[EM] Tom Ruen compares Approval, Condorcet, and IRV
Instant Runoff Voting supporter
donald at mich.com
Fri Dec 29 03:47:47 PST 2000
- - - - - - - - - - - - - - - - - - - - - - - - - - - - 12/29/00
Dear IRV Supporters,
Over the last week I held a sample election, asking people to rank their
favorite months.
Thank you all for participating! : )
This email contains the election results and analysis.
Sincerely,
Tom Ruen
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
Sample election results: What is your favorite month?
by Tom Ruen
**** Ballots *****
There were 81 ballots cast.
Sampling:
1) 37 Email-IRV
2) 18 Family-direct
3) 17 Friends-direct
4) 9 Work-direct
**** Voter Strategies *****
59 ballots were completely ranked 1-12
1 ballot was completely ranked with ties 1-10
PARTIAL RANKINGS: 21
1) 2 had ranks up to 9 or 10
2) 7 had ranks up to 6 or 7
3) 7 had ranks up to 4 or 5
4) 3 had ranks up to 2 or 3
5) 2 had rank 1 alone
Note on partial rankings: In IRV elections, there is no real advantage to
partial rankings since your ballot will be ignored if all your choices are
exhausted. Majority is computed after each round as half the number of
ballots with choices remaining.
TIES: Only 4 voters used tied rankings - three voters had 3 or 4 first
ranks. One thoughtful voter (My Uncle John) wanted two 7's and two 9's!
Note on ties: Ties are easy to handle for a computer (fractional votes),
but have little strategic value. They are more a matter of voting laziness
if preference is uncertain. The best argument I have to disallow ties in
ranked elections is that this makes it easier to detect misread/mistyped
ranks - by voters or election judges (like me)!
********* Results ********
September is the winner by both Condorcet and IRV
IRV can produce a win ranking by eliminating the winner at the end and
applying IRV over again to the remaining candidates. In this election that
process produced the same order as Condorcet: (3 pair-ties)
1. September
2. April-May
3. June
4. July
5. August-October
6. December
7. November
8. February-March
9. January
********* Ballots: *********
If you want to apply your own analysis of this election, the ballots are
online at:
http://home.talkcity.com/computerct/datatom/delphi/months.txt
This is a tab-delimited table file which can be read by spreadsheet programs.
The ballots are labeled by personal or code names voters provided,
otherwise by date/time of email arrival.
The program I used to analyze the election is also online: (This is a MS
Windows application I wrote using Borland Delphi 3.0. It is a fairly
user-friendly interface if you don't mind some playing with it.)
http://home.talkcity.com/computerct/datatom/delphi/irv.zip
********* In detail: ********
1. Approval vote:
This vote measures how many ballots each candidate was ranked on.
Apr 76 ( 93.8%)
May 76 ( 93.8%)
Jun 73 ( 90.1%)
Jul 73 ( 90.1%)
Sep 72 ( 88.9%)
Oct 72 ( 88.9%)
Aug 69 ( 85.2%)
Mar 65 ( 80.2%)
Nov 65 ( 80.2%)
Dec 65 ( 80.2%)
Feb 63 ( 77.8%)
Jan 60 ( 74.1%)
2. Condorcet pair election winners:
This method runs all combination of pair-wise elections between candidates.
Ideally, any candidate that wins all pair-wise elections is the winner.
Condorcet is usually similar to IRV, although it is much more
computationally intensive, requiring N*(N-1)/2 pair election runs to start
the analysis. This would be a pain to tally by hand if there are more than
4 or 5 candidates.
This table (below) shows pair-wins listed by rows, loses by columns.
