[EM] Tom Ruen compares Approval, Condorcet, and IRV
Bart Ingles
bartman at netgate.net
Sat Dec 30 10:02:18 PST 2000
I just noticed that Tom Ruen's analysis is incorrect regarding
Approval. He appears to count any non-truncated ranking as an approval
vote. This is NOT approval voting.
A better, but very rough, approximation of Approval would have been to
count only the top half of each voter's choices.
A still better approximation of approval voting, whose data would have
usable to find other methods' results as well, would have been to
solicit [0..100] ratings instead of rankings. Then you could calculate
each voter's average rating for the candidates, and count the ratings
which were above average as an approval vote (this is usually considered
the best voter strategy when no polling or other strategy information is
available). For other methods, the rankings would be implicit in the
ratings.
Of course the only real way to demonstrate an Approval election is to
conduct an Approval election.
I hope somebody points this out to the IRV list, as well as to the
author of this comparison. Please forward this message to both.
Bart
Instant Runoff Voting supporter wrote:
>
> - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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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