Realistically, how many copies of a book does a publisher give away for possible reviews? Does the author have any say or input in these decisions?
And the definitive answer is: it depends.
It depends on the type of book (fiction vs non-fiction), the genre, the initial buzz and excitement about the book, the budget, how many copies we printed in the first print run, the number of reviewers we have a positive relationship with, the number and size of papers/local magazines in the authors home town, when the book is released (near Christmas or other related holidays or events), how much energy the author is going to put into promoting the book, what kind of mood the marketing department is in, whether it's raining outside,...
The author may or may not have a say in it. We make up our list and if the author wants us to add to it, they have to make a good argument for it. For example, let's say the author lives in Kaysville, UT. We would send review copies to the Salt Lake City papers. If the author wanted us to send a review copy to his/her local Kaysville paper, we'd probably decline, UNLESS a bookstore in Kaysville was going to do a launch party/signing for the author and the paper was agreed to do a timely and positive review in connection with that launch.
Another issue we have with review copies is when authors want us to send them to bloggers. (I'm not talking about online reviewers, such as Jennie Hansen at Meridian. I'm talking about non-professional bloggers.) We only consider this if the blog is targeted to our audience (LDS readers) AND if they get a respectable number of hits per day AND if we get pre-approval/kill vote on the post.
If an author wants to send the book to more reviewers than we're willing to send to, they're always free to do so using their own comp copies.