(2=win, 1=tie, 0=lose)
In this case, the candidates have a clear win-order with a few harmless
ties due to the small voter sampling. (April=May, August=October,
March=February)
In some elections there will be cycles of preferences and the top winner
will be less clear than in this case. (The Rock-Paper-Scissors game
demonstrates a cycle: Rock beats Scissors, Scissors beats Paper, and Paper
beats Rock)
S A M J J A O D M N F J
e p a u u u c e a o e a
p r y n l g t c r v b n
Sep - 2 2 2 2 2 2 2 2 2 2 2
Apr 0 - 1 2 2 2 2 2 2 2 2 2
May 0 1 - 2 2 2 2 2 2 2 2 2
Jun 0 0 0 - 2 2 2 2 2 2 2 2
Jul 0 0 0 0 - 2 2 2 2 2 2 2
Aug 0 0 0 0 0 - 1 2 2 2 2 2
Oct 0 0 0 0 0 1 - 2 2 2 2 2
Dec 0 0 0 0 0 0 0 - 2 2 2 2
Mar 0 0 0 0 0 0 0 0 - 2 1 2
Nov 0 0 0 0 0 0 0 0 0 - 2 2
Feb 0 0 0 0 0 0 0 0 1 0 - 2
Jan 0 0 0 0 0 0 0 0 0 0 0 -
3. IRV:
Instant Runoff voting totals first rank votes to begin with, and then
iteratively eliminates the candidate with the lowest votes and moves votes
to the next highest candidate on affected ballots. The process can be
stopped when a candidate gains the majority.
In this analysis, I don't worry about ties in last place for determining
elimination order. This can be shown to be stable if the remaining tied
candidate is eliminated immediately after. (Example: March and November in
round 1 and 2)
IRV is so easy, you don't even need a computer - this election could be
done by hand on a few sheets of paper.
Note: {NOTA means None-Of-The-Above or ballots with all choices eliminated,
also known as exhausted ballots)
Round # 1 Sep=16.0 May=12.3 Aug=9.3 Jul=9.1 Apr=8.5 Oct=6.3 Jun=4.3
Feb=4.0 Jan=4.0 Dec=3.3 Mar=2.0 Nov=2.0
Eliminate: Nov
Round # 2 Sep=16.0 May=13.3 Aug=9.3 Jul=9.1 Apr=8.5 Oct=6.3 Jan=5.0
Jun=4.3 Feb=4.0 Dec=3.3 Mar=2.0
Eliminate: Mar
Round # 3 Sep=16.0 May=13.3 Jul=10.1 Apr=9.5 Aug=9.3 Oct=6.3 Jan=5.0
Jun=4.3 Feb=4.0 Dec=3.3
Eliminate: Dec
Round # 4 Sep=16.0 May=13.3 Jul=11.3 Aug=10.3 Apr=9.5 Oct=7.5 Jan=5.0
Jun=4.3 Feb=4.0
Eliminate: Feb
Round # 5 Sep=16.0 May=14.3 Aug=11.3 Jul=11.3 Apr=9.5 Oct=7.5 Jun=5.3
Jan=5.0 [NOTA=1]
Eliminate: Jan
Round # 6 Sep=17.0 May=15.3 Aug=13.3 Jul=11.3 Apr=9.5 Oct=7.5 Jun=6.3 [NOTA=1]
Eliminate: Jun
Round # 7 Sep=18.0 May=16.3 Jul=14.3 Aug=13.3 Apr=9.5 Oct=8.5 [NOTA=1]
Eliminate: Oct
Round # 8 Sep=21.0 Jul=16.8 May=16.3 Aug=14.3 Apr=11.5 [NOTA=1]
Eliminate: Apr
Round # 9 Sep=25.0 Jul=20.8 May=18.3 Aug=15.8 [NOTA=1]
Eliminate: Aug
Round #10 Sep=29.0 Jul=28.0 May=23.0 [NOTA=1]
Eliminate: May
Round #11 Sep=41.0 Jul=38.0 [NOTA=2]
Eliminate: Jul
Round #12 Sep=72.0 [NOTA=9]
Winner: September
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<DIV><FONT size=2>Dear IRV Supporters,<BR><BR>Over the last week I held a
sample
election, asking people to rank their favorite months. </FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Thank you all for participating! : )<BR><BR>This email
contains the election results and analysis.<BR></FONT></DIV>
<DIV><FONT size=2>Sincerely,</DIV></FONT>
<DIV><FONT size=2>Tom Ruen</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>**** Ballots *****<BR><BR>There were 81 ballots cast.
