Re: [EM] Condorcet How? JL

2010-04-16 Thread Juho
On Apr 16, 2010, at 4:42 AM, Kevin Venzke wrote: Ok I see. A3 has no claim over A1 just from the bullet vote. So assume it's A3C2. In that case according to your analysis, the A candidates collectively beat B and C, Only A3 beats the B and C candidates, not all A candidates, no collective

Re: [EM] Condorcet How? JL

2010-04-15 Thread Kevin Venzke
Hi Juho, I don't have much to add except on one point. --- En date de : Mer 14.4.10, Juho juho4...@yahoo.co.uk a écrit : I think I did. For example sincere 49: AB, 49: CD, 1: DB could be one such example. WV elects D, and that could be considered less than perfect performance with

Re: [EM] Condorcet How? JL

2010-04-14 Thread Juho
On Apr 14, 2010, at 7:07 AM, Kevin Venzke wrote: Hi Juho, --- En date de : Mar 13.4.10, Juho juho4...@yahoo.co.uk a écrit : This time the election will be arranged using WV. B supporters note that they can win by not supporting C any more. C supporters do not have the same incentive since

Re: [EM] Condorcet How? JL

2010-04-13 Thread Juho
On Apr 13, 2010, at 4:20 AM, Kevin Venzke wrote: Hi Juho, Ok, I'm writing this as quickly as possible due to a lack of time. --- En date de : Dim 11.4.10, Juho juho4...@yahoo.co.uk a écrit : De: Juho juho4...@yahoo.co.uk Objet: Re: [EM] Condorcet How? À: Election Methods election-meth

Re: [EM] Condorcet How? JL

2010-04-13 Thread Kevin Venzke
Hi Juho, --- En date de : Mar 13.4.10, Juho juho4...@yahoo.co.uk a écrit : This time the election will be arranged using WV. B supporters note that they can win by not supporting C any more. C supporters do not have the same incentive since they are about to win. That's only true

Re: [EM] Condorcet How?

2010-04-12 Thread Kristofer Munsterhjelm
robert bristow-johnson wrote: i haven't been following closely this example scenario (for some reason they don't seem compelling to me), but i did see WV referred to several times and missed the definition. i can imagine it might stand for West Virginia or Working Voter or Winning Votes or

Re: [EM] Condorcet How?

2010-04-12 Thread Juho
On Apr 12, 2010, at 3:57 AM, I wrote: On Apr 11, 2010, at 7:25 PM, Kevin Venzke wrote: 49 A 5 B 19 BC 27 CB It remains bad. I can't see what criticism would remain of this, other than saying that in a real election we might be lucky enough to have some A voters vote AB and accidentally

Re: [EM] Condorcet How? Abd

2010-04-12 Thread Abd ul-Rahman Lomax
At 12:56 PM 4/11/2010, Kevin Venzke wrote: --- En date de : Dim 11.4.10, Abd ul-Rahman Lomax a...@lomaxdesign.com a écrit : In a given election yes, it is easy to miss the mark. But in general, aiming for the median voter is the most reliable. (That is assuming you don't know utilities, which

Re: [EM] Condorcet How?

2010-04-12 Thread Abd ul-Rahman Lomax
At 05:04 AM 4/12/2010, Juho wrote: The end result is also very unstable if B and C are about equally strong since then both could claim to be the leading candidate within the left wing and both recommend truncation (= A may win). Some supporters of both of them may truncate for any of the

Re: [EM] Condorcet How?

2010-04-12 Thread Juho
On Apr 12, 2010, at 10:59 PM, Abd ul-Rahman Lomax wrote: At 05:04 AM 4/12/2010, Juho wrote: The end result is also very unstable if B and C are about equally strong since then both could claim to be the leading candidate within the left wing and both recommend truncation (= A may win).

Re: [EM] Condorcet How?

