I'm going to refuse a girl I like because of her past dating decisions
Why are you refusing her based on her past?
I just think dating a bad person is a bad idea.
If you think the relationship would be bad for you, it's best to avoid it. However, you should be sure to be open and honest with her about it, everyone has feelings.
It's also bad to be in a relationship with a cheater.
Judging someone based on who they were will stop you from getting to know who they are. Everyone  has a past, but we are all capable of changing and becoming a better person.