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

[Chris Benham]

Dave Ketchum wrote:

> 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.
>
CB:  I  now think doing it either way might be ok. One is 
 "Generalised"-Bucklin/Condorcet  and the other is  plain 
Bucklin/Condorcet . The two reasons why I wavered were that (1) as a 
single-winner method  Generalised Bucklin is more highly regarded than 
plain Bucklin, and (2) not splitting would make counting the votes easier.
In describing the method, I forgot to mention that after each filling of 
a place and devaluations a new Droop quota should be calculated to take 
account of truncated ballots that have become "exhausted". In the 
split-votes version, an  alternative (probably equivalent) way to handle 
truncations would be to count them as equal last preference for all the 
unchecked candidates, and therfore keeping the Droop quota constant.

>> 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.
>
> CB: Condorcet is only used to fill the last seat, as a single-winner 
> method  based on the ballots after all the devaluations. So it just 
> looks at pairwise comparisons and I don't see how the splitting or not 
> splitting equal preferences is an issue.

>
> 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.

CB: The main difference that I can see is that in the no-split version, 
more ballots will be devalued, but because of the devaluations there is 
no "fairness" issue. A faction of voters with  X  mutual Droop quotas 
will elect X  candidates regardless.