[EM] Displaying intermediate results in Condorcet-based elections (re: Rob Brown's original question)

[Dave Ketchum]

On Wed, 29 Oct 2003 19:10:06 -0800 Rob Brown wrote:

> At 01:29 PM 10/29/2003, you wrote:
> 
>> Agree. They want Borda. You want Condorcet.
> 
> 
> Well, maybe.  I want to give them something as intuitive as Borda in 
> terms of showing a nice pretty set of scores that mere mortals can wrap 
> their heads around, as well as being "correct" in terms of being 
> non-strategic and non-sensentive to clone candidates as Condorcet, 
> whether those same mortals understand this concept or not.  I guess I 
> want to have my cake and eat it too.  So shoot me.  :)


I promote Condorcet because it combines reasonable simplicity with freedom 
from strategies:
      Voter selects preferred candidate, as in Plurality.
      If desired, voter repeats among remaining candidates, in order of 
preference.

Someone mentioned Approval - I object for, while the math is easier to 
implement, the voter must invest almost as much effert as for Condorcet, 
yet is unable to indicate BEST LIKED.

> 
>> This is why I suggested you display the 1-d list of votes by ballot
>> configuration. There is no ambiguity, and no information is lost. If you
>> display this then you don't need to display the pairwise matrix that 
>> you're
>> going to finally use to determine the winner, since anyone who cares can
>> construct it for themselves.
> 

It is true that a listing by configuration would be complete - BUT - not 
that easy to interpret when you get beyond a very short set of candidates.

> 
> I respectly note your suggestion, as well as your philosophical 
> objection to my approach.  Being as I am doing this for a client, 
> ultimately I have to abide by their wishes, and I don't think I could 
> sell them on displaying a matrix by default (I did mention it, and it 
> wasn't received well).  I suppose it comes down to a pragmatic marketing 
> decision.  I am *not* claiming, however, that I disagree with their 
> preference.


One reason for demanding the matrix is that it should be a required output 
in any serious Condorcet election.  Beyond being input for determining the 
winner, it shows what the voters, collectively, thought about each pair of 
candidates.

For convenient matrix display I think of TWO numbers in each matrix box:
      First, number of votes preferring this column's candidate over this 
row's candidate.
      Second, similar count for this row's candidate over this column's 
candidate.
      Agreed this displays each number twice, and the manipulation to pair 
numbers when only displayed once is simple - but the manipulation is ALSO 
a PAIN.

Also like sorting the candidates, starting with winner in col. 1, row 1. 
In fact, this could be your only needed list of winners.

> 
> If this puts me at odds with a more "pure" way of looking at election 
> methods, well, so be it and I'll have to take comfort in knowing that 
> the site will explain the formulas used so show the scores, and if 
> people don't like the method of displying results, they are in no way 
> forced to use the system.
> 
>> This is really disturbing to me. What Arrow got his Nobel prize for 
>> was the
>> proof that you CANNOT create a linear ranking from a pairwise matrix. Not
>> only can it be linearized in "a reasonable way", it can be linearized 
>> in an
>> infinite number of "reasonable" ways. But at the end of the day whatever
>> linearization you chose has to match up with your election method, and I
>> don't believe it is possible to do so for Condorcet-based methods. 
>> (That is
>> not in itself a bad thing, it is just that that the requirement to display
>> intermediate results is incompatible with an election method that only
>> selects a winner after all results are in).
> 
> 
> Well, if many others on this list can accept that Condorcet methods for 
> determining a winner are reasonable to use -- even though Arrow has 
> proven them to be imperfect -- I don't think I'll burn in hell for 
> showing a set of scores which is equally discredited by Arrow.


If we are doing an election for a single winner (a normal task) then, if 
Arrow objects to Condorcet, we ask:  WHAT does he have that is better? 
Seems like it should have been promoted in EM if such exists.  Of course 
IRV has promoters AND detractors.

> 
>> The matrix is LESS information than the the counts per ballot combination,
>> not more.
> 
> 
> Agree, I don't think I implied otherwise, I said:
>  "Full set of ballots -- all information
>  Pairwise matrix -- lots of information"
> 
> "lots" is less than "all", no?
> 
>> If "a simple
>> ranking of candidates is to little." I am very confused, because as I
>> understood it was the original request was for us to help come up with a
>> simple ranking of candidates....
> 
> 
> No, producing a simple ranking is easy, I would just pick a method such 
> as ranked pairs or beatpath, apply it iteratively, and be done with it.  
> If that was all I needed case I would not have needed to ask this question.
> 
> My original request was to suggest a way to produce a single scalar 
> score per candidate which enhances, but does not conflict with, a simple 
> ordered ranking.  I apologize if I did not make that clear enough.


Agreed that is a difficult task - we order the candidates based on matrix 
data because we must, but doing scalar scores beyond showing candidate 
order must lose too much information.

> 
> -rob

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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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