In a parody of the horror stories The Hunchback of Notre-Dame (1831) and Basket Case (1982), Bart and Lisa begin to hear strange noises, and think there is something in the attic. Homer claims not to know what they are talking about, although he is later seen grabbing a bucket of fish heads and heading into the attic. Bart and Lisa investigate, and discover there really is a monster. Homer and Marge go into the attic, and Homer says: "Oh no, it escaped". Marge immediately calls Dr. Hibbert, who explains that Bart had a conjoined twin brother named Hugo. The two were separated at birth, but it was discovered that Hugo was too evil to live in society, so the Simpsons did the "only humane thing to do": they kept Hugo chained in the attic, where Homer fed him a platter of fish heads once a week. The rest of the family leaves to find Hugo, leaving Bart behind, but he soon discovers that Hugo never left the house. Hugo takes Bart up to the attic and ties Bart up, so that he can reattach himself. Suddenly, Dr. Hibbert finds them and knocks out Hugo, commenting that the evil twin is always on the left side. But then he realizes that Hugo's scar is on the wrong side, and Bart is the evil twin. In a failed attempt to correct their wrong, Dr. Hibbert and the Simpson family sit down to a turkey dinner with Hugo, leaving Bart locked up in the attic eating fish heads.
In a parody of The Twilight Zone episode, "The Little People", Lisa performs a science experiment to see if cola will dissolve a tooth, and Bart shocks Lisa as part of his project to prove that nerds conduct electricity. The tooth is also shocked; it undergoes an unusual reaction and creates a race of miniature beings. Lisa discovers this the next day and marvels at how the people in her universe evolve at a rapid rate, going through the various ages humans have gone through into modern times and eventually, a society more advanced than current humanity. Bart destroys some of the ecosystem in Lisa's tub universe, and the people respond, sending a squadron of space ships to attack Bart, who vows revenge on the small universe as Lisa wonders what to do. Suddenly, she is shrunk and beamed down into the tub, where the citizens explain that they regard her as God, and they want her to do something about Bart, whom they regard as the Devil. She says she can help them if they can unshrink her, but they tell her they have not figured out the technology to do that. This angers Lisa, since they should have had both technologies figured out before shrinking her. At the same time, Bart grabs the tub and submits it in the science fair, and Lisa is forced to watch from within as Bart wins first prize. Realizing that she is now stuck in the small universe forever and having somehow lost her slippers, the very bitter Lisa orders her citizens to grovel and bring her some shoes, with one of the citizens adding that he will get some socks for her, too.
While out fishing, Homer is abducted by the two aliens Kang and Kodos. When they demand that Homer point them towards Earth's leader, Homer informs them of the then-upcoming presidential election and says the winner could be either Bill Clinton or Bob Dole. Kang and Kodos kidnap both Dole and Clinton, placing them in suspended animation tubes and assuming their forms through "bio-duplication" to ensure that one of them will become the next leader. Before returning Homer to Earth, the aliens soak him in rum, so nobody will believe him. As the election nears, the impostor candidates are seen to be acting strangely, holding hands in public and making bizarre declarations in unhumanlike monotone. Later on, Homer stumbles upon the badly hidden spaceship and tries to save the real Dole and Clinton, with both candidates agreeing they should join forces to defeat the aliens; however, Homer accidentally ejects them into space, killing them. On the day before the election, Homer crashes the spaceship into the Capitol and successfully reveals the candidates' real identities. However, despite being exposed, Kang and Kodos declare to the people that they have to choose between one of them because "it's a two-party system", since it is too late to get new candidates. One man in the crowd announces that he will vote for a third-party candidate, but Kang and Kodos mockingly encourage him to "go ahead [and] throw your vote away," prompting a bout of displeasure from Ross Perot. As such, Kang is subsequently elected President and quickly enslaves all of humanity into building a giant ray gun to aim at an unknown planet, while Homer smugly states that at least he voted for Kodos.