What is a word that describes a "mutual switch"?

Basically I am writing an essay that defines blame according to two specific pieces of literature. I discuss whether the author's main character is to blame according to their respective author and then proceed to discuss whether the other author would assign blame to the other book's character. Of course I define blame and all that good stuff as well.

Poorly worded thesis:

in this essay I will define whether author X would assign blame to character A, whether author Y would assign blame to character B, "and then ?invert? these definitions to determine the blame of character's A and B according to the other author." (need help with the part in quotation especially the word in question marks)

poorly worded, I can only go up from here, but I hope you get the point. Honestly any words to expand my vocabulary on an essay like this would be appreciated.