2010-04-12 Thread Abd ul-Rahman Lomax
At 05:28 PM 4/12/2010, Juho wrote: On Apr 12, 2010, at 10:59 PM, Abd ul-Rahman Lomax wrote: One point should be made clear: any candidate who recommends that voters not vote sincerely is probably shooting himself or herself in the foot. It isn't a winning strategy, generally, it really looks

Re: [EM] Condorcet How? JL

2010-04-12 Thread Kevin Venzke
Hi Juho, Ok, I'm writing this as quickly as possible due to a lack of time. --- En date de : Dim 11.4.10, Juho juho4...@yahoo.co.uk a écrit : De: Juho juho4...@yahoo.co.uk Objet: Re: [EM] Condorcet How? À: Election Methods election-meth...@electorama.com Date: Dimanche 11 avril 2010, 19h57

Re: [EM] Condorcet How? Abd

2010-04-12 Thread Kevin Venzke
Hi Abd, --- En date de : Lun 12.4.10, Abd ul-Rahman Lomax a...@lomaxdesign.com a écrit : De: Abd ul-Rahman Lomax a...@lomaxdesign.com Objet: Re: [EM] Condorcet How? Abd À: Kevin Venzke step...@yahoo.fr, election-meth...@electorama.com Date: Lundi 12 avril 2010, 10h30 At 12:56 PM 4/11/2010

Re: [EM] Condorcet How?

2010-04-11 Thread Juho
I think I already said most things that I had in my mind about the character of winning votes and margins. There are however still plenty of details in the answers and comments below (maybe already too many for many :-). On Apr 10, 2010, at 7:20 PM, Kevin Venzke wrote: Hi Juho, --- En

Re: [EM] Condorcet How? Abd

2010-04-11 Thread Kevin Venzke
Hi Abd, --- En date de : Dim 11.4.10, Abd ul-Rahman Lomax a...@lomaxdesign.com a écrit : In a given election yes, it is easy to miss the mark. But in general, aiming for the median voter is the most reliable. (That is assuming you don't know utilities, which I'm really not sure you

Re: [EM] Condorcet How?

2010-04-11 Thread Juho
On Apr 11, 2010, at 7:25 PM, Kevin Venzke wrote: 49 A 5 B 19 BC 27 CB It remains bad. I can't see what criticism would remain of this, other than saying that in a real election we might be lucky enough to have some A voters vote AB and accidentally give the election away. I'm not quite

Re: [EM] Condorcet How?

2010-04-11 Thread robert bristow-johnson
i haven't been following closely this example scenario (for some reason they don't seem compelling to me), but i did see WV referred to several times and missed the definition. i can imagine it might stand for West Virginia or Working Voter or Winning Votes or i dunno. can someone fill

Re: [EM] Condorcet How?

2010-04-10 Thread Juho
On Apr 10, 2010, at 12:39 AM, Kevin Venzke wrote: Hi Juho, --- En date de : Ven 9.4.10, Juho juho4...@yahoo.co.uk a écrit : I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I believe the possibility of this outcome is a disincentive for a candidate like C to

Re: [EM] Condorcet How?

2010-04-10 Thread Juho
On Apr 10, 2010, at 1:55 AM, Dave Ketchum wrote: On Apr 9, 2010, at 2:37 PM, Juho wrote: On Apr 9, 2010, at 3:03 AM, Kevin Venzke wrote: Hi Juho, --- En date de : Jeu 8.4.10, Juho juho4...@yahoo.co.uk a écrit : I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I

Re: [EM] Condorcet How?

2010-04-10 Thread Kevin Venzke
Hi Juho, --- En date de : Sam 10.4.10, Juho juho4...@yahoo.co.uk a écrit : I don't get why people assume that B voters secretly do like C. If I vote for a left-wing candidate, that doesn't mean I like all left-wing candidates better than all right-wing candidates. I don't want to make

Re: [EM] Condorcet How?

