Schulze winner and the MinMax winner are identical with a probability of 98.9%. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] simple definition of Schulze method?
Hallo, this is my suggestion: Shall the current election method be replaced by the Schulze method, a preferential and Condorcet-consistent single-winner election method? Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] simple definition of Schulze method?
Hallo, Bob Richard wrote (4 June 2009): I did not consider the possibility that the country in question would have a mixed member proportional system. In this case, there are 175 single-seat constituencies, plus two more tiers, one parallel (I think) and one compensatory. By the way, I have also proposed a mixed member proportional (MMP) method that uses proportional representation by the single transferable vote (STV) on the district level: http://m-schulze.webhop.net/schulze4.pdf http://m-schulze.webhop.net/schulze5.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet - let's move ahead
Dear Kristofer Munsterhjelm, you wrote (19 Jan 2009): So voters prefer MAM winners to Beatpath winners more often than vice versa. What method is the best in that respect? Copeland methods are the best methods in this respect. The fact, that the ranked pairs winner usually pairwise beats the Schulze winner in random simulations, is a direct consequence of the facts, that the Schulze winner is usually identical to the MinMax winner and that the MinMax winner usually has a very low Copeland score (compared to the winners of other Condorcet methods). Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV and Brown vs. Smallwood
Dear Terry Bouricius, you wrote (18 Jan 2009): Do you have any example of FairVote suggesting Condorcet methods might be unconstitutional? See appendices 3 and 4 of this study: http://www.lwvmn.org/LWVMNAlternativeVotingStudyReport.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet - let's move ahead
Hallo, Steve Eppley wrote (18 Jan 2009): MAM satisfies all the desirable criteria satisfied by Beatpath Winner (aka Cloneproof Schwartz Sequential Dropping--CSSD for short--aka Schulze's method). Many people consider the Simpson-Kramer MinMax method to be the best single-winner election method because it minimizes the number of overruled voters. The winner of the Schulze method is almost always identical to the winner of the MinMax method, while the winner of the ranked pairs method differs needlessly frequently from the winner of the MinMax method. For example, Norman Petry made some simulations and observed that the number of situations, where the Schulze method and the MinMax method chose the same candidate and the ranked pairs method chose a different candidate, exceeded the number of situations, where the ranked pairs method and the MinMax method chose the same candidate and the Schulze method chose a different candidate, by a factor of 100: http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html Jobst Heitzig made a thorough investigation of the 4-candidate case. In no situation, the Schulze method and the MinMax method chose different candidates. (Beatpath and Plain Condorcet are unanimous in all these examples!) But in 96 situations, the ranked pairs method and the MinMax method chose different candidates: http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html There are even situations where the winner of the ranked pairs method differs from the winner of the MinMax winner without any plausible reason. See section 9 of my paper: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet - let's move ahead
Hallo, the links to Norman Petry's and Jobst Heitzig's mail have changed. Norman Petry's mail is now here: http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004541.html Jobst Heitzig's mail is now here: http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012838.html Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV and Brown vs. Smallwood
Dear Terry Bouricius, you wrote (18 Jan 2009): FairVote is not responsible for reports by the League of Women Voters or lawyers writing scholarly articles. Tony Solgard was president of FairVote Minnesota when he wrote the quoted article in which he claims that Condorcet was unconstitutional in Minnesota. Also the report by the League of Women Voters of Minnesota refers to him as Tony Solgard, President of Board of FairVote Minnesota. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV and Brown vs. Smallwood
Hallo, FairVote always argued that Brown vs. Smallwood declared Bucklin unconstitutional because of its violation of later-no-harm. FairVote always claimed that, therefore, also Condorcet methods were unconstitutional. However, the memorandum of the district court doesn't agree to this interpretation of Brown vs. Smallwood. This means that this memorandum is a progress at least in so far as FairVote cannot use Brown vs. Smallwood anymore as an argument against Condorcet methods. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] IRV and Brown vs. Smallwood
Hallo, in 1915, the Supreme Court of Minnesota declared the preferential system unconstitutional. The decision (Brown vs. Smallwood) is here: http://rangevoting.org/BrownVsmallwood.pdf The crucial sentence is (page 508): We do right in upholding the right of the citizen to cast a vote for the candidate of his choice unimpaired by second or additional choice votes by other voters. Now, a county judge had to decide whether Brown vs. Smallwood also applies to IRV. The judge came to the conclusion that Brown vs. Smallwood doesn't apply to IRV. The decision is here: http://www.fairvotemn.org/sites/fairvotemn.org/files/IRV%20Lawsuit_Hennepin%20Cnty%20Crt%20Opinion%20011309_1.PDF In my opinion, the decision is very problematic. The judge judged the methods not by their properties, but by IRV's underlying heuristic. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko,
Kevin Venzke wrote (10 Jan 2009):
[Situation #1]
26 AB
25 BA
49 C
Mutual Majority elects {A,B}
Now add 5 A bullet votes:
[Situation #2]
26 AB
25 BA
49 C
5 A
Now Mutual Majority elects {A,B,C}.
