The premise of the old Marvel comic WHAT IF? is one I like to sometimes ponder in regard to novels. In other words, how would the outcome of the story be different if some different choice had been made, or some outcome differed, at a pivotal point in the narrative?
During my current reread of the earlier volumes of the series, in preparation for eventually reading the newest volume, that thought came to mind after I read Chapter 38 of A CLASH OF KINGS (vol. 2 of A Song of Fire and Ice). In that chapter, Arya is furious with the thuggish steward of Harrenhall, Weese, so when she finds Jaquen H'ghar, she whispers Weese's name. True to H'ghar's promise to give Arya three deaths of her choice in exchange for her having saved himself, Rorge and Biter from dying in a fire, he quickly dispatches Weese. Right before Weese's death, though, as Tywin Lannister, Gregor Clegane and leave Harrenhall to give battle to Robb Stark, Arya regrets having named someone so petty as Weese, or her earlier choice, Chiswyck, instead of someone of real importance from her "revenge list," such as Gregor Clegane or Lord Tywin. She goes to try to find H'ghar and change the assignment, but she is too late and comes upon Weese's demise.
So, the question is, how might the narrative have been substantially different from that point forward had Arya made a different choice in the first place, and named Tywin Lannister as H'ghar's next victim? How would that have impacted the military events? Or the political? For example, Tyrion's authority as Hand flowed directly from Lord Tywin, so with Tywin gone, Cersei would have been able to push Tyrion out of power, or at least to the sidelines, and done what she wanted with relative impunity. Do you think she would have done so? How might that have impacted the smallfolk's perception of the Lannisters? Or the defense of King's Landing against Stannis? What else might have happened from that crucial point in the story due to Lord Tywin's earlier demise?