@psephomancy Just to add a bit more to this then - It's quite difficult to come up with the Condorcetness of a winner. Different Condorcet methods have different ways of determining a winner, so when there isn't a Condorcet winner, they can pick different winners. But by their own measure you'd say that they are picking the "most Condorcet" winner.
For example, you talk about the number of pairwise defeats. That's basically Copeland's Method, so would consider the Copeland winner to be the most Condorcet, but it fails independence of clones, and is generally not considered to be great from a theoretical point of view.
Similarly there's Minimax, which elects the candidate that has the smallest pairwise defeat (if there isn't a Condorcet winner). So your measure would be based on the size of the winner's worst single pairwise result. But this also fails independence of clones, among other criteria.
Then you have methods like Ranked Pairs and Schulze, which are known for their criterion compliance. However, candidates don't end up with a score that can be compared with the score of the best winner.
But we can perhaps use the Game Theory method, which I previously described as the ultimate in Condorcet. When there isn't a Condorcet winner, it is non-deterministic and picks between certain candidates with certain probabilities. But no strategy can beat it in the long term by the measure they are using (which I think is average pairwise win/loss).
So a method picks a winner, and you compare that winner against the Condorcet winner to see the pairwise result (which is just a draw if they are the same candidate). If there isn't a Condorcet winner, you compare the method winner against the Game Theory strategy overall. So if under the Game Theory method candidate A wins 50% of the time, B 40% and C 10%, you just looked at the weighted average result against these candidates.
So you now have this pairwise result. Say it's the margin of defeat or just 0 if it is the Condorcet winner. To turn it into the Pairwise Ranking Efficiency measure in the same way as the utility version, take the difference between that and the average defeat (use the positive value if better, negative if worse) and just divide by the average margin of defeat against the Condorcet winner (or lottery profile).
For example, candidate A wins by some method. But A is not the Condorcet winner and is beaten by a margin of 10 votes by the Condorcet winner. The average margin of defeat against the Condorcet winner for a candidate is 30 votes. So the PRE is (30-10)/30 = 2/3.
An alternative would be to use median margin of defeat rather than mean.