You wrote (10 Jan 2009):
I guess I don't understand mutual majority, then,
because after adding 5 votes it takes 53 votes to
have a majority, and only A has a majority. B is
51/105 and C is 45/105.
Five bullet-votes for A appear to change (A,B) to (A).
Mutual majority says: When a majority of the voters
strictly prefers every candidate of a given set of
candidates to every candidate outside this set of
candidates, then the winner must be chosen from this
set of candidates.
column1 = set of candidates
column2 = number of voters who strictly prefer every
candidate in column1 to every candidate outside column1
For situation #1, we get:
column1 / column2
A / 26
B / 25
C / 49
AB / 51
AC / 0
BC / 0
So mutual majority says that the winner must be
chosen from {A,B}.
For situation #2, we get:
column1 / column2
A / 31
B / 25
C / 49
AB / 51
AC / 0
BC / 0
So mutual majority says nothing.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko,
I wrote (10 Jan 2009):
For situation #2, we get:
column1 / column2
A / 31
B / 25
C / 49
AB / 51
AC / 0
BC / 0
So mutual majority says nothing.
You wrote (10 Jan 2009):
How can mutual majority say nothing? Only
if no combination has a majority. But A is in
the AB, BA, and new A's, so A is on 56 ballots,
which is a majority of ballots (and no one else is)
There are 105 voters. So a majority
requires at least 53 voters.
I have listed all solid coalitions.
And there is no solid coalition with
at least 53 voters.
So mutual majority says nothing.
There are only 31 voters who strictly prefer
candidate A to every other candidate. And
there are only 51 voters who strictly prefer
every candidate in {A,B} to every candidate
outside {A,B}.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko, you wrote (10 Jan 2009): The second scenario is 26 AB 25 BA 49 C 5 A which has 105 voters. 56 include A on any ballot and that's a majority. 51 include B, and that's not a majority. So how is B a possible winner under the second scenario? Mutual majority doesn't ask: How many voters rank all the candidates of set S? Mutual majority asks: How many voters rank all the candidates of set S ahead of all the candidates outside the set S? There are 56 voters who rank candidate A. But there are only 31 voters who rank candidate A ahead of every other candidate. Therefore, mutual majority says nothing in the scenario above. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko,
you wrote (10 Jan 2009):
The second scenario is
26 AB
25 BA
49 C
5 A
I ask again, in the post I replied to, it was claimed
mutual majority selected (A,B,C) in the 2nd case. I
wondered how that was possible, and you agree that it
isn't.
Kevin Venzke wrote: Mutual Majority elects {A,B,C}.
I wrote: Mutual majority says nothing in the scenario
above.
There is no contradiction between Kevin Venzke and me.
When the set of candidates is {A,B,C}, then saying that
the winner is chosen from {A,B,C} (Kevin Venzke) is the
same as saying that mutual majority says nothing (Markus
Schulze).
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? (was GMC compliance...)
