On 10 May 2005 at 19:56 UTC-0700, Abd ulRahman Lomax wrote: >At 01:25 PM 5/10/2005, Araucaria Araucana wrote: >>It appears that you are reading my comments out of context, and are >>also misunderstand the intent of a wiki -- it is a *collaborative* >>site. See these links: [deleted] > > Perhaps it doesn't matter, but I operate several wikis, and I've > contributed to Wikipedia (though I'm certainly not a wiki expert). I > don't know why Mr. Araucana got the idea that I didn't understand > this basic concept.
Please, call me Q (see sig). And please don't take offense [there's a bit too much of it on the list at present!]. I've heard it said that written language is only 7% effective -- much more is conveyed in intonation and body language. Email has a long time-lag, so to avoid too many separate messages, I tend to err on the side of too much information. You may choose to interpret this as being patronizing, but it isn't meant to be. I do apologize for underestimating your abilities, but it was your first posting, and I didn't have anything else to go on. My default assumption is that posters to this list usually are stronger at theoretical math than web skills. > So the least-approved candidate ... is the winner? Explain this > thing to me.... Okay, here goes: First, a Condorcet method is a procedure for holding a set of one-on-one elections simultaneously, using ranked ballots. Some on this list have proposed calling it Instant Round Robin. http://wiki.electorama.com/wiki/Condorcet_method Ranked ballots (equal ranking allowed) are tabulated into a pairwise matrix (call it M). A vote in location M(i,j) means a vote for candidate i against candidate j. So if the total M(i,j) is greater than M(j,i), candidate X(i) defeats candidate X(j). http://wiki.electorama.com/wiki/Condorcet_method#Counting_with_matrices Because the final total can sometimes be cyclic (i.e., no candidate is undefeated), we are interested in finding a satisfactory completion method. There are several strong methods (e.g. Ranked Pairs, CSSD, River) that use ranked ballot information alone, but they may be too complex for an initial reform proposal. Therefore, some have proposed combining Condorcet with Approval Voting. Here's some background on Approval: http://wiki.electorama.com/wiki/Approval_voting To combine approval with a ranked ballot, we use an approval cutoff: http://wiki.electorama.com/wiki/Approval_Cutoff When both pairwise and approval information are available, it is possible to reorder the pairwise array in descending order of approval. Here is an example of an election with approval cutoff ballots, before and after reordering: http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting#Example I'm excerpting the ballots and reordered pairwise matrix from that example. A winning off-diagonal score is 461 and greater. 98: Abby > Cora > Erin >> Dave > Brad 64: Brad > Abby > Erin >> Cora > Dave 12: Brad > Abby > Erin >> Dave > Cora 98: Brad > Erin > Abby >> Cora > Dave 13: Brad > Erin > Abby >> Dave > Cora 125: Brad > Erin >> Dave > Abby > Cora 124: Cora > Abby > Erin >> Dave > Brad 76: Cora > Erin > Abby >> Dave > Brad 21: Dave > Abby >> Brad > Erin > Cora 30: Dave >> Brad > Abby > Erin > Cora 98: Dave > Brad > Erin >> Cora > Abby 139: Dave > Cora > Abby >> Brad > Erin 23: Dave > Cora >> Brad > Abby > Erin +-----------------------------------------------+ | | against | | |----------------------------------| | | Erin | Abby | Cora | Brad | Dave | |------------+------+------+------+------+------| | | Erin | 708 | 410 | 461 | 298 | 610 | | |------+------+------+------+------+------| | | Abby | 511 | 645 | 461 | 458 | 485 | | |------+------+------+------+------+------| | for | Cora | 460 | 460 | 460 | 460 | 460 | | |------+------+------+------+------+------| | | Brad | 623 | 463 | 461 | 410 | 312 | | |------+------+------+------+------+------| | | Dave | 311 | 436 | 461 | 609 | 311 | +-----------------------------------------------+ There are no undefeated candidates ==> there is no Condorcet winner. So, using DMC (aka Ranked Approval Voting), let us begin by ignoring the row and column of the least-approved candidate, Dave. We then see that Brad defeats all remaining candidates. We're done -- Brad wins. As it happens, there are several candidates who are undefeated by other candidates with higher approval. Erin, Abby and Brad all qualify. In DMC, we call this set the definite majority set. Among the definite majority set, Brad defeats all others. *** It is a corollary of the definite majority set's construction that *** the winner is the least-approved member of that set. Compare with this idea: http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes See also the various criteria that have been proposed for voting methods. IMO, DMC/RAV may not be the best possible single-winner election method, but it has enough strong features that it will discourage insincere voting and give much more satisfactory results than single-vote or IRV. > Actually, even stupid and ignorant comments can be very useful. Yes, Socratic method, etc. But it's kind of a flimsy excuse for not doing your homework. ;-) > > I do have comments to make, lots of them. But not yet. > www.beyondpolitics.org > I now see you have your own political agenda. I would be interested to see, when you are ready, how your Free Association - Direct Proxy ideas compare with other similar proposals such as Direct Democracy or Candidate Proxy. BTW, does ul-Rahman means "the merciful and compasssionate one"? Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = "monkey/knot" -- see http://www.ship.edu/~cgboeree/alphabet.html ---- Election-methods mailing list - see http://electorama.com/em for list info
