Look what the cat dragged in!

[Blake Cretney]

On Fri, 16 Oct 1998 07:18:22   New Democracy wrote:
>Greetings,
>
>     MikeO is again subjecting us to his tirads on Choice Run-Off(IRO) - he
>is against it.
>     It should be noted that if the count of the first choices would give
>us a majority winner every time we would not need any of these methods.
>But, because we do not always get a majority on the first count we are
>seeking some method which will give us a majority winner. We should keep in
>mind that the point of using some method is the quest of a majority winner.
>     In other words: The main requirement of a method is to produce
>majority winners.

>     Condorcet is better than Approval Voting because Condorcet should give
>us a majority two out of three times. That third time, Condorcet gives all
>candidates a majority. Our quest is looking for something better than this.

>
>     Top Two Run-Off will give us a majority winner every time, except the
>rare case of a tie between the top two candidates in the run-off election.
>But Top Two Run-Off does have a flaw. When there are four or more
>candidates in which two or more are eliminated at one time, it is possible
>to eliminate the wrong candidate. The rule is that when two or more

I wonder what you mean by the "wrong" candidate.  What makes the
candidate wrong, being a plurality loser at some stage of IRO?  

>     Choice Run-Off only eliminates one candidate at a time, therefore it
>will not be eliminating the wrong candidate - this is a big improvement
>over Top Two Runoff. Besides, Choice Run-Off only needs one election vs two
>elections for Top Two Run-Off. Choice Run-Off also has means to solve any
>tie between two or more candidates.
>     It goes without saying, Choice Run-Off will give us a majority winner
>every time.
>     Remember, the main requirement of a method is to produce majority winners.
Perhaps this is my main disagreement with you.  I think we should think
of majority winners as produced by voters, and merely revealed by methods.

Consider, for example, I could have an election method that starts by
picking two candidates at random.  It would then eliminate all other 
candidates to get a pair-wise comparison between them.  The winner of 
this comparison would be a majority winner, by your definition.  But all
it accomplished was being pair-wise prefered to one other candidate.  
There may be plenty of candidates who are pair-wise prefered to both, 
although I suspect you wouldn't consider these "real" majorities.  As 
far as I can gather, you seem to think it is up to the method to declare 
which pair-wise majorities are and are not real majorities.

>
>     Choice Run-Off(IRO) is head and shoulders better than Top Two Run-Off,
>but Mike comes to the reverse conclusion - MikeO is wrong.

I'm not actually going to defend Mike's argument, which I don't
agree with.

>     Choice Run-Off will give us a majority winner every time - Plurality
>will never give us a majority winner, but MikeO concludes that Plurality is
>better than Choice Run-Off - MikeO is wrong again.
>
>     MikeO is often wrong, but in this case we can be kind to him and blame
>the means he used to reach his conclusions. MikeO used two of the methods
>as standards to compare the other methods. I quote MikeO:
>     "... it looks as if Runoff is clearly better than IRO, if it means
>anything to elect a CW--or a CW that's a plurality winner."
>
>     MikeO is using the Condorcet Winner(CW) and the Plurality winner as
>measures. When MikeO did this he gave himself away - he is showing us that
>he does not know how to compare apples and oranges. When we compare apple
>to oranges we cannot use the apple nor the orange as a standard to campare
>either fruit. Likewise we cannot use Condorcet nor Plurality nor any of the
>election methods to compare the other methods.

Its important not to confuse two different concepts with similar names

Condorcet's Method -- The method that gives victory to the candidate
with the smallest pair-wise loss.  

Condorcet Winner -- A candidate who, based on the ballots, would win
a pair-wise (one-one-one) comparison with any other candidate.

Although a Condorcet Winner will always win under Condorcet's method,
the winner of Condorcet's method is NOT necessarily the Condorcet
Winner.  Furthermore, many methods other than Condorcet's method will
always pick a Condorcet winner.  Of course, this is very confusing, but
it isn't Condorcet's fault for being so prolific and getting so many
things named after him. 

So, if someone says they like Condorcet's Method because it always
picks the Condorcet Winner, they are not using a circular argument.
What they are saying is that they don't want to avoidably over-rule
a majority preference, and they note that Condorcet's Method won't
do this. 

>     The position of being the Condorcet winner or the Plurality winner has
>no special value in our quest for a majority winner. Some of the Condorcet
>and/or Plurality winners will become majority winners and some will not.

Consider the following method
1.  First eliminate any candidate who has a pair-wise loss against
every other candidate.
2.  Now arrange candidates by their greatest pair-wise defeat.
Eliminate all candidates, but the two who are lowest on this
scale.
3.  Simulate a run-off between these two.  Declare the one with a
majority over the other, a "majority winner."

This is just a somewhat contrived way of describing using Condorcet's
method after eliminating the Condorcet loser.  Does this method fit
your "finding a majority" standard?  If so, other methods like Schulze
and Smith//Condorcet could also be described in such a way as to fit
it.




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