In The Son of Neptune, we see that Nico di Angelo, as the 'Ambassador of Pluto', joins in the Senate's meetings:
Reyna and Octavian led the procession of senators out of camp, with Reyna's metal greyhounds dashing back and forth along the road. Hazel, Frank and Percy trailed behind. Percy noticed Nico di Angelo in the group, wearing a black toga and talking with Gwen, who looked a little pale but surprisingly good considering she'd been dead the night before.
The senators passed through easily. The statue checked the tattoos on their forearms and called each senator by name.
"Gwendolyn, senator, Fifth Cohort, yes. Nico di Angelo, ambassador of Pluto - very well. Reyna, praetor, of course. Hank, senator, Third Cohort - oh, nice shoes, Hank! Ah, who have we here?"
The Heroes of Olympus, book 2: The Son of Neptune, chapter 13
Why does Nico come to the meetings? He's not a senator, he's not even always at Camp Jupiter. Why is he allowed to take part in the running of the camp like this?