<BR>Sampling:<BR>1) 37 Email-IRV<BR>2) 18 Family-direct<BR>3) 17
Friends-direct<BR>4) 9 Work-direct<BR><BR>**** Voter Strategies *****<BR><BR>59
ballots were completely ranked 1-12<BR>1 ballot was completely ranked with ties
1-10<BR><BR>PARTIAL RANKINGS: 21<BR>1) 2 had ranks up to 9 or 10<BR>2) 7 had
ranks up to 6 or 7<BR>3) 7 had ranks up to 4 or 5<BR>4) 3 had ranks up to 2 or
3<BR>5) 2 had rank 1 alone<BR><BR>Note on partial rankings: In IRV elections,
there is no real advantage to partial rankings since your ballot will be
ignored
if all your choices are exhausted. Majority is computed after each round as
half
the number of ballots with choices remaining.<BR><BR>TIES: Only 4 voters used
tied rankings - three voters had 3 or 4 first ranks. One thoughtful voter (My
Uncle John) wanted two 7's and two 9's!<BR><BR>Note on ties: Ties are easy to
handle for a computer (fractional votes), but have little strategic value. They
are more a matter of voting laziness if preference is uncertain. The best
argument I have to disallow ties in ranked elections is that this makes it
easier to detect misread/mistyped ranks - by voters or election judges (like
me)!<BR><BR>********* Results ********<BR><BR>September is the winner by both
Condorcet and IRV<BR><BR>IRV can produce a win ranking by eliminating the
winner
at the end and applying IRV over again to the remaining candidates. In this
election that process produced the same order as Condorcet: (3
pair-ties)<BR><BR>1. September<BR>2. April-May<BR>3. June<BR>4. July<BR>5.
August-October<BR>6. December<BR>7. November<BR>8. February-March<BR>9.
January<BR><BR>********* Ballots: *********<BR><BR>If you want to apply
your own
analysis of this election, the ballots are online at:<BR><A
href="http://home.talkcity.com/computerct/datatom/delphi/months.txt">http://
home.talkcity.com/computerct/datatom/delphi/months.txt</A></FONT></DIV>
<DIV><FONT size=2>This is a tab-delimited table file which can be read by
spreadsheet programs.</FONT></DIV>
<DIV><FONT size=2>The ballots are labeled by personal or code names voters
provided, otherwise by date/time of email arrival.</DIV>
<DIV><BR>The program I used to analyze the election is also online: (This is a
MS Windows application I wrote using Borland Delphi 3.0. It is a fairly
user-friendly interface if you don't mind some playing with it.)<BR><A
href="http://home.talkcity.com/computerct/datatom/delphi/irv.zip">http://hom
e.talkcity.com/computerct/datatom/delphi/irv.zip</A><BR><BR>*********
In detail: ********<BR><BR>1. Approval vote:<BR><BR>This vote measures how many
ballots each candidate was ranked on.<BR><BR>Apr 76 (
93.8%)<BR>May 76 ( 93.8%)<BR>Jun 73 (
90.1%)<BR>Jul 73 ( 90.1%)<BR>Sep 72 (
88.9%)<BR>Oct 72 ( 88.9%)<BR>Aug 69 (
85.2%)<BR>Mar 65 ( 80.2%)<BR>Nov 65 (
80.2%)<BR>Dec 65 ( 80.2%)<BR>Feb 63 (
77.8%)<BR>Jan 60 ( 74.1%)<BR><BR>2. Condorcet pair election
winners:<BR></DIV></FONT>
<DIV><FONT size=2>This method runs all combination of pair-wise elections
between candidates. Ideally, any candidate that wins all pair-wise elections is
the winner.</FONT></DIV>
<DIV><FONT size=2><BR>Condorcet is usually similar to IRV, although it is much
more computationally intensive, requiring N*(N-1)/2 pair election runs to start
