Do you live in the property? Bad behavior happens more often in properties where the guest lets themself in and the property owner is out of town, and there are a group of unrelated people (from what I've read here). You can have the guest sign a liability contract, but if the guest is not of "legal" age, they cannot be held responsible financially for any losses you may incur. Unfortunately, Airbnb does not even charge any security deposit that you may set for your property, until after a problem is reported, so the guest doesn't even have the potential loss of their security deposit to deter bad behavior. With all the mention of loss that is on the website, where hosts are not compensated, guests may not worry at all about their security deposit.
If the security deposit could be collected by the host, paid upon arrival, I suspect more guests would be careful about how they treat the property. That was how another website I worked with handled the deposit and I had no noticible damage for 3 years. But you don't have that option here.
Airbnb says a host can decline a request of they are "uncomfortable" with a potential booking. I'd go with my gut on this one.
However, if I had the chance to meet the guests and talk to them about my concerns via Skype where we could "meet" face to face, and my house rules were such that no one else could go into the property without my written permission, and I received agreement from the guests to abide by the rules, I might give them a chance to create a positive review for themselves on Airbnb. However that is also impossible to do on Airbnb unless the booking is accepted.