To clarify the "keeping the choice with the majority", take this example:
every townie votes for a different person with no clear majority. The mafia all vote for one person of their choice, making him the investigation, and then killing him.
In this way, the mafia know exactly who will be copped, and kill him, as opposed to doc, who really gains no advantage over any regular game.
So, with discussion, we at least KNOW who has a good chance of being copped, giving the doc an advantage, and making the mafia decide on killing that person or not out of fear of protection and losing the night kill.
That's the benefit, as I see it. However, this advantage is not as clear as it appears. If the mafia simply go after someone else, then it's basically a typical mafia game with no advantage on either side?
The thing we need to discuss is to who would discussion benefit most, and how to swing the benefit into town territory.