My take on what's going on:
Trump probably likes to enter a meeting with, say, 5 other people, with a list of candidates for any position he has. That list probably has around 20 names on it.
He then probably asks each of the 5 people he's meeting with to "veto" one of them and "boost" one of them. (This would give them a +1 or -1 point score) and if anyone has negative points, they are removed from the list.
I figure he then goes over anyone with a score of 0, makes that the new list, and goes around the table again, and if needed, again and again until he only has people left who have a positive score.
This should be a list roughly half the size, or 10 people.
Then - and again, this is all just guessing based on how he acts - I'd say he asks each person in the group to give 5 people a "boost" and 5 people a "veto"
Then he would ask the 5 people around the table if they are willing to "champion" any one of the candidates, and finds 5 candidates (ideally all those with positive scores from the last round) and each advisor champions one of them.
Then and only then do I think he bothers to ask anyone their thoughts. (Before now being simply yes/no answers and numbers)
Then I figure they hold a little mock debate, where each of the 5 advisors tries to "sell" trump on the candidate they are championing.
Then I figure he asks the advisors to vote on which person they'd pick except for their own champion. Then he takes the top two from this result, maybe the top three in some cases.
(at this point the meeting is halfway over)
Then he holds a long discussion about these top two candidates, asking for pros and cons and all sorts of stuff like that.
Then once that is over, he decides, himself, without a final vote, who his choice is.
(I figure this is where things went sideways picking the veep, they when it came to this point in time, he went with christie, but they kept hammering pence, who they wanted, until he broke)