Chakotay approached the hat with equanimity, as he did most things. He opened his mind to the probing.
"Hm, a caring, compassionate nature, a good listener, deeply spiritual—but a leader too, interesting. Not very fierce, though brave, intelligent, but you're very trusting, so…HUFFLEPUFF!
The Doctor remodulated his holographic matrix so it would be solid enough to support the hat, then sat down on the stool and put it on.
Expecting a litany of his good traits, the Doctor was surprised when the hat nearly screamed, falling off his head. With mechanical reflexes, the Doctor caught it.
"What's wrong?" he asked, looking down at the quivering black fabric in his holographic hand.
"I can't read you!" it exclaimed. "You're not really there!"
"You're talking to me, aren't you?" the Doctor replied irritably. "Photons and forcefields, flesh and blood, what does it matter?"
"It matters because I can't Sort you!" it wailed. "I've never had this problem before!"
"Why don't you let me choose, if you're so stressed?" the Doctor suggested.
"Go ahead," the hat sighed.
"I'll wait until after all my friends are Sorted," the hologram said cheerfully.
The hat sighed again, and the Doctor set it back down.
"Seven of Nine," the ex-Borg corrected, then sat down and put the hat on.
"I have researched the Hogwarts houses and have concluded that I am a Ravenclaw," she informed the hat. "Put me there."
"If you are Ravenclaw, I will put you there," the hat assured her. "But I do the Sorting. Hm…Ravenclaw is a good pick you are extremely intelligent, scientific and curious, and you did your research to pick it—very Ravenclaw."
"It is inefficient to continue, since it is obvious I am correct."
"Patience!" the hat cried. "I've encountered a part of your brain that is distinctly Slytherin…in fact, it's trying to attack me…"
"Those are Borg nanoprobes. They are attempting to assimilate you."
"I can fight them off…hm…a desire for perfection, a need for efficiency, and a willingness to eliminate those who impede it. Very clever, a disregard for rules that do not suit you…yes, I think you would be best for—"
"I noted the merits of Slytherin in my search, but I did not want to share a house with Dark wizards and witches," Seven interrupted. "I am Ravenclaw."
"Well, I do take choices into account…" the hat mused. "… and you're not a bad fit anyway, so…RAVENCLAW!"
A/N There will be three more chapters with three Sortings each, alphabetical order by last name. Reviews are nice, especially if you have an opinion about what houses characters should be in.