I've used as an
example of why Borda counts are a dumb way to rank sports teams as an analog of
election methods, and upon getting access to a complete set of ballots for the
Asscociated Press ranking following the 27 November American college football
games, I applied IRV to see how it would be different, with quite favorable
results.
It seemed to me that
the same program could be applied to summarize the results of computer rankings
of the same teams that the human voters ranked, and that was similarly
satisfactory but left me with some questions about the
fundamentals.
The situation is a
truncated ballot one: the task is to pick the top 25 teams from a field of 117,
so no one can vote for more than 25. I realize that a better approach to this
would be full ranked ballots and some form of PR-STV, but my audience is sports
fans and administrators and I'll consider myself lucky to be able to explain
that what they are using is really called Borda, much less why IRV is better
than that based upon logical criteria....
But here's my
question. The process I used to assign a team (candidate) to rank x was "team A
has the greatest majority of votes for rank x or higher than any team ranked
below x-1". In some cases there are multiple teams with a majority at ranking x,
so I select the largest majority for position x and proceed to calculating the
rankings for position x+1.
Now, if teams B and
C were second and third for position x and both had majorities, but when
they lose position x and we add in the votes for x+1, they are third and second,
respectively, did I make a mistake by not assiging ranks x+1 and x+2 at the x
step?
In the attachment, a
relevant example is the relative position of #11 and #12. In the battle for #10,
Miami was ahead of LSU, but once the votes for 11th place were added in, LSU was
ahead.
In this context it
would seem more correct than what I did to "fix" a ranking whenever the team
receives a majority, so I could've assigned 10th, 11th and 12th positions all in
step 10. Or not?
Which approach is
right?
Computer votes counted by IRV
8 Dec 2004
- How to read the table
- The number in each cell is the cumulative number of rankings that listed the team that high or higher. Rankings are assigned when the (largest) majority of the rankings list the team higher than every remaining team. This is an application of the selection method known as "Instant Run-Off Voting."
There are 98 computers in this "poll", so a majority is 50.
Source: College Football Ranking Comparison
Team 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 USC 67 90 98 2 Oklahoma 24 85 95 97 97 98 3 Auburn 7 10 65 75 87 93 96 98 4 Texas 4 40 65 91 94 96 97 97 98 5 California 5 19 40 64 81 92 97 97 97 97 97 98 6 Utah 6 11 33 58 80 87 91 93 93 94 94 96 97 98 7 Boise St 5 12 45 55 69 76 81 83 83 83 87 90 91 91 93 94 95 8 Virginia Tech 1 4 10 21 49 63 72 83 89 91 93 95 95 96 98 9 Louisville 2 7 9 12 26 43 55 63 66 73 75 82 86 90 94 96 96 97 97 98 10 Georgia 2 3 9 17 34 49 61 76 85 88 93 95 96 98 11 LSU 1 3 7 11 28 46 64 75 86 92 93 93 95 96 97 98 12 Miami FL 1 1 4 8 11 23 41 53 60 69 84 91 95 96 96 97 98 13 Arizona St 1 4 6 14 17 24 31 48 64 68 71 72 78 84 86 89 90 90 91 14 Iowa 3 4 15 22 24 32 41 53 58 64 69 75 79 82 85 88 92 94 97 15 Texas A&M 1 1 3 4 10 16 24 32 41 51 60 69 72 77 85 88 91 92 93 95 Team 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 16 Virginia 3 5 9 9 12 22 34 42 60 77 85 94 96 96 97 97 98 17 Florida St 2 4 9 14 16 23 42 51 70 82 86 90 95 98 18 Michigan 1 6 8 15 24 28 38 44 54 59 61 66 67 76 83 89 91 19 Tennessee 1 2 6 8 13 16 27 37 45 48 57 60 71 74 78 80 82 20 Oklahoma St 2 4 9 17 27 38 50 70 75 78 80 82 21 Texas Tech 1 2 4 5 7 9 12 17 20 27 34 51 78 83 89 91 22 Wisconsin 1 3 11 16 22 28 40 45 53 59 66 73 23 Oregon St 1 2 3 3 5 12 15 23 31 35 42 54 63 65 24 Purdue 1 1 1 1 3 4 6 7 8 13 18 22 25 38 41 52 25 Ohio St 1 1 1 1 3 3 3 3 5 6 6 11 14 20 34 49 Florida 2 2 3 3 3 6 7 9 11 16 19 22 33 39 47 North Carolina 1 1 1 1 1 1 1 2 2 3 4 4 7 11 17 24 29 UCLA 2 2 3 5 5 7 11 12 12 19 24 Fresno St 1 1 1 1 1 1 5 6 8 10 13 16 20 22 Colorado 1 1 4 10 19 Team 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Pittsburgh 3 8 8 8 8 8 11 Boston College 1 2 7 9 Texas-El Paso 1 4 7 8 West Virginia 3 5 6 7 Toledo 1 1 1 1 4 5 5 New Mexico 1 4 Bowling Green 1 2 2 2 2 3 4 Notre Dame 1 1 2 3 4 Alabama 1 1 1 1 1 1 1 1 3 Georgia Tech 1 1 1 1 1 3 Arkansas 2 Clemson 1 1 1 1 2 2 2 NC State 1 2 2 Penn St 1 1 1 2 Stanford 1 1 1 2 Maryland 1 1 1 1 1 Memphis 1 1 Syracuse 1 Teams / Spot 3 5 7 8 8 14 12 13 15 16 17 15 17 19 19 19 20 21 23 22 22 22 23 25 29 ---- Election-methods mailing list - see http://electorama.com/em for list info
