EM vote on SW methods: summary of votes to date
Steve Eppley
seppley at alumni.caltech.edu
Thu Jul 25 13:04:11 PDT 1996
Sorry it's taken me so long to finish this message.
Message Contents:
1. Raw ballots (plus some annotations)
2. Compact ballot summary
3. Pairwise tallies (Condorcet, Smith//Condorcet, and Regular-Champion)
4. Tally by Instant Runoff
Note: Mike wrote that Smith//Condorcet is winning by all the methods
he used to tally the votes cast so far, and that Instant Runoff is
in second place. But by my calculations, Condorcet is in second,
since it's losing only one pairing (to Smith//Condorcet), its largest
loss is only 3 votes against (in the 1 to 3 loss to Smith//Condorcet),
and it's the last one eliminated by Instant Runoff. Additionally,
if Smith//Condorcet is eliminated from all the ballots Condorcet
would win all pairings and would win by Instant Runoff.
* *
Here are the ballots received so far, which Mike found and forwarded
to me. It's not too late to vote or to change your vote, if you want;
just send your ballot to the EM list.
I haven't included the comments provided in the ballot messages,
but I've included the dates of the messages. (Thanks, Mike, for
including the dates.) The comments will also be included in the
draft report, but at the moment I just want to make sure there are
no mistakes in the votes. Please speak up if your vote is missing or
listed incorrectly.
Kevin Hornbuckle, 7-8-96 22:12:01
1 plain Condorcet, Smith//Condorcet
2 Approval
3 Smith//Random
Rob Lanphier, 7-7-96 00:54:23 -0700 (PDT)
1 Smith//Condorcet
2 Condorcet
3 Regular-Champion (aka Copeland with a Plurality tie-breaker)
4 Smith//Condorcet using rated, not ranked, ballots
5 Condorcet using rated, not ranked, ballots
6 MPV (aka Instant Runoff, aka Hare)
7 Double Complement (a modification of Runoff)
8 Approval
9 ------NONE OF THE BELOW--------
10 Winner take all (aka Plurality)
11 Smith//Random
[Rob didn't use a number for NOTB. I inserted the 9 and incremented
the numbers he gave for the two methods below it. This will make it
more straightforward to tally the NOTB "choice." --Steve]
Hugh R. Tobin, 7-7-96 00:21:19 -0700 (PDT)
1 Smith//Condorcet with a minor modification of the tiebreak count
(proposed in paragraph 10, below--if my voting for this modified
form cannot, under the counting system being used, impair the
prospects of my second place choice over others (if that is not
the case, disregard this vote).
2 Smith//Condorcet, as defined by Mr. Ossipoff
3 Smith//Random
4 Instant Runoff
5 plain Condorcet
6 Regular-Champion
7 Double Complement
8 Approval
9 all other methods (which, if it matters, I mean to cast 1/2 vote
for and against each in each pairwise contest between two of
those methods)
[I will call Hugh's first choice "Smith//Condorcet(Tobin 1/2)" for
the time-being. Maybe Hugh or someone else will come up with a
better name to use in our report. --Steve]
Donald Eric Davison, 7-4-96 11:01:33 -0700 (PDT)
1 Instant Runoff
DEMOREP1 at aol.com, 7-8-96 22:11:04 -0700 (PDT)
1 A mixture of rank voting, majority yes (approval), Condorcet
for the majority yes candidates, limited approval tie breaker
(limited combined choices).
See---- Subj: Single Person Elections 6/27/96
Date: Fri, Jun 28, 1996 12:20 AM EDT
2 Approval with rankings (dropping the last ranked choice- such as
having 5 candidates- only top 4 choices of a voter would count-
highest majority candidate wins)
3 Instant Run-Off (a.k.a. MPV)
[It looks to me like Demorep's first choice strongly resembles one of
the two "Condorcet & NOTB" variations, the one in which any candidate
beaten pairwise by NOTB is eliminated, since the NOTB "choice" acts
as the voter's dividing line between approval and disapproval.
