When you do a binary arithmetic operation, one of the things that dictates whether the left-hand side's __*__ method is called before the right-hand side's __r*__ method is if the left-hand side's __r*__ differs (there's also the fact __r*__ methods are not called if. the types are the same). Presumably this is because you only care about giving precedence to the right-hand side when it would actually matter due to a difference in implementation (with the assumption that there isn't a specific need to get the right-hand side special dispensation to participate in the operation). But with rich comparisons there doesn't seem to be an equivalent check for a difference in method implementation. Why is that? Is it because we don't want to assume that if someone bothered to implement both __gt__ and __lt__ that they would not necessarily be the inverse of each other like __add__ and __radd__?