Maybe there is some potential in doing the IRV style "never considering all the given opinions" in some better way. I don't have any opinion yet on if this is that case but maybe something can be found.
Juho Laatu On Oct 17, 2006, at 10:47 , Dave Ketchum wrote: > Remember that it better work with multiple polling places, such as for > governor. Condorcet arrays have no problem with this, for the > arrays are > simply summed. > > Remember that Condorcet and IRV promise, usually, to agree as to > winner. > There are two exceptions: > When IRV does not completely scan ballots, what was missed could > matter, and thus change the winner. > Condorcet cycles have no equivalent in IRV. > > Thus there should not be a third variety of counting, unless you > can sell > such as worth the headaches. > > DWK > > On Sun, 15 Oct 2006 19:31:42 -0700 (PDT) [EMAIL PROTECTED] wrote: >> Dave Ketchum wrote: >> >>> DO NOT DO any switching such as you describe below. >>> Even if it is far down in a voter's ranking, it is what this >>> voter said about this pair. If this pair is far down in the >>> list, there are many candidates this voter has ranked as >>> better. >> >> >> You're right, flipping the votes shouldn't be an option, because >> you could >> make your preferred candidate do worse simply by voting (since >> you'd have >> one more vote to flip). I therefore give you IFNOP (Ignore Fewest >> Number >> of Preferences) Method. >> >> (Note: someone may have already come up with this, I just gave it >> a name >> for my own convenience.) >> >> This is a work in progress, and it's definitely more complicated >> than it >> needs to be. In addition, I know I've made some (perhaps many) >> mistakes, >> but I'm coming off a caffeine/sugar high and I'm a bit tired to re- >> read >> everything, so I will put this out there for comment. Feel free to >> rip it >> apart -- I'm really just trying to get a feel for it, to see if >> something >> interesting might come out of it. >> >> BTW, if the formatting turns all weird, it's because of the annoying >> webmail program I'm using. >> >> IFNOP method >> >> 1. Each voter ranks as many candidates as desired. >> >> 2. If there is a Condorcet order (or a Condorcet winner in a >> single-winner >> race), congratulations! No more work is necessary. >> >> 3. If there isn't a strict preference order (one or more circular >> ties), >> create an NxN matrix, where N is the number of candidates. >> (Actually, only >> half of the boxes would be needed -- the final result will be shaped >> somewhat like a triangle.) >> >> 4. For every pair that is part of a circular tie, place the number >> and the >> preference in the corresponding box (ties=0). For example, if 50 >> people >> put A in the 7th position and B in the 12th position on their >> ballot, then >> put (50 A>B) in box (7,12). Preferences from other voters can be >> in the >> same box (B>C could be in (7,12)), and the same preference (A>B in >> this >> example) can be in multiple boxes. >> >> 5. If a person ranks two or more candidates the same, they are >> assumed to >> be in the closest available ranking to any candidate they are >> compared to. >> For example, in the order A>B>C=D>E, C and D are both ranked 4th when >> compared with E (you would have C>E and D>E in the box (4,5), and >> both are >> ranked 3rd when compared with A and B (A>C, A>D in box (1,3), and >> B>C, B>D >> in box (2,3) respectively). For this ballot, there is no score >> added for >> C>D or D>C. >> >> 6. Ignore preferences one group at a time, starting with the >> lowest-ranked >> ballots and working your way up. With this restriction, start with >> the >> ballots closest together and work your way apart. The order is >> determined >> when the circular tie is broken. (Basically, try ignoring one >> group, and >> if it doesn't break the tie stop ignoring it and try the next >> group. If >> none of the groups in the box are sufficient to break the tie, add >> the >> next box and try again.) >> >> Here is how it would work out. Let's say you have six candidates, >> with 1 >> as the top candidate and 6 as the bottom candidate. You would >> process the >> boxes in the following order: >> >> (5,6) >> (4,5) >> (4,6) >> (3,4) >> (3,5) >> (3,6) >> (2,3)... >> >> More generally, let's say you have a total of X candidates. >> Setting 1 as >> the top candidate and X as the bottom candidate, you would check >> the boxes >> in the following order: >> >> (X-1,X) >> (X-2,X-1) >> (X-2,X) >> (X-3,X-2) >> (X-3,X-1) >> (X-3,X) >> (X-4,X-3) >> ... >> (1,X-1) >> (1,X) >> >> Beginning with the first box on the list ((X-1,X) in the example >> above), >> try ignoring each group of preferences inside and see if the >> circular tie >> is broken. If there is a unique way to resolve a particular tie, >> then this >> determines the final order. >> >> If there are several ways to resolve a tie (say if both A>B and >> B>C were >> in the current box, and ignoring either one broke the circular tie >> A>B>C>A) pick the order that requires the smallest number and >> lowest level >> "ignores" necessary. (There are multiple ways to do this, but it's >> not >> really necessary for this brief description.) If it's a true tie, >> pick one >> order randomly. >> >> Continue up the list until all the ties are resolved. If it's a >> single-winner race, you can stop after the top circular tie is >> broken. >> >> The thought behind this method is, I prefer (by definition) my >> highest-ranked candidates more than my lowest-ranked candidates. >> If there >> is a preference that needs to be removed to break a tie, I prefer >> it to be >> at the bottom of my list -- better to ignore the difference between >> candidate #99 and #100 than between candidates #1 and #2, even >> though both >> are a single position apart. In addition, it is more important to >> keep >> preferences that are far apart over those that are close together >> -- I can >> tolerate a change between #1 and #2 more than I can a change >> between #1 >> and #100. >> >> The method above *does* put more weight between #1 and #2 than >> between #2 >> and #100, but (especially in a single-winner race), maximizing my >> highest-rated candidate is the most important to me -- plus, it's >> impossible to pick a cutoff or scaling function that would work >> for every >> voter in every election. >> >> Of course, this method fails IIA, and is open to compromising. On the >> other hand, bullet voting would be ineffective -- the top >> candidate vs. >> every other one in the (1,2) box, rather than with a wider order >> -- and >> burying would be most effective where it is least useful, in a >> race with >> two strong candidates and a majority of weaker candidates. >> >> To see why burying wouldn't be as effective as with some systems, >> assume >> you have three strong candidates A,B,C. If you prefer A, and you >> *think* >> C is stronger than B, you can rank A...B,C. However, the last two >> ranks >> are the very first ones we check for "ignorable" orders. If there >> is a >> three-way tie between A>B>C>A, and if ignoring B>C breaks the tie, >> then C >> would have to be the winner. If you gave both B and C the same >> ranking at >> the bottom of the list, they are more likely to be ignored because of >> section 5 above. The best strategy would be to bury the biggest >> threat and >> raise the second-biggest threat as high as possible, to push their >> rank >> comparison later in the list. This is more difficult than simply >> burying >> all threats. >> >> As I mentioned above, this is more brainstorming than anything -- >> I'm just >> interested if any useful method might come out of it. Comments are >> welcome, of course. I apologize for any confusing sections or >> errors, and >> I *especially* apologize if someone else has already came up with it >> (which happens with depressing frequency). >> >> Michael Rouse >> [EMAIL PROTECTED] > -- > [EMAIL PROTECTED] people.clarityconnect.com/webpages3/ > davek > Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 > 607-687-5026 > Do to no one what you would not want done to you. > If you want peace, work for justice. > > > ---- > election-methods mailing list - see http://electorama.com/em for > list info Send instant messages to your online friends http://uk.messenger.yahoo.com ---- election-methods mailing list - see http://electorama.com/em for list info
