Roy and Irmgard Baty are perhaps the most functional couple in the novel, and that's really saying something when you consider that they're two Martian androids on the lam who have no qualms over a little murder and torture.
Roy and Irmgard escaped with the other eight androids, but that's about all we know for sure. Pris said they ran a drugstore on Mars, but this may have been a lie (13.37). Either way, Roy became the group's leader, and he and Irmgard show up at Isidore's apartment to hide out with Pris and prepare for the confrontation with Rick.
Roy is the big boss of the androids. If this were a video game, he'd be the guy waiting at the end of the level with a health bar extending the entire screen.
He's intelligent and brutal, and maybe the most android of the androids. By that we mean his intelligence is mechanical and calculating, taking no account of others in its equations. Without empathy, he doesn't worry about how his actions will hurt others, only how they'll affect him.
We can see Roy's self-centered survival instinct when the group is trying to decide what to do with Isidore. When it comes time to vote, Roy simply says, "I vote we kill Mr. Isidore and hide somewhere else" (15.3). He's not even embarrassed that Isidore is listening to them discuss the matter. It's so matter of fact it would make a mafia hitman blush. But not Roy. Isidore poses a potential threat to his survival, so the guy has got to go.
As if that weren't enough, Roy also sets up a security system that uses a Penfield mood organ that induces panic in organic life, including Isidore (14.67). He explains it'll put Isidore at risk but provide them with cover (14.70). (And you thought living with your parents was awful.)
Well hello there, mechanical sociopath.
Isidore glimpses his mechanical nature during a mild hallucination, seeing him briefly as "a frame of metal, a platform of pullies [sic] and circuits and batteries and turrets and gears" (14.39). Unlike Luba Luft or even Rachael, there's little question where Roy sits on human-android scale. This guy is a machine built for a solitary purpose, and that purpose is survival.
We can't really say much about Irmgard except that she's sexy—Greta Garbo sexy to be exact (13.65)—and she's a good mechanical match for Roy.
While she does vote to keep Isidore alive, let's not fool ourselves into thinking it is because she cared for him. She doesn't give any specific reasons, but we're betting she agrees with Pris that his "'value to us outweighs his danger'" (15.4). A big clue to her character comes when she and Pris are talking about that poor spire. When Isidore tries to explain that spiders have eight legs, Irmgard says, "Why couldn't it get by on four? Cut four off and see'" (18.28). Yikes.
So, Pris cuts the spider's legs off while Irmgard watches Buster Friendly's expose on the swindler that is Mercer. During the program Irmgard asks:
Isn't [empathy] a way of proving that humans can do something we can't? Because without the Mercer experience we just have your word that you feel this empathy business, this shared, group thing. How's the spider? (18.59)
The irony of her words is lost on her. (Can androids understand irony?) She complains that humans can't prove empathy, but she doesn't understand the concept either. Someone page the wizard; this tin woman needs a heart.
Both Irmgard and Roy meet their obsolescence date when Rick arrives. When he enters the apartment, Irmgard tries to get behind him for a shot in the back, but he sees the move and nails her instead. And then comes one of the more interesting passages in the novel: "Roy Baty, in the other room, let out a cry of anguish" (19.43).
If Roy was only about his survival and had no empathy toward others, then would he really let out this cry? Is it possible that he really did care for at least one other life in the world, or was the cry the result of his own selfish desires?
Unfortunately, the world will never know: Rick shoots and kills Roy not two sentences later.