Dear Chris Benham, you are the only one who uses the fact, that criterion X doesn't imply criterion Y, as an argument against criterion X. That's the same as rejecting monotonicity for not implying independence of clones. Your argumentation is not complicated. It is simply false. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? (was GMC compliance...)
criterion with that absurd feature? Your argumentation doesn't make any sense. Example: The fact, that the Borda method satisfies monotonicity and violates independence of clones, demonstrates that monotonicity doesn't imply independence of clones. You rejected beatpath GMC because it doesn't imply mono-add-plump. But with the same logic, you could reject the concept of monotonicity for the absurd feature of not implying independence of clones or for being spectacularly vulnerable to clones. The fact, that Schulze(winning votes) satisfies beatpath GMC and mono-add-plump, demonstrates that these two criteria are not incompatible. But you claim that already the fact, that beatpath GMC doesn't imply mono-add-plump, was an absurd feature of beatpath GMC. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Does IRV elect majority winners?
Dear James Gilmour, you wrote (2 Jan 2009): So let's try a small number of numbers. At a meeting we need to elect one office-bearer (single-office, single-winner). There are four candidates and we decide to use the exhaustive ballot (bottom elimination, one at a time) with the requirement that to win, a candidate must obtain a majority of the votes. First round votes: A 40; B 25; C 20; D 15. No candidate has a majority, so we eliminate D. Second round votes: A 47; B 25; C 20. It seems that some of those present who voted for D in the first round did not want to vote in the second round - but that is their privilege. QUESTION: did candidate A win at the second round with 'a majority of the votes'? Whatever the statement the winner always wins a majority of the votes means, this statement must be defined in such a manner that you only need to know the winner for every possible situation (but you don't need to know the used algorithm to calculate the winner) to verify/falsify the validity of this statement. Otherwise, this statement is only a tautology. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Does IRV elect majority winners?
Dear James Gilmour, you wrote (2 Jan 2009): So let's try a small number of numbers. At a meeting we need to elect one office-bearer (single-office, single-winner). There are four candidates and we decide to use the exhaustive ballot (bottom elimination, one at a time) with the requirement that to win, a candidate must obtain a majority of the votes. First round votes: A 40; B 25; C 20; D 15. No candidate has a majority, so we eliminate D. Second round votes: A 47; B 25; C 20. It seems that some of those present who voted for D in the first round did not want to vote in the second round - but that is their privilege. QUESTION: did candidate A win at the second round with 'a majority of the votes'? I wrote (2 Jan 2009): Whatever the statement the winner always wins a majority of the votes means, this statement must be defined in such a manner that you only need to know the winner for every possible situation (but you don't need to know the used algorithm to calculate the winner) to verify/falsify the validity of this statement. Otherwise, this statement is only a tautology. You wrote (2 Jan 2009): Markus, I don't know where the statement the winner always wins a majority of the votes came from, but it is not mine, and in my opinion, it does not take the discussion any further forward.. What I wrote, very specifically, was with the requirement that to win, a candidate must obtain a majority of the votes. Statements of this kind, and in these words (or words almost identical to these), are used when elections are held at meetings and are conducted either by show of hands or by informal paper ballot This form of words distinguishes such elections from those where a single-round plurality result would be accepted, when the corresponding statement from the Returning Officer would be something like and the winner will be the candidate with the most votes. This thread is about the meaning of the expression a majority of the votes. I presented the simple scenario above to see what views there might be about the meaning of a majority of the votes in that specific situation. This thread is rather about the meaning of the expression to win a majority of the votes. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Does IRV elect majority winners?
