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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