Condorcet methods are frequently more computationally complex. Schultz is O(n3) and RP is O(n4).

We must note the categorical aspect here. Ordinal is a class of voting, not a specific one. Condorcet is a class of ordinal methods (that optimize the condorcet criteria) but not a specific method. You're right that this isn't true for all methods but I'm mentioning these specific methods because they are the ones that are better and commonly discussed. Unfortunately we can't just look at one aspect of a voting method to rule it in or out.

Ah when you mention parallelizing I was assuming you were referring to the issue of requiring that ballots all be centralized in order to tally them for IRV, rather than summing at each precinct individually. The data that has to be in a central location for a condorcet method would only be O(n2) since it's just computed from the h2h table, I was not trying to discuss the complexity of actually computing the final results.

Well cardinal methods could easily be calculated in a distributed manner. And complexity of computing the final results is quite important. It is an important part of what the entire thread is about.

Yes you're correct. but cardinal methods are just generally better all around.