Perhaps Demorep would wish to amend his/her ballot to include that
variation? Also, Demorep's truncated ballot omits some of the
methods like plain Condorcet and Smith//Condorcet which seem to be
strong contenders based on the votes received so far. As posted,
this ballot will be treated as ranking those equally last, along with
the other omitted methods. Since Demorep's first choice resembles
Condorcet, I wonder if this truncation was inadvertent, and perhaps
Demorep would wish to amend his/her ballot to explicitly rank those
methods. --Steve]
Steve Eppley, 6-2-96 04:40:44 -0700 (PDT)
1 Smith//Condorcet
2 Smith//Condorcet using rated, not ranked, ballots
3 plain Condorcet
4 plain Condorcet using rated, not ranked, ballots
5 ------None Of The Below--------
6 Instant Runoff
7 Approval
8 all the methods omitted from my ballot
9 Runoff
10 Double Complement
11 Plurality
[I've changed the bottom of my ballot a bit, to clarify my rankings
on choices I disapprove (indicated by my ranking them less preferred
than NOTB), by elevating Instant Runoff & Approval above a few, and
downgrading and distinguishing between the vote-for-only-one methods.
I've also used a ballot feature no one else used: ranking some methods
explicitly less preferred than the unranked.]
Mike Ossipoff, 5-26-96 23:41:56 -0700 (PDT)
1 plain Condorcet
2 Smith//Condorcet
3 Approval
4 Smith//Random
[This is Mike's latest ballot. He told me he couldn't locate his old
ballots in his EM folder and that this new one will count. I've found
his original ballot, and the date shown above is for the old ballot
since that's where he made his ballot comments. --Steve]
* *
Here's a more compact summary, using the following table of codes.
Code Method
---- --------------------------
IR Instant Runoff (aka MPV, aka Hare)
RC Regular-Champion (aka Copeland//Plurality)
C Condorcet
Cw Condorcet with weighted (aka rated), not ranked, ballots
SC Smith//Condorcet
SCw Smith//Condorcet with weighted (aka rated), not ranked, ballots
SCt Smith//Condorcet(Tobin 1/2)
SR Smith//Random
A Approval
P Plurality (aka Winner Takes All, aka First Past The Post)
DC Double Complement
R Runoff
D1 Demorep's 1st (Approved//Condorcet//Approval ??)
D2 Demorep's 2nd (Approval of top n-1 ranked choices)
NOTB [not a method. It marks one's approval/disapproval threshold.]
Compact Summary
---------------
Kevin: C = SC > A > SR
Rob: SC > C > RC > SCw > Cw > IR > DC > A > NOTB > P > SR
Hugh: SCt > SC > SR > IR > C > RC > DC > A
Don: IR
Demorep: D1 > D2 > IR
Steve: SC > SCw > C > Cw > NOTB > IR > A > the_unranked > R > DC > P
Mike: C > SC > A > SR
There are 15 pairings (14 methods plus the NOTB approval/disapproval
dividing line) included in our ballots, so that will be 105 = 15*14/2
pairings to compute. I've computed using Smith//Condorcet, Condorcet,
Regular-Champion, and Instant Runoff. If you want the ballots
computed by different methods, or if you want to doublecheck my
math, go ahead and post your tallies too. I do hope several people
will doublecheck my math, since I did it all by hand in a very error-
prone manner.
The 15 x 15 pairwise matrix will barely fit in an 80-column email
message. (Apologies if your email software has trouble with 80 columns.)
Here's the matrix, which I did by hand in a very error-prone manner.
Please double-check my work. (Note: the number in each cell shows how
many voters prefer the choice at the row's left more than the choice at
the column's top. The suffix 'L' after a number denotes that the choice
at the column's top lost the pairing.)
