Sorry it's taken me so long to get to this.
Heads of House (Masters, Presidents, Mistresses, Wardens, Provosts - there's a lot of words for the same job!) don't get involved in Admissions decisions. Who to take from the Pool is a decision made by the Admissions Tutor and Director(s) of Studies. The way it usually works is that, depending on how many students the college is looking for and how big the pool is, the Director(s) of Studies and any Fellows helping them will spend anything up to a couple of days reading files of applicants who are in the Pool. Then before the poolside meeting, the Director of Studies and the Admissions Tutor will discuss the list. The Admissions Tutor will often be able to provide a steer (e.g. how the college is doing for numbers overall or in sciences vs arts, which might have an impact on how many offers they can make in a particular subject) and provide advice.
Groups of Directors of Studies might discuss Pool files together. Some might be looking for fewer students than others and might therefore recommend some to colleagues, if they know they won't have space ot make an offer. If they are looking for the same characteristics (some colleges might place more emphasis on certain parts of the application), then this porcess can work really well. Some Directors of Studies prefer to work alone, only speaking to colleagues when they have a question about a file. It's really just a question of preferred practice.
Hope this helps!