Well, at the end, I feel the best job of persuasion was done by Anne, of all people, persuading Captain Wentworth that he still hand grounds for hope. And in a very harsh condition, while talking to someone else, with umpteen other people listening.

"Poor Fanny! she would not have forgotten him so soon!"

"No," replied Anne, in a low, feeling voice, "that, I can easily believe."

...
All the privilege I claim for my own sex (it is not a very enviable one: you need not covet it), is that of loving longest, when existence or when hope is gone!"

And yet, these are not logical, rational arguments, that my 7th form history teacher would have accepted. Anne does not cite a dozen studies to prove that women have loved longest, when existance or when hope is gone! Persuasion is maybe not rational, but works on the emotions of the best of us as much as the reason. The difference between the best and the worst is that of our emotions - that Anne and Frank are moved by the emotions of others, while Elizabeth and Sir Walter moved by appeals to their vanity. One could hardly see Sir Walter being moved by such a speech as Anne's.

It is indicative perhaps of the complexity of JA's thought that even at the end Anne does not think her decision, persuaded by Lady Russell, was completely wrong: "I have been thinking over the past, and trying impartially to judge of the right and wrong, I mean with regard to myself; and I must believe that I was right, much as I suffered from it, that I was perfectly right in being guided by the friend whom you will love better than you do now. I think, after reading the novel, JA saw a lot of value in persuasion. By persuasion, Elizabeth and Sir Walter are led to retrench. Through lack of persuasion, Lousia Musgrove is dangerously wounded. And even Anne cannot condemn the initial act of persausion, though it may be the source of her problems.