[EM] Addendum to condorcet method theory

[Antonio Oneala]

David Cary <dcarysysb at yahoo.com> 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.  Under an election with N+1 candidates and N seats, someone will ALWAYS have a droop quota of votes.  This is the point of the original Condorcet method, that somebody will always have a droop quota (which is a majority in a two-way race) of votes.  There will always be a droop quota of people who always prefer one candidate to all others whenever they are pitted against each other, except in the case of a cyclic ambiguity.

An election in a condorcet method is a comparison between  candidates to pick N-winners pitted against each other in several N+1 elections. It seems very simple to simply change N to 2 whenever you want two proportional winners, and to three whenever you want three winners... etc, and then simply pick the two, or three etc... who were never defeated in any of the elections.  Just like a normal condorcet election, except all we change is the value of N.  A rather simple concept.




To see this, take any 1-winner, 2 candidate election with a definite
winner.  Clone the winner.  Now you have a 2-winner, 3 candidate
election, where the two clones are the two weak Condorcet winners and
would be the two winners under the proposed plan.  But those two
winners would exactly duplicate representation, not diversify it.  In
such an election, it seems that any reasonable definition of
proportional representation would prefer instead picking one of the
clones and the non-clone candidate as winners.

-- David Cary
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.

Let me show you an example of a two way race with four candidates and 50 voters with 2 different types of ballots:

28 A1 < A2 < B1 < B2
23 B1 < B2 < A1 < A2

I have picked a very simple election where the vote transfer mechanism is uneeded, as no one group has more than one droop quota worth of votes anyway.

There are four possible three way matchups between the four, 

A1, A2, B1: A1 and B1 win

28 like A1 the most out of the three, 0 like A2 the most, and 23 like B1 the most.  That makes A1 and B1 the winners of that round.

A2, B2, B1: A2 and B1 win
A2, A1, B2: A1 and B2 win
A1, B1, B2: A1 and B1 win

A1 and B1 have the most are unbeaten except by each other, so they are the two winners of the election.


--- Antonio Oneala  wrote:

> I've been told in the past that the Condorcet method "wasn't meant
> to be applied to proportional elections".  In it's original form it
> was not, because Condorcet oversimplified it into two-way races. 
> However, if we expand the definition to any perfect, strategy free
> race, then it would.
> 
> In a single-seat election a perfect race would be between two
> opponents.  If you vote for one you are definitely voting against
> the other one and the worst of the two will always be eliminated. 
> In a two-seat election, it follows, a perfect election would be
> between three opponents.  Only the worst could be eliminated.  In 
> a three-seat it would be a four opponent race, and etc... etc...
> 
> It seems to me that basing a proportional Condorcet method off of
> this observation would allow any of the currently proposed
> single-winner Condorcet methods to be easily extendend into the
> proportional realm, simply be replacing two-way races in a single
> seat election with three-way races in a two-seat election, and
> electing the two that were unbeaten, or only beaten by each other. 
> Vote-splitting wouldn't happen in such circumstances, so an
> STV-like transfer mechanism would be unnecessary.
> 
> It seems a rather obvious assertation to make, and I wonder why so
> many people have come up with some many ridiculously complicated
> schemes whenever all you have to do is expand the definition of the
> method.
> 
> Just a simple observation... in all reality I believe the
> reweighted range voting scheme is superior.
> 
>    
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