[EM] Re: Bucklin-Condorcet PR (also Bucklin PR)

[Dave Ketchum]

On Tue, 12 Aug 2003 06:57:33 +0930 Chris Benham wrote in part:

>  Previously, on Friday, August 8, 2003  I posted a suggested 
> ranked-ballot PR method that combines Generalized Bucklin and Condorcet. 
> It wrongly included: "Equal preferences are divided into equal fractions 
> (which sum to 1)". I now think it is fine if equal preference for A and 
> B are counted Approval-style as a whole vote for each.


Looks wrong.

First, let's look at Condorcet:

A and B tied:  If one voter ranked A first, and one ranked B first, A and 
B would each get credited with one whole vote.
      If two voters ranked them in a tie, each should STILL get one whole 
vote - 1/2 for each such ballot.

A, B, and C tied:  If six voters did the six possible rankings then, for 
each of the three candidate pairs, each candidate would get credited with 
three whole votes.
      If six voters ranked them in a tie, each should STILL get three 
whole votes in each pair - 1/2 for each such ballot.

Back to the current PR method:

A and B tied:  Anything other than the above 1/2 looks like unfair penalty 
or credit for voting ties.

A, B, and C tied:  Because A was top ranked in 1/3 of the six ballots, as 
were B and C, and this method is concerned with one preference at a time, 
my reading is that 1/3 to each paired candidate for each paired ballot 
would be fair when the pairs first became visible; 1/6 to each candidate 
in the next round (this gets too messy, so maybe 1/2 ala Condorcet when 
the pair becomes visible and nothing on the next rounds when we should 
still be looking at the pairs).
      What I am certain about is that this is not Approval, and what 
Approval might do does not help here.
-- 
davek at clarityconnect.com  http://www.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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