All I can say is THANK YOU. I've argued this point before with certain people in this community, who don't seem to understand this. Veronica is the least sympathetic of the Carnations for this reason - other than Lucy, as you also pointed out, but I guess she's half a Carnation?
Well, thank you too! When it comes to who of the Carnations needs the win the most, I agree with you it is Rosi. Who is in dire straits without being responsible for the mess she is in.
Followed by Felicia, who is in the competition for gaining personal influence, but it is obvious that she wants to use this influence to help others too. Like rebuilding the school in her hometown. As I mentioned before, a win by Felicia, if you have a good rapport/freindship with her, might be the best for all, since she could help the other Carnations with it.
Next is Veronica for reasons already stated before.
Last is Lucy for reasons likewise mentioned earlier. But I would not call her scum. While Lucy has the worst reason for participating, just gaining entrance to an elite school for her kid without a pressing need to do so, it seems the slimy school director just waited for someone he felt would be wanting access to the school so much, she fell for the competition. He might even have undervalued Lucy´s son´s grades to push her into this position. Still, even in this hypothetical case, Lucy fell for this game because of some selfish desire, which remains the weakest reason for being in the Club.