How does rationality amplify the persuasion theme in Jane Austen's novel, Persuasion?

Throughout Persuasion, Anne Elliot
observes just how irrational others are around her,
regardless of how rational the characters think they are. We especially
see rationality, or irrationality, played out in
Lady Russell's opinions of whom Anne should and should not
marry. Anne admires Lady Russell as a very wise friend and good counselor, even though
she repeatedly proves herself to be prejudicial. It was Lady Russell's prejudicial
perspectives that persuaded Anne to reject Captain Wentworth in the past, just as she is
trying to persuade Anne in the present. However, Lady Russell rationalizes her
prejudicial beliefs on her analysis of a person's character, showing us that
rationality, or lack of it, is a major part of the
persuasion theme, amplifying the theme by showing how
others try to persuade based on rationality. Instead, Lady
Russell's beliefs are proved to be ill-founded, or
irrational.

Lady Russell judged Captain
Wentworth to be a poor match for Anne, not just because he had no wealth
or wealthy connections, but because, even though he had already earned a lot in his Navy
career, he had also already spent it. She believed it was a sign that he was impetuous
and not to be trusted, as we see in the line, "[Captain Wentworth] had been lucky in his
profession; but spending freely, what had come freely, had realized nothing," meaning
saved nothing, and again later in the line, "[Lady Russell] had been too quick in
suspecting [his character traits] to indicate a character of dangerous impetuosity" (Ch.
4; Ch.24). However, now that Captain Wentworth has returned with a substantial fortune
and a great deal of praise and admiration, she is forced to realize that she judged him
incorrectly, showing us that what she felt was her rationalization for persuading Anne
not to marry him was actually very incorrect, even prejudiced and
irrational.

In addition, Lady Russell
also judged Mr. Elliot, Anne's cousin, to be an excellent match for her.
He was believed to still be wealthy and was also found to have excellent manners, which
she felt showed he had an excellent character. His manners are seen when he reconciles
himself with Sir Walter Elliot, whom he had offended by not courting Elizabeth and
marrying someone else. However, Mr. Elliot is now very open and friendly with Sir Walter
and has apologized for the past, so much so that Sir Walter has readily forgiven him.
Even Lady Russell is impressed with Mr. Elliot's manners. However, Anne is suspicious.
She believes there must be an ulterior motive for Mr. Elliot wanting to re-establish
himself in the Elliot family. Later it is discovered that Elliot has only re-established
connections with the Elliot family and begun courting Anne because he is determined to
keep his Kellynch Hall inheritance and become
the next Sir Elliot. However, Sir Walter is presently being pursued by
the designing Mrs. Clay, and should she marry Sir Walter, they could produce the next
heir together, rather than it being passed down to Mr. Elliot. Therefore Mr. Elliot's
design in courting Anne is to both secure Anne's fortune while allowing himself to get
close enough to Mrs. Clay that he can intervene in her schemes. Not only is Mr. Elliot
proved to be conniving, he is also proved to be a "disingenuous, artificial, worldly
man" (Ch. 21). Therefore, Lady Russell is proved to be wrong about Mr. Elliot as well,
showing once again that her rationalization for her persuasion is based on
prejudice.