[EM] Philosophical question for IRV experts

[Paul Kislanko]

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?
 
  

The great tragedy of Science - the slaying of a beautiful hypothesis by an
ugly fact. 

Thomas H. Huxley <http://www.quotationspage.com/quotes/Thomas_H._Huxley> 

---------------------- 

Paul Kislanko 

 
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