For the Republic, Part 2 is active and the player reports back to Colonel Moore that Mr. House has been killed or disconnected from his mainframe.

The House Always Wins, part V is active, and the player reports back to Mr. House that the Brotherhood of Steel bunker has been wiped out.

Wild Card: Change in Management is active and the player installs Yes Man into the Lucky 38 mainframe.

1 point for traveling with Arcade to the Crashed Vertibird. (The approval doesn't increase until Arcade comments on it.)

1 point for traveling with Arcade into the REPCONN Headquarters building. (The approval doesn't increase until Arcade comments on the company.)
Traveling to The Fort with Arcade triggers a dialogue with Arcade inquiring why they are there.
2 points for saying, "Let's just listen to him, figure out what he's up to, and get out."
1 point for saying, "I just want to hear Caesar out."
1 point for saying, "With how messed up New Vegas is, do you really think Caesar has nothing to offer?", followed by, "I'm just trying to be open-minded."

Speaking to Thomas Hildern about anything at all (any conversation that ends with Hildern saying, "Yes...Goodbye." or "Wrong turn?...") with Arcade along will cause Arcade to start a conversation afterwards about Hildern and his motives (one time).
2 points for saying, "Good thing there are still people like you around."
1 point for saying, "I'm sure he means well."

During the quest That Lucky Old Sun, when the player gets to the mainframe, Arcade will spontaneously suggest that the power should be directed to Fremont and Westside.
1 point for saying, "Of course."
1 point for saying, "Why not to the whole area equally?", then passing an intelligence check of 7, saying, "Redundancy. If Caesar takes the dam and cuts off power, it will be chaos all over New Vegas." when Arcade asks why.
Note that it is not necessary for the player to do what Arcade wants; the trigger is the pre-diversion dialogue, not the action of diverting the power.

There are several triggers associated with the quest The White Wash:
1 point for saying, "If you say so. I'm not arguing." when Arcade mentions that he's heard about Anderson, if the player visits Westside with him after having already completed The White Wash without him along.
2 points for completing The White Wash by blaming the problem on the Scorpions and letting Tom Anderson go. (The approval doesn't increase until Arcade comments on it.)
1 point for completing The White Wash by getting Tom Anderson to turn himself in with a fake story about fighting over Dazzle, but letting Westside Co-op continue to have the water. (The approval doesn't increase until Arcade comments on it.)
1 point for passing an intelligence check of 7, saying, "You're assuming a motive without evidence. Please be rational." when Arcade gets mad about killing Tom Anderson at the end of The White Wash. (Obviously, this only happens if the player kills Tom Anderson.)
1 point for saying, "It's cleaner this way, without bringing NCR in. No connecting Anderson back to the locals." in answer to Arcade's followup question to the above, asking why the player killed Anderson.