[EM] Addendum to condorcet method theory

[Antonio Oneala]

David Cary <dcarysysb at yahoo.com> wrote: --- Antonio Oneala , on 10/24/2006 wrote:

> David Cary  wrote: 
> > Besides its severely
> > limited range of application, the other major
> > drawback of the proposed method is that it is not proportional.
> 
> I have no idea how the application of the method is "limited".  You
> have rather severly misinterpreted my suggestion.  

Yes, I did severely misinterpret your suggestion.  I withdraw what I
said about it.


> It IS cloneproof.  However, a made slight error in my original
> proposal.  Whenever a candidate fulfills the droop quota he should
> automatically be declared one of the winners of one of the rounds,
> and then the value of the votes should be reduced (as it would
> whenever you declare a winner in STV), and the new values of the
> persons vote should be transferred to the next person they had on
> their list.  Whenever this is through you can declare the next
> winner, and you repeat this until you have all the winners.  The
> reason for this is rather obvious.  Under the original erronous
> proposal it would have ended up with a situation simialar to SNTV
> in which surplus votes are wasted.

I think I'm getting a better understanding, but I'm still not sure I
completely understand what is being proposed.  I think you are
saying: 

1. For an N-seat election, use the voted ranked ballots to conduct an
STV-style, N-seat election between every possible combination of N+1
candidates and record the loser of each such contest.

2. If there are exactly N candidates that are unambiguously without
any losses in the N-out-of-N+1 contests, those N candidates are the
winners, corresponding to being the standard Condorcet winner of a
single-winner election.  

3. Otherwise (if there are fewer or more than N candidates without
any losses, or ties and/or tie-breaking makes the number of
candidates without any losses ambiguous), then the result corresponds
to a Condorcet ambiguity in a single-winner election, and some
additional ambiguity resolution is needed to determine the N winners.

Does that restatement reflect what you had in mind?

-- David Cary

Yes, that was the general gist of what I was saying.

Although I may have confused people at first by saying that no STV style transfer would be neccessary because there would be no vote-splitting.  I meant that unlike most PR Condorcet methods that have been proposed, this one would rely on any sort of eliminations.  It is cloneproof in the normal sense.  But of course, selecting multiple winners complicates things, and without some sort of surplus vote transfer mechanism like in STV it would be strictly a minority representation system like SNTV instead of proportional system like STV, and it would be vulnerable to surplus vote-splitting.

But if you are designing a proportional Condorcet method this seems like the most logically step.  I've seen several designs of PR Condorcet methods that tried to use two-way races to produce proportionality, or confusing examples like STV by Condorcet Loser Elimination.  Interestingly, Tideman also incoroporated this logic into his Condorcet STV method (and apparently Shulze did too), although I believe they designed rather complicated elimination formulas and such in the process of doing so, whenever all that was needed of a proportional Condorcet method was to change the value of N and use a surplus vote transferring mechanism.


 
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