@Janie44, what are your booking settings? If you don't have Instant Book turned on, they won't be able to book without sending a request (in which case you decline). If you do have it on, make sure your IB criteria is set to only allow guests with previous recommendations from other hosts to book.
I always thought that if you click "No, you would not recommend them" that they will not be able to automatically book with you again. I always click no as if to reassure myself that they will not be back.
This has changed recently, and now regardless of what your booking settings are, if when you come to step 6 with the heading "Would you recommend this guest" and you check the NO box, the guest will be prevented from, using Instant Book to book your property again. They will still be able to message you and send you a reservation request (which you can handle in any way you see fit) but, they won't be able to sneak a booking in on you again! You will need to approve a future stay!
And because the system recognises you have previously stated you would not recommend this guest a decline will have no affect on your stats!
Recommending to other hosts and wanting to host the guest again are two different things in my mind. We had two recent guests were were fine, but they had a bit higher expectations for what our "simple room" booking had to offer. My husband and I call them "hotel people." Anyway, I'd recommend them to hosts that have a higher end offering, maybe a separate space entirely instead of a guestroom in a house (like ours), but personally, we don't want to host them again.
Does anyone know how selecting NO to "would you host this guest again?" affect their stats or our stats? I kind of thought maybe it's just a data thing for airbnb to see the statistics behind people who would reocmmend a guest vs host them again vs the star reviews they leave for the guest. In our case, there was really no reason to leave less than 5 stars to the questions that airbnb asked...