the analysis. This would be a pain to tally by hand if there are more than 4 or
5 candidates.<BR></FONT><FONT size=2></DIV></FONT>
<DIV><FONT size=2>This table (below) shows pair-wins listed by rows, loses
by columns. (2=win, 1=tie, 0=lose)</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>In this case, the candidates have a clear win-order with
a few
harmless ties due to the small voter sampling. (April=May, August=October,
March=February)<BR><BR>In some elections there will be cycles of
preferences and
the top winner will be less clear than in this case. (The Rock-Paper-Scissors
game demonstrates a cycle: Rock beats Scissors, Scissors beats Paper, and Paper
beats Rock)<BR><BR><FONT face="Courier New"> S A M J J A
O D M
N F J <BR> e p a u u u c e a o e a <BR> p r
y n l g t c r v b n <BR>Sep - 2 2 2 2 2 2 2 2 2 2 2<BR>Apr 0 - 1 2 2 2 2 2
2 2 2
2<BR>May 0 1 - 2 2 2 2 2 2 2 2 2<BR>Jun 0 0 0 - 2 2 2 2 2 2 2 2<BR>Jul 0 0
0 0 -
2 2 2 2 2 2 2<BR>Aug 0 0 0 0 0 - 1 2 2 2 2 2<BR>Oct 0 0 0 0 0 1 - 2 2 2 2
2<BR>Dec 0 0 0 0 0 0 0 - 2 2 2 2<BR>Mar 0 0 0 0 0 0 0 0 - 2 1 2<BR>Nov 0 0
0 0 0
0 0 0 0 - 2 2<BR>Feb 0 0 0 0 0 0 0 0 1 0 - 2<BR>Jan 0 0 0 0 0 0 0 0 0 0 0
-<BR></FONT><BR>3. IRV:<BR><BR>Instant Runoff voting totals first rank
votes to begin with, and then iteratively eliminates the candidate with the
lowest votes and moves votes to the next highest candidate on affected ballots.
The process can be stopped when a candidate gains the majority.<BR><BR>In this
analysis, I don't worry about ties in last place for determining elimination
order. This can be shown to be stable if the remaining tied candidate is
eliminated immediately after. (Example: March and November in round 1 and
2)<BR></FONT></DIV>
<DIV><FONT size=2>IRV is so easy, you don't even need a computer - this
election
could be done by hand on a few sheets of paper.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Note: {NOTA means None-Of-The-Above or ballots with all
choices eliminated, also known as exhausted ballots)</DIV>
<DIV><BR>Round # 1 Sep=16.0 May=12.3 Aug=9.3 Jul=9.1 Apr=8.5 Oct=6.3
Jun=4.3 Feb=4.0 Jan=4.0 Dec=3.3 Mar=2.0 Nov=2.0<BR>Eliminate: Nov<BR>Round #
2 Sep=16.0 May=13.3 Aug=9.3 Jul=9.1 Apr=8.5 Oct=6.3 Jan=5.0 Jun=4.3
Feb=4.0 Dec=3.3 Mar=2.0<BR>Eliminate: Mar<BR>Round # 3 Sep=16.0 May=13.3
Jul=10.1 Apr=9.5 Aug=9.3 Oct=6.3 Jan=5.0 Jun=4.3 Feb=4.0 Dec=3.3<BR>Eliminate:
Dec<BR>Round # 4 Sep=16.0 May=13.3 Jul=11.3 Aug=10.3 Apr=9.5 Oct=7.5
Jan=5.0 Jun=4.3 Feb=4.0<BR>Eliminate: Feb<BR>Round # 5 Sep=16.0 May=14.3
Aug=11.3 Jul=11.3 Apr=9.5 Oct=7.5 Jun=5.3 Jan=5.0 [NOTA=1]<BR>Eliminate:
Jan<BR>Round # 6 Sep=17.0 May=15.3 Aug=13.3 Jul=11.3 Apr=9.5 Oct=7.5
Jun=6.3 [NOTA=1]<BR>Eliminate: Jun<BR>Round # 7 Sep=18.0 May=16.3
Jul=14.3
Aug=13.3 Apr=9.5 Oct=8.5 [NOTA=1]<BR>Eliminate: Oct<BR>Round # 8 Sep=21.0
Jul=16.8 May=16.3 Aug=14.3 Apr=11.5 [NOTA=1]<BR>Eliminate: Apr<BR>Round #
9 Sep=25.0 Jul=20.8 May=18.3 Aug=15.8 [NOTA=1]<BR>Eliminate: Aug<BR>Round
#10 Sep=29.0 Jul=28.0 May=23.0 [NOTA=1]<BR>Eliminate: May<BR>Round
#11 Sep=41.0 Jul=38.0 [NOTA=2]<BR>Eliminate: Jul<BR>Round #12
Sep=72.0 [NOTA=9]<BR>Winner: September</DIV>
<DIV> </DIV></FONT>
<br>
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