[EM] thoughts on the pairwise matrix

[Dave Ketchum]

On Tue, 29 Nov 2005 12:32:29 -0600 Paul Kislanko wrote:

>  
> 
>>-----Original Message-----
>>From: Dave Ketchum [mailto:davek at clarityconnect.com] 
>>Sent: Monday, November 28, 2005 10:33 PM
>>To: Paul Kislanko
>>Cc: 'rob brown'; election-methods at electorama.com
>>Subject: Re: [EM] thoughts on the pairwise matrix
>>
>>This one seems to identify the problem we have been stumbling 
>>over, though 
>>not doing much for a fix:
>>
>>We have a method called Condorcet with its way of expressing ranking, 
>>producing an array of intermediate results, and determining a winner.
>>
>>You prefer a method that starts with different voting.  Rather than 
>>throwing sand in our gears, you would be more productive if 
>>you gave your 
>>method a name, such as "PaulK", and initiated discussion as 
>>to its merits.
>>
> 
> I do believe I've tried that, and been dismissed as being "irrational", and
> of course, "not an expert." However, I can try again.


As to your previous effort, unless you were clearly offering something 
with positive value, you properly got rejection, and time to give up 
unless you could present a better argument.

As to your current effort, seems like you had a serious problem with 
clarity until the current exchange.  Now I see PaulK as not enough better 
than Condorcet to be worth the pain.

> 
> My suggestion was to axiomitize the study of EMs sort of the way Turing did
> for computing about the same time Arrow was doing his work. Divide "election
> method" into two different things, a method for collecting votes and a
> method for counting them. An "ideal" collection method for
> Condorcet-counting might not be the ranked ballot. But a generalized
> collection method that can support Approval, Condorcet, or anything else is
> entirely possible. 
> 

While PaulK may process the array in the same manner as Condorcet, its 
demands on the voter differ enough that it needs its own name for 
differing voter requirements and differing reading of ballots.

There are enough differences that IRV and Condorcet are separate methods 
even though Condorcet uses the same ballot as IRV, while normally 
permitting "=" in the ranking.

As to methods, Plurality and Approval can be voted with a Condorcet 
ballot, also IRV if "=" is not permitted.  Some of the more exotic methods 
demand more of the voter than the Condorcet or PaulK ballots provide for.

> 
> 
>>On Mon, 28 Nov 2005 16:44:09 -0600 Paul Kislanko wrote:
>>
>>
>>>I think the only pairwise-matrix that is defensible is one 
>>>
>>constructed 
>>
>>>by ballots. If the Ballot says "Choose one, choose both, 
>>>
>>choose neither" 
>>
>>>for each pair of alternatives then there's a clear path 
>>>
>>from voters' 
>>
>>>choices to the resulting PM. Otherwise, it's a matter of 
>>>
>>how the ballots 
>>
>>>were processed to get the PM.
>>>
>>>
>>What weakens that paragraph is that the Condorcet matrix 
>>produced from 
>>Condorcet Ballots is as correct for the Condorcet method as 
>>your array is 
>>for your method.
>>
> 
> I actually have no method. But "Condorcet ballots" is an ambiguous term as
> used in the reply to me. I actualy suggested that there BE a well-defined CB
> such that for each pair of choices I vote "A, B, Either, or Neither". Then
> the matrix can be guaranteed to reflect the voters' pairwise preferences,
> instead of having to infer them (under different rules depending upon
> whether equal rankings and/or truncation is allowed).


"=" is discussed above, as is the fact that most recognize that Condorcet 
ballots are NOT LIKE PaulK ballots.  Those who wish to forbid truncation 
would likely use the same arguments with PaulK.

> 
> Mind, this is a theoretical consideration, not yet a practical one. Sort of
> like using the Universal Turing Machine to proove a program's correctness.

-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
            Do to no one what you would not want done to you.
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