I do not like this system and believe it is improper to call it "Condorcet". It seems to have all the same flaws as IRV - hiding the lower choice votes of voters, except if the voter voted for some of the less popular candidates. Thus, I can see there may be lots of cases when it eliminates the Condorcet winner.
> Date: Fri, 1 Jul 2011 22:20:52 -0700 (PDT) > From: Ross Hyman <[email protected]> > To: [email protected] > Subject: [EM] Condorcet divisor method proportional representation > Message-ID: > <[email protected]> > Content-Type: text/plain; charset="utf-8" > > > > A Condorcet divisor method proportional > representation procedure is presented that is a variant of Nicolaus Tideman?s > Comparison > of Pairs of Outcomes by Single Transferable Vote (CPO-STV) and Shultz STV but > requires the determination of fewer candidate set comparisons than either.? > The method will produce the same result as a party > list election that uses the same divisor method provided that each voter votes > their party?s list.? The procedure is a Condorcet variant of the procedure > presented in the February 2011 issue of Voting Matters. > > > ? > > For an N-seat > election, one primary election electing N > candidates must be performed for each set of N + 1 candidates.? For > example, for a two-seat election involving candidates A,B,C and D, primary > elections for the candidate sets ABC, ABD, ACD and BCD are held. > > ? > > For each of these primary elections, the > winning set and its priority over loosing sets is determined by the following > procedure (the method is presented for the d?Hondt divisor method but is > easily > generalized to other divisor methods.): > > > Step 1. Every candidate in the N+1 primary sub-election candidate set > is hopeful and every candidate not in that set is excluded.? The seat value > of every ballot is set to zero. > > Step 2. The priority, PC, > for each hopeful candidate C that is the topmost hopeful candidate on at least > one ballot is determined from PC > = VC/(SC+1) where VC > is the total number of ballots where C is the topmost hopeful candidate and > SC is the sum of the seat > values of ballots where C is the topmost hopeful candidate.? The candidate > with the highest priority is > elected. If the total number of elected candidates is N, the count is ended > and > the N elected candidates are declared > the winning candidate set of the primary with its priority over losing sets > equal > to the priority of the Nth elected candidate.? Otherwise, if candidate C is > elected, the > seat value for each ballot that contributed to electing C is increased to > (SC+1)/VC. Repeat Step 2 until N candidates are elected. > > ? > > Each loser set from a primary contains the > candidate from the primary candidate set that is not in the winning set plus > N-1 additional candidates from the winning > set. For a two-seat election in which AB is the winning set of the primary > candidate set ABC, AC and BC are the loser sets.? > > ? > > Only the priority of the winning set for > each primary is calculated.? The method > determines the priorities of fewer relations than Shultz STV but still elects > the Condorcet winner candidate set if there is one since the Condorcet winner > candidate > set cannot be a losing set.? > > ? > > Once every primary election has been held, winning > set > losing set relations are then elected from highest priority to lowest. > However, if electing a relation would violate transitivity then that relation > is > excluded instead of elected.? In > practice, only loosing sets that are the winning set of at least one primary > election need be considered.? When every > relation has been elected or excluded, the highest ranked candidate set is > declared the elected candidate set.? An > example with a Condorcet cycle is the two-seat election presented in Election > 1. > > ? > > Election 1 > > 7 A B C D > > 6 B C D A > > 5 C D A B > > 4 D A B C > > ? > > Primary ABC > > 11 ABC > > 6 BCA > > 5 CAB > > AB > AC and AB > BC. Priority: 8.5 > > ? > > Primary ABD > > 7 ABD > > 6 BDA > > 9 DAB > > AD > AB and AD > BD.? Priority: 8 > > ? > > Primary ACD > > 7 ACD > > 11 CDA > > 4 DAC > > CD > AC and CD > AD. Priority: 7.5 > > ? > > Primary BCD > > 13 B C D > > 5 C D B > > 4 D B C > > BC > BD and BC > CD. Priority: 9 > > ? > > The winning sets are AB, AD, CD and > BC.? Since a candidate set must be a > winning set in at least one primary to win the election, only relations > involving winning sets need be considered.? > The relevant candidate relations are > > ? > > BC > CD. Priority: 9 > > AB > BC. Priority: 8.5 > > AD > AB.? > Priority: 8 > > CD > AD. Priority: 7.5 > > AB > CD.? > Priority: 6.5 > > ? > > Transitivity can be preserved by electing > relations in priority order that preserve transitivity and excluding those > that > do not.? When the three highest priority > relations are elected, they produce the transitive candidate set order AD > > AB > BC > CD.? The next highest > priority relation CD > AD is excluded since the higher priority relations have > determined that AD > CD.? According to this procedure, candidates A and > D are elected. > -Ross Hyman > -- Kathy Dopp http://electionmathematics.org Town of Colonie, NY 12304 "One of the best ways to keep any conversation civil is to support the discussion with true facts." Fundamentals of Verifiable Elections http://kathydopp.com/wordpress/?p=174 View some of my research on my SSRN Author page: http://ssrn.com/author=1451051 ---- Election-Methods mailing list - see http://electorama.com/em for list info