Hallo, usually, the term majority winner refers to a candidate who is strictly preferred to every other candidate by a majority of the voters. However, IRV supporters usually use the term majority winner for a candidate A who can win a majority (or at least half of the votes) in a runoff between candidate A and some other candidates. Question: Who can win a majority (or at least half of the votes) in a runoff between himself and some other candidates? Answer: Everybody but a Condorcet loser. So when IRV supporters say that IRV always elects a majority winner then this is EXACTLY the same as saying that IRV never elects a Condorcet loser. Question: So why don't IRV supporters just say that IRV never elects a Condorcet loser? Answer: IRV supporters don't want IRV to be judged by its properties but by its own underlying heuristic. We all know that every election method is the best possible election method when judged by its own underlying heuristic. If IRV supporters just said that IRV never elects a Condorcet loser, then this argument could also be used by the supporters of other election methods that satisfy the Condorcet loser criterion. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] GMC compliance a mistaken standard? (was CDTT criterion...)
Dear Chris Benham, you wrote (29 Dec 2008): The Generalised Majority Criterion says in effect that the winner must come from Woodall's CDTT set, and is defined by Markus Schulze thus (October 1997): Definition (Generalized Majority Criterion): X Y means, that a majority of the voters prefers X to Y. There is a majority beat-path from X to Y, means, that X Y or there is a set of candidates C[1], ..., C[n] with X C[1] ... C[n] Y. A method meets the Generalized Majority Criterion (GMC) if and only if: If there is a majority beat-path from A to B, but no majority beat-path from B to A, then B must not be elected. With full strict ranking this implies Smith, and obviously Candidates permitted to win by GMC (i.e.CDTT), Random Candidate is much better than plain Random Candidate. Nonetheless I think that compliance with GMC is a mistaken standard in the sense that the best methods should fail it. The GMC concept is spectacularly vulnerable to Mono-add-Plump! [Situation #1] 25: AB 26: BC 23: CA 04: C 78 ballots (majority threshold = 40) BC 51-27, CA 53-25, AB 48-26. All three candidates have a majority beat-path to each other, so GMC says that any of them are allowed to win. [Situation #2] But say we add 22 ballots that plump for C: 25: AB 26: BC 23: CA 26: C 100 ballots (majority threshold = 51) BC 51-49, CA 75-25, AB 48-26. Now B has majority beatpaths to each of the other candidates but neither of them have one back to B, so the GMC says that now the winner must be B. The GMC concept is also naturally vulnerable to Irrelevant Ballots. Suppose we now add 3 new ballots that plump for an extra candidate X. [Situation #3] 25: AB 26: BC 23: CA 26: C 03: X 103 ballots (majority threshold = 52) Now B no longer has a majority-strength beat-path to C, so now GMC says that C (along with B) is allowed to win again. (BTW this whole demonstration also applies to Majority-Defeat Disqualification(MDD) and if we pretend that the C-plumping voters are truncating their sincere preference for B over A then it also applies to Eppley's Truncation Resistance and Ossipoff's SFC and GFSC criteria.) Several versions of the Generalized Majority Criterion (GMC) have been discussed at the Election Methods mailing list in the past. Therefore, I recommend that you should use the term beatpath GMC for my 1997 proposal to distinguish it from the other proposals. Your argumentation is incorrect. Example: In many scientific papers, the Smith set is criticized because the Smith set can contain Pareto-dominated candidates. However, to these criticisms I usually reply that the fact, that the Smith criterion doesn't imply the Pareto criterion, is not a problem as long as the used tie-breaker guarantees that none of these Pareto-dominated candidates is elected. It would be a problem only if the Smith criterion and the Pareto criterion were incompatible. You made the same mistake as the authors of these papers. You didn't demonstrate that the GMC concept is spectacularly vulnerable to mono-add-plump. You only demonstrated that beatpath GMC doesn't imply mono-add-plump. However, the fact, that Schulze(winning votes) satisfies mono-add-plump and always chooses from the CDTT set and isn't vulnerable to irrelevant ballots, shows that these properties are not incompatible. In all three situations, Schulze(winning votes) chooses candidate B. Therefore, you demonstrated neither a spectacular failure of mono-add-plump nor a vulnerability to irrelevant ballots for methods that satisfy beatpath GMC. You wrote: All three candidates have a majority beatpath to each other, so GMC says that any of them are allowed to win. No! Beatpath GMC doesn't say that any of them are allowed to win; beatpath GMC only doesn't exclude any of them from winning. Similarly, the Smith criterion doesn't say that even Pareto-dominated candidates must be allowed to win; that would have meant that the Smith criterion and the Pareto criterion were incompatible; the Smith criterion only doesn't imply the Pareto criterion. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] CDTT criterion compliance desirable?
