[EM] New (?) Condorcet method: LeastSchwartzBeat

[Ernest Prabhakar]

Hi all,

I've been working on how best to implement a Condorcet-compatible 
algorithm such as Ranked Pairs (or should I say  MAM?) and SSD.   I 
think I agree with Mike that the most important critieria -- given that 
several algorithms are about equally good -- is simplicity and 
transparency, so that it can be explained to ordinary voters (and 
politicians!)

I've come up with an algorithm which is similar to MAM and SSD, and 
easy to implement (and I hope explain) but I'm not sure if its 
identical, or has the same beneficial properties. I call it 
LeastSchwartzBeat. Perhaps someone here could help me analyze it.

The basic steps are:

1.   Calculate the pairwise 'beats' between each pair of candidates

2.  Identify a 'least beaten' candidate (L)
- The one with the greatest number of wins
- If several have the same # of wins, pick the one which beats the 
others
- If several with the same # of wins form an internally unbeaten cycle, 
pick one at random

3.  Collect all candidates which recursively beat L
- e.g., if A & B beat L, C beats A, F & G beat B, and  C, F & G are 
beaten by L, then the set = A, B, C, F, G, L
- I believe this is identical to the Schwartz set - is that correct?

4.  If L is the only member, that's the Condorcet winner, and the 
algorithm ends.  Otherwise:

5.  For each candidate in the Schwartz set, calculate his/her lowest 
beat against other members of the Schwartz set (LeastSchwartzBeat, or 
LSB)

6.  The candidate with the highest LSB in absolute votes is the winner. 
  If there's a tie in absolute votes, compare relative votes.    If 
still tied, compare the Next Least Schwartz Beat, etc.  If all their 
beats are equal, declare a tie.

While the terminology might be a little confusing, this would be easy 
to demonstrate graphically, and to even calculate manually (given the 
Condorcet matrix, and a reasonably small Schwartz set).   I think it 
would seem intuitively reasonable to most people,

I have a suspicion this is close to RP (or MAM), in that  you are 
effectively locking the first candidate to get all four beats.  The 
only area where I think it differs is how it handles 'inner loops' 
within the Schwartz set, but I'm not sure how much that matters.

Can anyone help me figure this out?

Thanks,
- Ernie P.
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