Yes, in theory you should keep the ones who have no chance of winning, to boost your chance of winning. However, for me, some things trump that. I would vote for Lawson and Cat because they disgust me and I wouldn't want to share my time with them.
And, this year is ridiculous anyway, so strategy doesn't really matter. The HOH's power has been pretty much a waste of time. People are getting money, left and right, and I expect that to continue. So, the final prize money means less and less. Because there is no rhyme or reason, to the season, other than the network wanting it to end ASAP, I'd just nominate who I don't want to live with. And, if I'm morally opposed to something, that person is going up, no question about it. In fact, nominating someone for questionable behavior, could very well ingratiate you to the public.
And, this year is ridiculous anyway, so strategy doesn't really matter. The HOH's power has been pretty much a waste of time. People are getting money, left and right, and I expect that to continue. So, the final prize money means less and less. Because there is no rhyme or reason, to the season, other than the network wanting it to end ASAP, I'd just nominate who I don't want to live with. And, if I'm morally opposed to something, that person is going up, no question about it. In fact, nominating someone for questionable behavior, could very well ingratiate you to the public.