Dear Chris Benham, you wrote (25 Dec 2008): I had already proposed this criterion in 1997. Why then do you list it as Woodall's CDTT criterion instead of your own Generalised Majority Criterion? Did, as far as you know, Woodall ever actually propose the CDTT criterion as something that is desirable for methods to meet (instead of just defining the CDTT set)? Woodall's main aims are to describe and to investigate the different election methods. Compared to the participants of this mailing list, Woodall is very reluctant to say that some election method was good/bad or that some property was desirable/undesirable. You wrote (25 Dec 2008): Would you agree that it (and your GMC) is essentially the same thing as the Truncation Resistance criterion on Steve Eppley's MAM page? http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm One of several wordings given there: Truncation Resistance: If no voter votes any insincere strict preferences, alternative x is not in the sincere top cycle, and an alternative in the sincere top cycle is ranked over x by more than half of the voters, then x must not be chosen. And also to Mike Ossipoff's Strategy-Free Criterion? http://www.barnsdle.demon.co.uk/vote/stfree.html Strategy-Free Criterion (SFC): Preliminary definition: A Condorcet winner (CW) is a candidate who, when compared separately to each one of the other candidates, is preferred to that other candidate by more voters than vice-versa. Note that this is about sincere preference, which may sometimes be different than actual voting. SFC: If no one falsifies a preference, and there's a CW, and a majority of all the voters prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win. [end of definition] As Ossipoff's strategy-free criterion refers to situations with a Condorcet winner, I guess you mean Ossipoff's generalized strategy-free criterion instead of his strategy-free criterion: Generalized Strategy-Free Criterion (GSFC): Preliminary definition: The sincere Smith set is the smallest set of candidates such that every candidate in the set is preferred to every candidate outside the set by more voters than vice-versa. There's always a sincere Smith set. When there's a CW, that CW is the sincere Smith set. GSFC: If no one falsifies a preference, and X is a member of the sincere Smith set, and Y is not, and if a majority of all the voters prefer X to Y and vote sincerely, then Y shouldn't win. [end of definition] Suppose candidate B is not in the sincere Smith set. Then, to guarantee that candidate B isn't elected, Eppley's truncation resistance criterion and Ossipoff's generalized strategy-free criterion presume that there is a candidate A, who is in the sincere Smith set and who is strictly preferred to candidate B by a majority of the voters according to the cast preferences. However (as, when no voter votes any insincere strict preference, there cannot be a majority beatpath according to the cast preferences from a candidate B outside the sincere Smith set to a candidate A inside the sincere Smith set), it is --to fulfil the presumption of my criterion-- sufficient that there is a majority beatpath according to the cast preferences from some candidate A of the sincere Smith set to candidate B. [This doesn't necessarily mean that a majority of the voters strictly prefers candidate A to candidate B according to the cast preferences. It could also mean e.g. that, according to the cast preferences, (1) a majority of the voters strictly prefers candidate A to some candidate C outside the sincere Smith set and (2) a majority of the voters strictly prefers this candidate C to candidate B.] As the presumption that a majority of the voters strictly prefers candidate A to candidate B according to the cast preferences is stronger than the presumption that there is a majority beatpath from candidate A to candidate B according to the cast preferences, my criterion is stronger than Eppley's truncation resistance criterion and Ossipoff's generalized strategy-free criterion. *** You wrote (25 Dec 2008): In the interesting link you gave, and elsewhere in the EM archive, I see reference to the Smith//Condorcet[EM] method. What is that method, and what does the [EM] stand for and mean? I gather Condorcet meant 'MinMax'? In the beginning of this mailing list, MinMax(winning votes) was called Condorcet[EM], where Condorcet refers to the MinMax method and [EM] refers to winning votes. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I think IRV isn't a serious alternative 2
