The Condorcet Paradox in Iron Chef Judging

Every year, Grace Christian Fellowship has an “Iron Chef” event where students are broken up into teams, given a secret ingredient and 30 minutes to create a dish to impress the "judges". Last night, the secret ingredient was eggs (my favorite food), and I was given the honor to be one of three judges.

Our judging process went like this: after each dish, each judge would rate it based on creativity, taste, and aesthetic. According to Simon Mujumdar, this is pretty similar to how he used to judge dishes on the actual show. After all the rounds, we came together to rank the six dishes as a whole using majority rule. This is really the Borda count voting procedure, where voters rank their candidates and the candidate with the highest number of points is declared the winner.

There were six dishes, but for simplicity of explanation, I will talk about three of them to explain how I experienced the Condorcet paradox in our judging process. One was an avocado toast with a fried egg and Trader Joe's (amazing) Everything but the Bagel Sesame Seasoning Blend (“A”), one was fried “angel” (deviled) eggs with a mystery sauce (“B”), and one was a burger with fried eggs as the buns (“C”). Each judge had their own transitive individual preferences, but we realized our group preferences were intransitive. To list out our individual preferences, mine were C > A > B, another judge’s were A > B > C, and the last judge's were B > C > A. As a group, that meant that we had the following intransitive preferences: A > B, B > C, C > A and there was no Condorcet winner.  We discussed in class that under such circumstances the outcome will be at best random, but at worst manipulative when the voting order is decided. Because this was a fun Friday night activity and we weren't making pairwise decisions, no one tried to manipulate the results and we arbitrarily decided on a winner. However, when teams wanted to know how their amazing dishes didn't win, we found ourselves explaining that we all liked different dishes and it was really hard to agree on a winner, and I had to hold myself back from trying to explain to people that there was no Condorcet winner in this competition.