2010-04-10 Thread Abd ul-Rahman Lomax
At 12:20 PM 4/10/2010, Kevin Venzke wrote: To me the only thing that matters is whether there is even one scenario that could realistically arise and which is bad. Two problems: what does realistically mean? and What's bad. Let me propose an answer. If a good model is built of voter

Re: [EM] Condorcet How? Abd

2010-04-10 Thread Kevin Venzke
Hi Abd, --- En date de : Sam 10.4.10, Abd ul-Rahman Lomax a...@lomaxdesign.com a écrit : It remains bad. There is absolutely no way to tell that an outcome is bad unless underlying utilities are studied. This is a classic vote-splitting outcome. That's why I prefer the version that

Re: [EM] Condorcet How? Abd, edit

2010-04-10 Thread Kevin Venzke
--- En date de : Sam 10.4.10, Kevin Venzke step...@yahoo.fr a écrit : I can't study the underlying utilities because I don't have them. If I did I could make them say anything I wanted. I would have to come up with a general rule anyway, or else give up and say all methods are the same.

Re: [EM] Condorcet How? Abd

2010-04-10 Thread Abd ul-Rahman Lomax
At 08:32 PM 4/10/2010, Kevin Venzke wrote: In a given election yes, it is easy to miss the mark. But in general, aiming for the median voter is the most reliable. (That is assuming you don't know utilities, which I'm really not sure you showed how to find.) To see this, you assume utility is

Re: [EM] Condorcet How? Abd, edit

2010-04-10 Thread Abd ul-Rahman Lomax
At 08:37 PM 4/10/2010, Kevin Venzke wrote: --- En date de : Sam 10.4.10, Kevin Venzke step...@yahoo.fr a écrit : I can't study the underlying utilities because I don't have them. If I did I could make them say anything I wanted. I would have to come up with a general rule anyway, or else

Re: [EM] Condorcet How?

2010-04-09 Thread Kristofer Munsterhjelm
Abd ul-Rahman Lomax wrote: At 05:57 AM 4/8/2010, Raph Frank wrote: On Wed, Apr 7, 2010 at 11:25 PM, Dave Ketchum da...@clarityconnect.com wrote: Write-ins permitted (if few write-ins expected, counters may lump all such as if a single candidate - if assumption correct the count verifies

Re: [EM] Condorcet How?

2010-04-09 Thread Juho
On Apr 9, 2010, at 3:03 AM, Kevin Venzke wrote: Hi Juho, --- En date de : Jeu 8.4.10, Juho juho4...@yahoo.co.uk a écrit : I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I believe the possibility of this outcome is a disincentive for a candidate like C to run.

Re: [EM] Condorcet How?

2010-04-09 Thread Kevin Venzke
Hi Juho, --- En date de : Ven 9.4.10, Juho juho4...@yahoo.co.uk a écrit : I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I believe the possibility of this outcome is a disincentive for a candidate like C to run. The story behind these votes

Re: [EM] Condorcet How?

2010-04-09 Thread Dave Ketchum
On Apr 9, 2010, at 2:37 PM, Juho wrote: On Apr 9, 2010, at 3:03 AM, Kevin Venzke wrote: Hi Juho, --- En date de : Jeu 8.4.10, Juho juho4...@yahoo.co.uk a écrit : I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I believe the possibility of this outcome is a

Re: [EM] Condorcet How?

2010-04-09 Thread Abd ul-Rahman Lomax
At 03:55 AM 4/9/2010, Kristofer Munsterhjelm wrote: I'll note here that Bucklin is not cloneproof, and in some cases it can reward cloning. See http://www.mail-archive.com/election-methods-electorama@electorama.com/msg02705.html . Thus it might pay for voters of some opinion to add lots

Re: [EM] Condorcet How?

2010-04-08 Thread Raph Frank
On Wed, Apr 7, 2010 at 11:25 PM, Dave Ketchum da...@clarityconnect.com wrote: Write-ins permitted (if few write-ins expected, counters may lump all such as if a single candidate - if assumption correct the count verifies it; if incorrect, must recount). How do you handle write-ins. Are

Re: [EM] Condorcet How?

