It's not very scientific. Perhaps, "Fair Chance Democratic Choice" would be better, though still not taxonomically descriptive.
I don't think it has quite enough randomness in it for the tough examples.
Here's how we might change it:
Use a random approval ballot order in place of the approval order.
[Thanks to you for that idea in your Chain Climbing post.]
Then when the pairwise defeat agrees with the random approval ballot order, instead of calling it a "strong defeat" call it a "confirmed defeat."
From there on everything else is the same; the set of candidates withoutconfirmed defeats form a chain P whose pairwise order is the exact opposite of the random approval ballot order.
We choose from P either by (ordinary) random ballot or by (another) set of random approval ballots, how ever many it takes to determine a winner.
Forest ---- Election-methods mailing list - see http://electorama.com/em for list info
