[EM] Proportional Condorcet Voting

[Antonio Oneala]

All of the proportional condorcet methods I've heard of so far rely on STV to some extent.  While this may be useful for ease of use (I'm not sure, I still don't completely understand them) in CPO-STV and sequential STV, it isn't really the best way to apportion the votes, as it introduces some of the flaws present in STV into the Condercet methods.  What I'm thinking of is something that reduces completely to condercet whenever reduced, and doesn't introduce any new elements that mess up propotionality.  This is based off of PAV voting, and would require far mroe computation than even PAV, as it compares every single outcome, and doesn't simply assign a score to them.  It is much "purer" than the CPO-STV and sequential STV methods, but it may be quite a bit more problematic (still not sure about that, being that the methods are very complicated to understand).

The ballot is a normal preference ballot.

The first thing that is needed is a list of all outcomes, like PAV.

Then, all outcomes are compared against each other pairwise.  Each voters preferences are compared, and each voter gives a score to either outcome based on which candidates were ranked higher on their ballot.  The score is assigned by determing which outcome has more people that were ranked higher on the voters ballot.  If the outcome had 1 person ranked higher, that outcome gets a score of 1.  If it had 2 ranked higher, it get 1 + 1/2 .  If it had 3 ranked higher, it get 1 + 1/2 + 1/3, and so on.  

The scores of all the voters given to each outcome are all added up to get the voters total "satisfaction" with the score, and the outcome with the highest satisfaction wins.  

I haven't thought about how to apply completion methods yet.  I don't really read up on the things that much.

Obviously, this method is going to require quite a bit of computational power.  A prohibitive amount.  But I believe this is probably the Proportional Condercot Method that comes closest to actual Condercet, and is therefore at least worthy of note.  If only we could find a way to do these kinds of elections without the lengthy comparison of all outcomes method...

		
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