Hallo, James Gilmour wrote (24 Dec 2008): IRV has been used for public elections for many decades in several countries. In contrast, despite having been around for about 220 years, the Condorcet voting system has not been used in any public elections anywhere, so far as I am aware. That could perhaps change if a threshold were implemented to exclude the possibility of a weak Condorcet winner AND if a SIMPLE method were agreed to break Condorcet cycles. I don't agree to your proposal to introduce a threshold (of first preferences) to Condorcet to make Condorcet look more like IRV. As I said in my 21 Dec 2007 mail: http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-December/021063.html I don't think that it makes much sense to try to find a Condorcet method that looks as much as possible like IRV or as much as possible like Borda. The best method according to IRV's underlying heuristic will always be IRV; the best method according to the underlying heuristic of the Borda method will always be the Borda method. It makes more sense to propose a Condorcet method that stands on its own legs. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I think IRV isn't a serious alternative 2
Hallo, Terry Bouricius wrote (22 Dec 2008): In a crowded field, a weak CW may be a little-considered candidate that every voter ranks next to last. Markus Schulze wrote (23 Dec 2008): As the Borda score of a CW is always above the average Borda score, it is not possible that the CW is a little-considered candidate that every voter ranks next to last. Juho Laatu wrote (23 Dec 2008): Except that there could be only two candidates. But maybe the CW wouldn't be little-considered then. Even when there are only two candidates, the Borda score of the CW is always above average. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] CDTT criterion compliance desirable?
Dear Chris Benham, you wrote (23 Dec 2008): In one of your recent papers and on the Schulze method Wikipedia page you list Woodall's CDTT criterion as one of the criteria satisfied by the Schulze (Winning Votes) method. What, in your opinion, is supposed to be the positive point of compliance with that criterion? In other words, how would Schulze(WV) be worse if it satisfied all the criteria presently on your list of satisfied criteria except that one? Woodall's CDTT criterion can be rephrased as follows: When (1) the partial individual rankings can be completed in such a manner that candidate A is a Schwartz candidate and candidate B is not a Schwartz candidate and (2) the partial individual rankings cannot be completed in such a manner that candidate B is a Schwartz candidate and candidate A is not a Schwartz candidate, then candidate B must not be elected. This guarantees that not needlessly a candidate is elected who would not have been a Schwartz candidate when not some voters had cast only a partial ranking because of strategic considerations or other reasons. When Woodall's CDTT criterion is violated, then this means that casting partial individual rankings could needlessly lead to the election of a candidate B who is not a Schwartz candidate; needlessly because Woodall's CDTT criterion is compatible with the Smith criterion, independence of clones, monotonicity, reversal symmetry, Pareto, resolvability, etc.. I had already proposed this criterion in 1997. See e.g.: http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-October/001569.html In that mail, this criterion is formulated as follows: X Y means, that a majority of the voters prefers X to Y. There is a majority beat-path from X to Y, means, that X Y or there is a set of candidates C[1], ..., C[n] with X C[1] ... C[n] Y. A method meets the Generalized Majority Criterion (GMC) if and only if: If there is a majority beat-path from A to B, but no majority beat-path from B to A, then B must not be elected. The motivation for this criterion was that I wanted to find a truncation resistance criterion (a) that is compatible with the Smith criterion and with independence of clones and that is otherwise as strong as possible and (b) that is defined on the cast preferences and not on the sincere preferences. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I think IRV isn't a serious alternative 2
Hallo, Terry Bouricius wrote (22 Dec 2008): In a crowded field, a weak CW may be a little-considered candidate that every voter ranks next to last. As the Borda score of a CW is always above the average Borda score, it is not possible that the CW is a little-considered candidate that every voter ranks next to last. Terry Bouricius wrote (22 Dec 2008): The phrase wins by a majority creates the image in the reader's mind of a happy satisfied group of voters (that is more than half of the electors), who would feel gratified by this election outcome. In fact, in a weak CW situation, every single voter could feel the outcome was horrible if the CW is declared elected. Using a phrase like wins by a majority creates the false impression that a majority of voters favor this candidate OVER THE FIELD of other candidates AS A WHOLE, whereas NO SUCH MAJORITY necessarily exist for there to be a Condorcet winner. On the other side, IRV supporters usually use the term majority winner in such a manner that it could refer to every candidate, except for a Condorcet loser. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I Prefer IRV to Condorcet
