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This would be kinda fun to play with from a "game theory" standpoint too. Unscrupulous people could attempt to maximize their pizza consumption and minimize their capital investment by claiming to not be very hungry and being willing to eat the most common toppings.
Perhaps the app could have a function at the end to "rate" the participant diners? You could pass your phone around one more time and people could assign a "trustworthiness score" to one another.