[EM] C//A

[fsimmons at pcc.edu]

Kristofer,

I think the following complete description is simpler than anything possible for ranked pairs:

1.  Next to each candidate name are the bubbles (4) (2) (1).  The voter rates a candidate on a scale from 
zero to seven by darkening the bubbles of the digits that add up to the desired rating.

2.  We say that candidate Y beats candidate Z pairwise iff Y is rated above Z on more ballots than not.

3.  We say that candidate Y covers candidate X iff Y pairwise beats every candidate that X pairwise 
beats or ties.

[Note that this definition implies that if Y covers X, then Y beats X pairwise, since X ties X pairwise.]

Motivational comment:  If a method winner X is covered, then the supporters of the candidate Y that 
covers X have a strong argument that Y should have won instead.

Now that we have the basic concepts that we need, and assuming that the ballots have been marked 
and collected, here's the method of picking the winner:

4.  Initialize the variable X with (the name of) the candidate that has a positive rating on the greatest 
number of ballots.  Consider X to be the current champion.

5.  While X is covered, of all the candidates that cover X, choose the one that has the greatest number of 
positive ratings to become the new champion X.

6.  Elect the final champion X.

7.  If in step 4 or 5 two candidates are tied for the number of positive ratings, give preference (among the 
tied) to the one that has the greatest number of ratings above level one.  If still tied, give preference 
(among the tied) to the one with the greatest number of ratings above the level two.  Etc. 

Can anybody do a simpler description of any other Clone Independent Condorcet method?

----- Original Message -----
From: Kristofer Munsterhjelm 
Date: Sunday, June 12, 2011 3:09 am
Subject: Re: [EM] C//A
To: fsimmons at pcc.edu
Cc: election-methods at lists.electorama.com

> fsimmons at pcc.edu wrote:
> > Kristofer Munsterhjelmwrote ...
> > 
> >> Some methods pass the Condorcet criterion without seeming 
> >> Condorcet-like 
> >> at all. 
> > 
> > Here's a good example:
> > 
> > Initialize a variable X to be the candidate with the most approval.
> > 
> > While X is covered, let the new value of X be the highest 
> approval candidate that covers the old X.
> > 
> > Elect the final value of X.
> > 
> > For all practical purposes this is just a seamless version of 
> C//A, i.e. it avoids the apparent 
> > abandonment of Condorcet in favor of Approval after testing 
> for a CW.
> > 
> > 
> > Assuming cardinal ballots, candidate A covers candidate B, 
> iff whenever B is rated above C on more 
> > ballots than not, the same is true for A, and (additionally) A 
> beats (in this same pairwise sense) some 
> > candidate that B does not.
> 
> I would prefer this to C//A (even though I would prefer methods 
> without 
> approval cutoffs to both). However, it is more complex and the 
> logic is 
> harder to get at by the public, kind of like Ranked Pairs in 
> that respect.
> 
>