Mutual Annihilation

Today I noticed that Ann Althouse and I have mutually exclusive dietary habits.

Althouse: "I'm always using the Atkins diet. I love it for precisely the reason stated in the post: it's excitingly transgressive!"

My cycling/(slightly) high cholesterol diet emphasizes carbohydrates very much so over exclusion of fats and protein. I've joked in the past that this diet is the anti-Atkins diet.

Question is: if an anti-Atkins dieter and an Atkins dieter dine together, what happens?