2010-04-08 Thread Dave Ketchum
On Apr 8, 2010, at 5:57 AM, Raph Frank wrote: On Wed, Apr 7, 2010 at 11:25 PM, Dave Ketchum da...@clarityconnect.com wrote: Write-ins permitted (if few write-ins expected, counters may lump all such as if a single candidate - if assumption correct the count verifies it; if incorrect, must

Re: [EM] Condorcet How?

2010-04-08 Thread Juho
On Apr 8, 2010, at 3:29 AM, robert bristow-johnson wrote: On Apr 7, 2010, at 6:25 PM, Dave Ketchum wrote: This is some thought about keeping it simple, yet doable. I will lean toward Ranked Pairs with margins, not sure what with margins does. There are different approaches to determining

Re: [EM] Condorcet How?

2010-04-08 Thread Dave Ketchum
On Apr 7, 2010, at 8:29 PM, robert bristow-johnson wrote: On Apr 7, 2010, at 6:25 PM, Dave Ketchum wrote: This is some thought about keeping it simple, yet doable. I will lean toward Ranked Pairs with margins, not sure what with margins does. i'll read below... vs comparing per winning

Re: [EM] Condorcet How?

2010-04-08 Thread Abd ul-Rahman Lomax
At 05:57 AM 4/8/2010, Raph Frank wrote: On Wed, Apr 7, 2010 at 11:25 PM, Dave Ketchum da...@clarityconnect.com wrote: Write-ins permitted (if few write-ins expected, counters may lump all such as if a single candidate - if assumption correct the count verifies it; if incorrect, must

Re: [EM] Condorcet How?

2010-04-08 Thread robert bristow-johnson
On Apr 8, 2010, at 2:02 PM, Dave Ketchum wrote: On Apr 7, 2010, at 8:29 PM, robert bristow-johnson wrote: On Apr 7, 2010, at 6:25 PM, Dave Ketchum wrote: This is some thought about keeping it simple, yet doable. I will lean toward Ranked Pairs with margins, not sure what with margins

Re: [EM] Condorcet How?

2010-04-08 Thread Juho
On Apr 8, 2010, at 10:30 PM, robert bristow-johnson wrote: i do not know why anyone would back the winning votes metric for beat strength. I guess the main driver has been that winning votes is more tolerant than margins against strategic burying in some scenarios. (There are however

Re: [EM] Condorcet How?

2010-04-08 Thread Kevin Venzke
Hi, --- En date de : Jeu 8.4.10, robert bristow-johnson r...@audioimagination.com a écrit : Juho just explained it, so now i know (earlier i had wondered if margins was a normalized or percentage beat strength).  i've always thought that the Tideman RP was *only* framed in terms of margins. 

Re: [EM] Condorcet How?

2010-04-08 Thread Juho
On Apr 8, 2010, at 11:00 PM, Kevin Venzke wrote: I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I believe the possibility of this outcome is a disincentive for a candidate like C to run. The story behind these votes seems to be that C is ideologically close

Re: [EM] Condorcet How?

2010-04-08 Thread Dave Ketchum
Being the you that Raph was addressing, I offer what I was proposing. As the subject indicates, the topic is Condorcet voting. Also, listing a candidate who is on the ballot, and could be voted for as such, should be counted as a misdeed - such could be voted for in the normal manner

Re: [EM] Condorcet How?

2010-04-08 Thread Kevin Venzke
Hi Juho, --- En date de : Jeu 8.4.10, Juho juho4...@yahoo.co.uk a écrit : I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I believe the possibility of this outcome is a disincentive for a candidate like C to run. The story behind these votes seems

Re: [EM] Condorcet How?

2010-04-08 Thread Dave Ketchum
On Apr 8, 2010, at 8:03 PM, Kevin Venzke wrote: Hi Juho, --- En date de : Jeu 8.4.10, Juho juho4...@yahoo.co.uk a écrit : I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I believe the possibility of this outcome is a disincentive for a candidate like C to run.

