How does Jane Austen show a preference for strong females in Pride and Predjudice?
This is a fascinating question, made all the more interesting because I disagree with it. I assume that you would explain "preference" by saying that the text makes clear Austen thinks favourably about the strong female characters in this book. Whilst I think you are perfectly correct about Elizabeth Bennet and the way that the author obviously shows a preference for her, I would disagree with the presentation of other strong female characters, most notably Miss Caroline Bingley and Lady Catherine de Bourgh, who are clearly strong female characters but also not presented favourably in the text. Consider, for example, the way she tries to turn Mr. Darcy against Lizzie and thereby advance her own position:
She often tried to provoke Darcy into disliking her guest by talking of their supposed marriage, and planning his happiness in such an alliance.
Clearly such mean behaviour does not indicate that a character such as Caroline Bingley has a firm place in the affections of Jane Austen. In addition, consider the way that Lady Catherine de Bourgh takes Lizzie to task for the supposed alliance that exists between her and her nephew. Both of these strong ladies are therefore not shown in the most flattering of lights. Lastly, you might like to consider the way in which female characters who are not strong are presented in a better light than these strong female characters, such as Jane and Georgiana Darcy.
The question of, "How does Jane Austen show a preference for strong females in Pride and Prejudice?" has an in-depth answer. The author's design was to create emotionally, morally, and physically capable female characters, which would have gone against the typical expectations for females in her day.
In Austen's other works, we see other strong female characters, such as Elinor and Marianne in Sense and Sensibility, who carry the story as they brave difficult decisions. Elizabeth Bennet is a similar character. Elizabeth, although not from the most esteemed family in her region, manages to help her sister and herself remain dignified, although scoffed at, scorned, and eventually confronted by those who consider themselves her betters.
Austen shows her preference for these characters by having Jane and Elizabeth prevail at the end of the story when their refusal to be brought down to the level of the malicious Lady Catherine's and Miss Bingley's schemes to separate them from the men that they would marry by the end of the story. The two young women each have their own manner of strength - Jane in her patient manner and will to move on and Elizabeth in the way she is unafraid of confronting others with the truth.
The author also demonstrates a lack of favorable portrayal when it comes to the mother and the three younger daughters of the Bennet family. Their silly, wanton, and often morally ambiguous decisions show them to be less than dignified.
The fact that the heroines of Pride and Prejudice are women of character and are willing to forgive those who have hurt them, shows a deep strength, as they are portrayed as admirable and they ultimately wind up with the two men in the story who themselves show a strength of character and with a far greater fortune than their sister, Lydia, who runs off with a man known for having less than desirable intentions on women.