So I've made two assumptions about the NIV(Night Investigation Vote)
1) The investigator is at the mercy of the NIVs, based on the rule, "A Draw will give the investigator the posibility to choose his target freely, between the persons who got the most votes." If this isn't the case then there's really not much harm in speaking about who people should NIV for.
2) Mafia also have NIVs, based on the rule, "Missusing the nighttime investigation vote may result in losing the ability to vote, the investigator losing his investigative Ability or Mafia manipulating the vote completely." It certainly is possible they have no vote or only one collective vote, so I'll list the pros and cons for each scenario:
A) Mafia each get a NIV:
If there's no discussion then it is fairly likely that they can completely manipulate the vote already, agree on a target to vote for and also kill said target, thereby wasting the investigation.(unless a doc gets lucky and guesses the same target)
If we choose a single target and most townies actually go along with it, then mafia can't control the vote and town will decide who is investigated. Mafia could simply kill the target,(if Town of course) but a doc could also protect him. It becomes WIFOM of scum chancing a doc save or doc gambling on protecting someone not chosen.
If we choose a small pool of targets, then mafia can try to control the vote, but it isn't a certainty they will be able to. They can pool votes and try to kill their chosen target, but they may end up chosing wrong AND hitting the doc's chosen save, which would "confirm" the alignment of two players at once.
B) Mafia get a single NIV:
No discussion then there's no real drawback.(Compared to your typical cop choosing for themselves)
Same as above if we choose a single target.
Similar to above if we choose a small pool, but they'd have an even smaller chance of controlling the vote.
C) Mafia get no NIV:
No drawback for no discussion.
Still just WIFOM.
No chance of controlling vote and better odds of "confirming" two players if mafia try to eliminate someone in the pool.
Addressing Wonk&Vette's Points: http://gamrconnect.vgchartz.com/post.php?id=4328770
1. Vette's what if scenario has no relevance. The investigator can wish to scan one person all he wants, but it seems to be out of his hands unless there's a tie including that person. Discussing our choices or not has zero bearing on this.
2. Doc-fear is for scum to worry about. As Wonk just said, unless it is known that there isn't protection, then scum must worry about their kill potentially not going through.
3. As I show above, the number of NIVs that mafia has doesn't really change the optimal strategy. It would be a pretty broken mechanic if there are 3 mafia and they all have a NIV, but that's a matter of post-game discussion.
So, 2-man pool as Wonk suggests or 3-man? I'm thinking 2 is good if we no lynch or mislynch, but 3 is better if mafia is lynched since they'd have less control in the event that each gets a NIV.