Re: [EM] Condorcet How?

2010-04-08 Thread Kevin Venzke
Hi Dave, --- En date de : Jeu 8.4.10, Dave Ketchum da...@clarityconnect.com a écrit : --- En date de : Jeu 8.4.10, Juho juho4...@yahoo.co.uk a écrit : I more or less despise the election of A in this scenario: 49 A 24 B 27 CB I believe the possibility of this outcome is a

[EM] Condorcet How?

2010-04-07 Thread Dave Ketchum
This is some thought about keeping it simple, yet doable. I will lean toward Ranked Pairs with margins, but amending toward other types of Condorcet should be doable. Voting: Voter can rank one or more candidates. Equal ranking permitted. Counters care only which of any pair of

Re: [EM] Condorcet How?

2010-04-07 Thread Markus Schulze
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

Re: [EM] Condorcet How?

2010-04-07 Thread Dave Ketchum
Thanks - there are so many Condorcet methods that I chose to describe what I see as a better one, while giving up on getting understood via naming. On Apr 7, 2010, at 6:50 PM, Markus Schulze wrote: Hallo, Dave Ketchum (7 April 2010): For RP I see deleting the smallest margins from the

Re: [EM] Condorcet How?

2010-04-07 Thread robert bristow-johnson
On Apr 7, 2010, at 6:25 PM, Dave Ketchum wrote: This is some thought about keeping it simple, yet doable. I will lean toward Ranked Pairs with margins, not sure what with margins does. i'll read below... but amending toward other types of Condorcet should be doable. Voting: Voter can

Re: [EM] Condorcet How?

2010-03-24 Thread Kristofer Munsterhjelm
robert bristow-johnson wrote: On Mar 23, 2010, at 9:01 AM, Terry Bouricius wrote: [...] Since the bill, as passed, actually used a top-two contingent system (only the top two initial candidates would advance), the tally would be relatively easy. so the regional venues would report

Re: [EM] Condorcet How?

2010-03-24 Thread robert bristow-johnson
On Mar 24, 2010, at 4:42 AM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: On Mar 23, 2010, at 9:01 AM, Terry Bouricius wrote: [...] Since the bill, as passed, actually used a top-two contingent system (only the top two initial candidates would advance), the tally would

Re: [EM] Condorcet How?

2010-03-24 Thread Raph Frank
On Wed, Mar 24, 2010 at 4:54 AM, robert bristow-johnson r...@audioimagination.com wrote: is that why IRV (under whatever name) was first plugged for government elections in multiparty environments? It seems that what Fairvote want is PR-STV. The hope is presumably, that if they can get voters

Re: [EM] Condorcet How?

2010-03-24 Thread Terry Bouricius
- Original Message - From: robert bristow-johnson r...@audioimagination.com To: election-methods List election-meth...@electorama.com Sent: Wednesday, March 24, 2010 12:54 AM Subject: Re: [EM] Condorcet How? On Mar 23, 2010, at 9:01 AM, Terry Bouricius wrote: Robert, Two corrections... always

Re: [EM] Condorcet How?

2010-03-24 Thread James Gilmour
robert bristow-johnson wrote: It seems that what Fairvote want is PR-STV. The hope is presumably, that if they can get voters used to ranked ballots and eliminations with IRV, they can then argue that moving onto PR-STV is just changing to the multiseat version of IRV. Surely a major

Re: [EM] Condorcet How?

2010-03-23 Thread Markus Schulze
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

Re: [EM] Condorcet How?

2010-03-23 Thread Raph Frank
On Tue, Mar 23, 2010 at 2:46 AM, robert bristow-johnson r...@audioimagination.com wrote: and, i'm not sure who, but someone introduced a measure in the state legislature to elected the governor by IRV (there is a perennial Prog candidate that doesn't get any traction because Vermont is not all

Re: [EM] Condorcet How?

