Wow this is really a tough one. The think Amy has to be PM this next time - otherwise she could be faulted for not wanting to lead like Heidi.
So if Troy and Kwame do pick her, and she is PM, and they win ... it will solidify the opinion that she is the very best because she was largely responsible for the rickshaw win. Bill and Troy would then be on even footing for second place.
But if Troy and Kwame pick her and they lose ... it will be Amy's first loss and it will solidify the opinion that Troy is not as good as Bill.
If Troy and Kwame pick Katrina and she is PM - she will be nice to them because she is the leader and leaders always have to be good to their troops. In this case, if they win, Troy will look better than Bill; Amy's first loss will help solidify this opinion.
Yet if Troy loses with Katrina and she is PM - she or Kwame will be the one to go.
So, therefore, I think they should pick Katrina and let her be PM. That way they will surely survive.