The episode begins with a news report of a vandalism spree started by Bender, which ends with him being arrested by Smitty and URL. While bailing Bender out of jail, Amy flirts with several inmates. Infuriated at her obsession with "bad boys" and paranoid that she might cheat on him with one of the inmates, Kif breaks up with her. The break-up severely upsets Amy, and to make her feel better, Leela, Fry and Bender take her to Forbidden Planet Hollywood. Bender mocks her all night, insulting and infuriating her. However, they end up in bed together. After this, Amy and Bender discover a mutual attraction for each other and enter into a robosexual relationship, which is taboo in the 31st century, so they keep quiet about their relationship, even to their friends and co-workers. The rest of the Planet Express crew grow suspicious, but think nothing of it.
While at the planet Tornadus, collecting tornado wind for the Professor's entry for the county fair, the crew is shocked to learn that Bender and Amy are missing. They discover their clothes flying around in the tube with the tornado winds, so the Professor shuts off the machine and when the winds go away, the crew is shocked to see Bender and Amy making love to each other. Discovering this, the Professor immediately disapproves of it. The rest of the crew accepts Bender and Amy's relationship, which they thank them for, as she knows herfamily will disapprove. The professor informs Amy's parents of the relationship, then calls Reverend Preacherbot for Bender. While at her parents' ranch, Amy is saved by Fry, who poses as her new beau to get her parents off her back. Amy then rescues Bender from the "re-education" camp that Reverend Preacherbot sent him to. They go back to the Planet Express building, where Bender proposes to Amy. The Professor reminds them that robosexual marriage is illegal in New New York. To fight against this, Bender and Amy launch a campaign for the legalization of robosexual marriage.
They launch Proposition ∞, which slumps in the polls a few days before the referendum. Amy loses hope, but Bender says that they will win due to his upcoming debate against Professor Farnsworth, the leader of the Prop∞ opposition. At the debate (moderated by the head of George Takei), Bender gives a heartfelt speech about how much he loves Amy, which the audience applauds. The Professor follows with his rebuttal, saying that he was in love with a fellow scientist named Eunice and, 43 years later, discovered her in bed with a robot. This does not impress the audience and Amy calls the Professor out for hating robosexuals just because he lost his girlfriend to a robot. However, he then accidentally admits that she was actually a robot named Unit 47, who left him for another robot. Farnsworth's heart was broken, so he took his anger out on other robosexuals. After admitting the truth, the Professor withdraws his argument, fully in support of Prop∞. The next day, the proposition is approved by an overwhelming majority. Amy is ecstatic, saying that she and Bender can have a normal, monogamous marriage now. Upon hearing the word "monogamous", Bender dumps Amy and leaves her for a pair of robot hookers, while Amy goes back to Kif, who adopts a "bad boy" persona for her.