Hallo, Juho Laatu wrote (28 Nov 2008): I didn't quite get this. When evaluating candidate X minmax just checks if voters would be interested in changing X to some other candidate (in one step), while methods like Schulze and Ranked Pairs may base their evaluation on chains of victories leading to X. Suppose the MinMax score of a set Y of candidates is the strength of the strongest win of a candidate A outside the set Y against a candidate B inside the set Y. Then the Schulze method (but not the Ranked Pairs method) guarantees that the winner is always chosen from the set with minimum MinMax score. See section 9 of my paper: http://m-schulze.webhop.net/schulze1.pdf Because of this reason, the worst pairwise defeat of the Schulze winner is usually very weak. And, in most cases, the Schulze winner is identical to the MinMax winner. This has been confirmed by Norman Petry and Jobst Heitzig (with different models): http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I think IRV isn't a serious alternative
Dear Jonathan Lundell, Greg argued that every IRV election for public office ever held in the United States ... Now you use Florida 2000 as a counterexample. Do you see the problem? Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I think IRV isn't a serious alternative
Dear Jonathan Lundell, I wrote (25 Nov 2008): Greg argued that every IRV election for public office ever held in the United States ... Now you use Florida 2000 as a counterexample. Do you see the problem? You wrote (25 Nov 2008): No, I don't. Which election method was used in Florida 2000? Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I think IRV isn't a serious alternative
Dear Terry Bouricius, you wrote (25 Nov 2008): That observation is incorrect, as there was a come-from behind winner in the November Pierce County IRV election, as well as in the famous Ann Arbor mayoral election in the 70s. Well, Pierce County and Ann Arbor were counterexamples only when the IRV winners were identical to the Condorcet winners in these examples. Because only then these examples show that IRV chose the right winner and plurality voting chose a wrong winner (according to Greg's logic). You wrote (25 Nov 2008): But also, your logic is odd...Quite often plurality rules will happen to elect a Condorcet-winner candidate...but that fact is not compelling since it also frequently elects the Condorcet-loser. I can point to MANY examples where plurality has failed to elect a rightful winner (often electing the Condorcet-loser). In none of the IRV elections has the Condorcet-loser been elected (and cannot be). The point is that IRV does NOT always elect the plurality leader. Greg demands real-life examples with complete ballot data when someone wants to argue that IRV sometimes performs worse than Condorcet voting. Therefore, it is only fair when also Condorcet supporters demand real-life examples with complete ballot data. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I think IRV isn't a serious alternative
Dear Jonathan Lundell, Greg Dennis wrote (25 Nov 2008): I've studied every IRV election for public office ever held in the United States, most of which have their full ranking data publicly available, and every single time IRV elected the Condorcet winner, something I consider to be a good, though not perfect, rule of thumb for determining the right winner. I wrote (25 Nov 2008): If I remember correctly, Abd wrote that, in every IRV election for public office ever held in the USA, the IRV winner was identical to the plurality winner. Doesn't that mean that -- when we apply your logic -- plurality voting always elects the right winner? You wrote (25 Nov 2008): Plurality failed in Florida 2000, so we can conclude that plurality voting always elects the right winner is false. And when you apply Abd's claim to your conclusion (that the statement plurality voting always elects the right winner is false), what can you conclude about Greg's claim? Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why I think IRV isn't a serious alternative
