This seems to happen all the damn time. Cheese is almost always the first one gone. The leftovers are almost always the one with tons of stuff on it. I suspect that anyone would eat a slice that has a subset of the toppings they like. For example, if your first choice is mushrooms and olives, you would probably be almost as happy with a pizza with only mushrooms or only olives. This leads to the conclusion that in the general case, pizzas with fewer toppings will have the greatest utility. Toppings should only be selected when there is a high degree of probability that sufficient people will prefer that combination as their first choice to account for the whole pizza.
I think with the collective intellegence of the xkcd fora, we can come up with an optimum strategy for ordering pizza for a group.
Here is my initial take, based on casual observation over my life:
- 1/3 Plain Cheese
- 1/3 Pepperoni
- 1/6 Other single topping (Veggie before meat)
- 1/6 Other multi-topping (Meat before veggie)
These are my suggested cases, based on total count.
3 -> 1 Cheese, 1 Pepperoni, 1 Single Veggie
4 -> 1 Cheese, 1 Pepperoni, 1 Supreme, 1 Single Veggie
5 -> 2 Cheese, 1 Pepperoni, 1 Supreme, 1 Single Veggie
6 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie
7 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie, 1 Sausage
8 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie, 1 Sausage, 1 Veggie Supreme
9 -> 3 Cheese, 3 Pepperoni, 2 Supreme, 1 Single Veggie, 1 Sausage, 1 Veggie Supreme
Thoughts? Improvements? I'm working on an Excel function for it . . .