What's the running joke about "well, I didn't vote for president Steady Freddy"? All I can think of is that he lost the election but jiggered the results...? Because surely somebody had to vote for him if he's president now, right?
If Beta Colony has some type of ranked preferential voting system, they might not have, especially if they've got multiple major parties. If, say, 20% of the public wanted candidate A, but would rather have Steady Freddy than candidates B,C, D, or E, and another 20% feels the same way about each of the other preferred candidates, then you wind up with a situation where no one's first choice has enough votes to win, so all the votes get punted to second choice, and you get a guy that no one likes, but everyone hates less than the people it could have been, and they all really voted for candidates A,B,C,D and E, not this jerk who's actually president.
The dust-up that got Ensign Corbeau and his prejudiced fellow-soldiers arrested is said to have happened in Garnet Five's living quarters. Later Corbeau comments that he didn't start fighting till the other soldiers dumped Garnet Five out of her float chair. Therefore the fight happened on the artificial-gravity side of the station; quaddies don't use float chairs in free-fall nor could anyone be "dumped" out of one without gravity. But why on Graf Station does a quaddie dancer have living quarters on the gravity side?
"Dumped out of her chair" probably means "thrown out of the chair". Alternately, floatsider rooms can have gravity if desired, and Garnet turned it on to be nice to Corbeau.
If she was in her chair in the first place then that almost certainly means there was gravity and it was turned on. As previously mentioned, quaddies don't need float chairs in zero-G.
In quaddie culture, each person has only a first name, plus a number if their name is popular enough to have been chosen by others (eg. Garnet Five, Leo Ninety-Nine.) The names all sound like first names from some culture or other (Garnet, Pramod, Teris, Leo) except the names of the quaddie authorities Miles meets, which are given with their titles and sound very much like last names: Sealer Greenlaw, Adjudicator Leutwyn, and Boss Watts. What happened here: did some quaddie moms really give their kids the names Greenlaw, Leutwyn and Watts, are the "last names" an oversight on Bujold's part, or is there some other explanation?
Presumably yes. We know quaddies name themselves after their historical heroes, maybe "Greenlaw" was a particularly heroic downsider.