Dear Jonathan Lundell, Greg wrote (25 Nov 2008): While complete ballot data is ideal, I think a convincing case as to how a voting method might perform in a particular election can sometimes be made from polling data. For example, there's good exit polling data for the Senate race in Minnesota that's being recounted, showing that supporters of the Independence party candidate would have preferred Al Franken over Norm Coleman by a 5% margin. That would have given Franken at least another 20,000 votes, way more than the 215 votes he trailed by pre-recount. I think that's a pretty good case that IRV would have selected Franken, regardless of the results of the plurality recount. I wrote (25 Nov 2008): Then what do you say about the opinion polls that said that Bayrou was a clear Condorcet winner in the 2007 French presidential elections (although IRV would have chosen Sarkozy)? You wrote (25 Nov 2008): We don't actually know who IRV would have chosen, since the polling (and the campaign) didn't happen in the context of an IRV election. It's not an unreasonable conjecture that Bayrou would have gotten a larger percentage of first choices (some from Sarkozy and Royal) under IRV. Nor do we know how the smaller party votes would have transferred. So is it feasible to use polling data to show that an election method would have violated some desirable criteria? Or is complete ballot data needed? Or are only IRV supporters allowed to use polling data to show the greatness of IRV, while advocates of other methods have to use complete ballot data? Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] In defense of the Electoral College (was Re: Making a Bad Thing Worse)
Hallo, in my opinion, the electoral college has two advantages to the popular vote. First: It gives more power to the voters in smaller states. [In the USA, the Senate is significantly stronger than the House of Representatives. For example: To appoint a Cabinet member or some other federal officer, the President needs the approval of the Senate, but not of the House of Representatives. Therefore, a deadlock between the President and the Senate would be more harmful than a deadlock between the President and the House of Representatives. Therefore, it makes sense to elect the President in a manner that corresponds more to the election of the Senate than to the election of the House of Representatives.] Second: It makes it possible that the elections are run by the governments of the individual states and don't have to be run by the central government. [Currently, to guarantee that the Equal Protection Clause is fulfilled, it is only necessary to guarantee that all the voters within the same state are treated equally. A popular vote would make it necessary that also all the voters across the USA are treated equally. This would mean that also the regulations on eligibility, absentee ballots, early voting, voting machines, opening hours of the polling stations etc. would have to be harmonized across the USA.] * In section 8 of the current version (3 November 2008) of my paper, I explain how the electoral college should be combined with Condorcet voting: http://m-schulze.webhop.net/schulze1.pdf The basic ideas are: 1. Each voter gets a complete list of all candidates and ranks these candidates in order of preference. The individual voter may give the same preference to more than one candidate and he may keep candidates unranked. 2. For each pair of candidates A and B separately, we determine how many electoral votes Elect[A,B] candidate A would get and how many electoral votes Elect[B,A] candidate B would get when only these two candidates were running. To determine the final winner, we apply a Condorcet method to the matrix Elect[X,Y]. 3. To calculate Elect[A,B] and Elect[B,A], the electoral votes of a state should be distributed to candidate A and candidate B in proportion of the number of voters who strictly prefer candidate A to candidate B and the number of voters who strictly prefer candidate B to candidate A. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] In defense of the Electoral College (was Re: Making a Bad Thing Worse)
Dear Jonathan Lundell, I wrote (7 Nov 2008): Second: It makes it possible that the elections are run by the governments of the individual states and don't have to be run by the central government. [Currently, to guarantee that the Equal Protection Clause is fulfilled, it is only necessary to guarantee that all the voters within the same state are treated equally. A popular vote would make it necessary that also all the voters across the USA are treated equally. This would mean that also the regulations on eligibility, absentee ballots, early voting, voting machines, opening hours of the polling stations etc. would have to be harmonized across the USA.] You wrote (7 Nov 2008): And this would be, on balance, a bad thing because...? First of all: There are many people in the USA who argue that the central government should pass regulations only where absolutely necessary and that the individual states should have as much say as possible. Furthermore: Currently, there are always also many elections on the state level and on the local level parallel to the presidential elections. The states would either have to run the presidential elections separately from the state elections and the local elections (which would increase the costs) or they would have to apply the same regulations for the presidential, the state, and the local elections (which would increase the power of the central government even further). Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
