There's no good reason to order a small pizza. That's just because more pizza always equals better pizza. But if you need some real math to justify that large order, ASAP Science has the math to prove there's no good reason to order a small, ever.
They use a little bit of grade school math to show that calculating the area of a circle is your best friend when trying to get the most bang for your buck. Using Area = πr(adius)2 it becomes clear that the amount of pizza you get as the size of a pizza increases is almost never commensurate with the increase in price, making small pizzas a sucker's game.
For instance, the area of an eight-inch pizza is about 50 square inches. Compare that to a 16-inch pizza, which on first glance you might assume is twice as big. In reality, a 16-inch pizza has over 200 square inches of pizza. That's four times as much pizza, and it's certainly not coming at four times the price.
ASAP Science goes a step further, using pricing research done by NPR's Planet Money in 2014. A 20-inch pizza on average cost $20.77 in 2014. It has more area than two 14-inch pizzas, which would cost $29.59 on average. A 20-inch pizza also has more area than six eight-inch pizzas, which costs $51.56 on average. Math says you need more pizza.