2010-03-23 Thread Terry Bouricius
: Monday, March 22, 2010 10:46 PM Subject: Re: [EM] Condorcet How? On Mar 22, 2010, at 6:06 PM, Markus Schulze wrote: Dear Robert, are you the questioner at 00:42:00 -- 00:44:25? it could be. i dunno if i wanna load the video again and figure that out. i was pointing out that the purpose we

Re: [EM] Condorcet How?

2010-03-23 Thread robert bristow-johnson
On Mar 23, 2010, at 9:01 AM, Terry Bouricius wrote: Robert, Two corrections... always happy to correct my misconceptions. Bills to use IRV for certain statewide elections have been introduced in Vermont in every session since 1998, and it was passed by the Vermont House and Senate a few

Re: [EM] Condorcet How?

2010-03-22 Thread Markus Schulze
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

Re: [EM] Condorcet How?

2010-03-22 Thread robert bristow-johnson
On Mar 22, 2010, at 6:17 AM, Markus Schulze wrote: 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've seen them. if i had reacted

Re: [EM] Condorcet How?

2010-03-22 Thread Markus Schulze
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?

2010-03-22 Thread robert bristow-johnson
On Mar 22, 2010, at 6:06 PM, Markus Schulze wrote: Dear Robert, are you the questioner at 00:42:00 -- 00:44:25? it could be. i dunno if i wanna load the video again and figure that out. i was pointing out that the purpose we adopted IRV in the first place was to relieve the split

Re: [EM] Condorcet How?

2010-03-21 Thread Kristofer Munsterhjelm
Markus Schulze wrote: Hallo, of course, I am leaning towards the Schulze method. This method is by far the most wide-spread Condorcet method. It is used by about 50 organizations with about 100,000 eligible members in total. It has also become very popular among scientists:

Re: [EM] Condorcet How?

2010-03-21 Thread Markus Schulze
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

Re: [EM] Condorcet How?

2010-03-21 Thread robert bristow-johnson
sorry if this is too long On Mar 21, 2010, at 7:45 AM, Markus Schulze wrote: 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

Re: [EM] Condorcet How?

2010-03-21 Thread robert bristow-johnson
On Mar 21, 2010, at 1:30 AM, robert bristow-johnson wrote: On Mar 20, 2010, at 5:04 PM, Markus Schulze wrote: Here are the proposed statutory rules: http://m-schulze.webhop.net/propstat.pdf __ Suppose d[V,W] is the number of valid ballots on which candidate V is strictly

[EM] Condorcet How?

2010-03-20 Thread Dave Ketchum
This is some thought about keeping it simple, yet doable. I will lean toward Ranked Pairs with margins, but amending toward other types of Condorcet should be doable. Voting: Voter can rank one or more candidates. Equal ranking permitted. Counters care only which of any pair of

Re: [EM] Condorcet How?

2010-03-20 Thread robert bristow-johnson
On Mar 20, 2010, at 12:08 PM, Dave Ketchum wrote: Counting: Besides the N*N matrix, i dunno why the common layout of the NxN matrix is popularly used. it should be like a triangle, e.g. for the 2009 Burlington election: M 4064 K 3477 M 4597 K 4313 W 3664 W 4061

Re: [EM] Condorcet How?

2010-03-20 Thread Kristofer Munsterhjelm
robert bristow-johnson wrote: On Mar 20, 2010, at 12:08 PM, Dave Ketchum wrote: Counting: Besides the N*N matrix, i dunno why the common layout of the NxN matrix is popularly used. it should be like a triangle, e.g. for the 2009 Burlington election: [snip] It's used to handle equal

Re: [EM] Condorcet How?

2010-03-20 Thread robert bristow-johnson
On Mar 20, 2010, at 5:04 PM, Markus Schulze wrote: Here are the proposed statutory rules: http://m-schulze.webhop.net/propstat.pdf thanks Markus. this is nice. and more concise than the Wikipedia procedure. __ Suppose d[V,W] is the number of valid ballots on which