'Twas the Friday of fall break, when all through the house, not a roommate was stirring, not even a mouse. It was because I was working, my roommate Alyssa was at studio (she's in the a school), and my other roommate Alison was on the couch watching Pretty Little Liars. All was at peace until we convened at about 10pm when I got off my shift, and we began to discuss what we should do for the night. My first pick was to watch Harry Potter in honor of Dumbledore dying, Alyssa wanted to go out, and Alison just wanted to hang out and chat. A simple majority was all we needed, but somehow we were stuck.
As our discussions for what we wanted to do played out, I was able to pick up on everyones preferences. Since I was tired from being around people at work, I wanted a quiet group activity like watching a movie first, talking next, and going out dead last. Alyssa felt cooped up from a long day of classes and wanted activity, so going out was first, movie watching was second, and hanging around was third. Alison had spent the day on screens but likes small groups, so her preferences went hanging out, going out, and last watching a movie.
If Alison and I voted together chatting would win over going out. If Alison and Alyssa voted together going out would win over watching a movie. But if Alyssa and I voted together watching a movie would win over chatting. So chatting can beat going out which can beat watching a movie which can beat chatting. Uh oh! No one activity beat the others, and we couldn't come to a consensus. Even though everyone had transitive preferences individually, our group preferences violated transitivity under majority rule. Condorcet and his darn paradox! If only he came up with a solution too.
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