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Currently, designated-reviewer processing happens after business-role processing, so it will take precedence over automatic assignment that happen because of business roles.
Automatic assignment to resource owners takes precedence over designated reviewer assignments.
Review-delegate processing happens last of all. So if, for instance, a user’s designated reviewer has a review delegate, the review will go to the designated reviewer’s review delegate.
One exception to the above: if the review delegate happens to be the person whose permission is being reviewed, and the campaign has a setting forbidding self-review, that setting will be honored.