C

I recently read more about the class of "improved" Condorcet methods. Which use the tied at the top rule to redefine the notion of a Condorcet winner. It is claimed that this fixes favorite betrayal and possibly the chicken dilemma, while also being close to Condorcet methods.
This seems promising, so I wonder why there isn't much talk about them. Even from a practial viewpoint they are easier to explain than for example Schulze, or Smith//score.
In particular I am talking about Improved Condorcet Approval and Symmetrical Improved-Condorcet-Top.
The first article also describes a variant:
The above definition defines t[a,b] to be the number of voters tying a and b in the top position. ... However, it might be more intuitive, and preferred, if t[a,b] were defined rather as the number of voters ranking a equal to b and explicitly voting for both.
Why would that be preferred? And does this only work when explicitly ranking/approving both, or also for bottom ranks? In that case one could state the rule as just: "A candidate is unbeaten if there is no other candidate that is ranked higher by more than half of all voters." Which also would be easier to calculate and visualize.
Is there any reason not to extend ICA to ICscore using a rated ballot? ICscore could then be easily explained as "Rate all candidates on a scale from 0 to 5. Remove all candidates where some other candidate is preferred by more than half of voters. Of the remaining, elect the one with highest score."