[EM] Condorcet divisor method proportional representation

[Kathy Dopp]

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 <rahyman at sbcglobal.net>
> To: election-methods at lists.electorama.com
> Subject: [EM] Condorcet divisor method proportional representation
> Message-ID:
>        <1309584052.63357.YahooMailClassic at web83607.mail.sp1.yahoo.com>
> 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