IR RC C wC SC wSC SCt SR A P DC R D1 D2 NOTB
IR - 4L 3 3L 2 3L 4L 4L 5L 5L 5L 5L 4L 4L 4L
RC 1 - 2L 2L 1= 1 2 3L 3L 3L 2L 2L 2L
C 4L 5L - 5L 1 4L 4L 4L 5L 5L 5L 5L 5L 5L 5L
wC 2 1 - 2L 2 2 2L 2L 2L 2L 2L 2L
SC 5L 5L 3L 5L - 5L 4L 5L 5L 5L 5L 5L 5L 5L 5L
wSC 2 1 1 2L - 2L 2 2 2L 2L 2L 2L 2L 2L
SCt 1 1= 1 1 1 1 - 1 1 2L 2L 2L 1= 1= 1
SR 3 3L 1 3L 3L 3L - 1 4L 4L 5L 4L 4L 3L
A 2 3L 3L 3L 4L 4L - 5L 3L 5L 5L 5L 4L
P 1 - 1=
DC 1 1 1= 1 2 3L - 2L 2= 2= 2L
R 1= 1 -
D1 1 1 1 1 1 1 1= 1 1 2L 2= 2L - 1L 1
D2 1 1 1 1 1 1 1= 1 1 2L 2= 2L - 1
NOTB 1 1 2L 2 1 2L 1 2L 2L 2L -
--- --- --- --- --- --- --- --- --- --- --- --- --- --- ---
Wins 12 8 13 7 14 8 2 10 11 1 3 3 2 5
Losses 2 5 1 7 6 8 4 3 12 9 13 9 10 14
Ties 1 4 1 2 1 2 2
WorstL 5 5 3 5 - 5 4 5 5 5 5 5 5 5 5
Smith//Condorcet beats all other methods pairwise, so it wins when our
votes are tallied by Smith//Condorcet, Condorcet, and Regular-Champion.
Condorcet finishes second according to Smith//Condorcet, Condorcet, and
Regular-Champion. Its Copeland score of 12 (wins - losses) is larger
than any but SC. Its Condorcet score of 3 (worst "votes against") is
smaller than any but SC.
Tallying our votes by Instant Runoff:
(Question for Instant Runoff aficionados: How should Kevin's equal
first choices be tallied? An invalid ballot? As full-strength first
choices? As half-strength first choices? I'll assume 1/2 unless
someone corrects me.)
Round 1:
Eliminate SCt, IR, D1 since they tie for the least first-ranked votes:
Kevin: C = SC > A > SR
Rob: SC > C > RC > SCw > Cw > DC > A > NOTB > P > SR
Hugh: SC > SR > C > RC > DC > A
Don: --wasted--
Demorep: D2
Steve: SC > SCw > C > Cw > NOTB > A > the_unranked > R > DC > P
Mike: C > SC > A > SR
Round 2:
Eliminate D2:
Kevin: C = SC > A > SR
Rob: SC > C > RC > SCw > Cw > DC > A > NOTB > P > SR
Hugh: SC > SR > C > RC > DC > A
Don: --wasted--
Demorep: --wasted--
Steve: SC > SCw > C > Cw > NOTB > A > the_unranked > R > DC > P
Mike: C > SC > A > SR
Round 3:
Eliminate C:
Kevin: SC > A > SR
Rob: SC > RC > SCw > Cw > DC > A > NOTB > P > SR
Hugh: SC > SR > RC > DC > A
Don: --wasted--
Demorep: --wasted--
Steve: SC > SCw > Cw > NOTB > A > the_unranked > R > DC > P
Mike: SC > A > SR
Result: Smith//Condorcet wins by 5 votes to 0.
Finding the second place finisher using Instant Runoff:
Method 1: Find the method eliminated last (see above):
C was eliminated last, so it finishes second.
Method 2: Eliminate the winner (SC) from the initial rankings:
Kevin: C > A > SR
Rob: C > RC > SCw > Cw > IR > DC > A > NOTB > P > SR
Hugh: SCt > SR > IR > C > RC > DC > A
Don: IR
Demorep: D1 > D2 > IR
Steve: SCw > C > Cw > NOTB > IR > A > the_unranked > R > DC > P
Mike: C > A > SR
Round 1:
Eliminate SCt, IR, D1, and SCw, which are tied with fewest
first-rank votes:
Kevin: C > A > SR
Rob: C > RC > SCw > Cw > DC > A > NOTB > P > SR
Hugh: SR > C > RC > DC > A
Don: --wasted--
Demorep: D2
Steve: C > Cw > NOTB > A > the_unranked > R > DC > P
Mike: C > A > SR
Round 2:
Eliminate SR and D2, which are tied with fewest:
Kevin: C > A
Rob: C > RC > SCw > Cw > DC > A > NOTB > P
Hugh: C > RC > DC > A
Don: --wasted--
Demorep: --wasted--
Steve: C > Cw > NOTB > A > the_unranked > R > DC > P
Mike: C > A
Results: Condorcet finishes 2nd, 5 votes to 0.
Assuming I haven't made any errors interpreting or calculating,
Smith//Condorcet and Condorcet are the one-two finishers by the
four methods by which I tallied.
---Steve (Steve Eppley seppley at alumni.caltech.edu)
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