Bart and Lisa go fishing downstream of the Springfield Nuclear Power Plant, and Springfield Shopper reporter Dave Shutton pulls up just as Bart catches a three-eyed fish, much to both the kids' and Shutton's surprise. The fish, nicknamed Blinky by the media, makes headlines around the state, and incumbent governor Mary Bailey calls in a government inspection team to investigate nuclear waste coming from the plant that could have caused the fish to mutate. After the inspection, the plant's owner, Mr. Burns, is presented with a list of 342 violations, which would cost $56 million to rectify. Distraught, Burns talks to plant employee Homer, who half-heartedly suggests Burns run for governor against Bailey so that he could change the standards and prevent the plant from being shut down. Burns instantly pounces on the idea.
Burns's political advisers break the news to Burns that he is greatly despised by many people while Bailey is beloved by all. To compensate for this, they force Burns to try being friendly and even smile. Burns makes a television commercial discussing Blinky with an actor portraying Charles Darwin, who claims Blinky is an evolutionary step and not a mutated fish. Combined with a promise to lower taxes and a smear campaign against Bailey, Burns ties with her in the polls. On the night before the election, Burns's advisers suggest that Burns have dinner at the home of a middle-class family as an opportunity to put himself in the lead. Burns scans his employees for the most average man he can find, and Homer is chosen.
The impending dinner with Burns divides the Simpson household. Homer supports Burns, while Marge and Lisa oppose him. Before the dinner arrives, Burns's advisers prepare the family for the event, even giving them pre-written questions to ask in lieu of conversation. Lisa becomes disillusioned by it all, but Marge tells her not to worry. To everyone's surprise, Marge serves Blinky for dinner. Burns tries to act as if it does not bother him, but is not able to keep from spitting it out. The cameras flash as the bite flies through the air, and by the time the chunk hits the floor the press is gone and his gubernatorial campaign dissolves. Bailey wins the election and, despite Burns saying that Homer's dreams will be unfulfilled for as long as he is alive, the Simpson family happily get together again.