Axiomatic Mexican platter theory, with Elvis
At Marginal Revolution there is a post up about the phenomenon of random combination platters at Tex-Mex restaurants. It does seem as if as if this is more characteristic of those sorts of restaurants than those of other types.
Rather than the economic perspective they adopt, I prefer to think of it from a mathematical point of view. Consider S, the set of all n individual dishes they sell on the menu. The maximum variety of combination platters which could be assembled from these is the set of all subsets of S, known as the power set of S, P(S) and has 2n elements, ranging from an order of no dishes at all ("I'll just have a coffee, thanks.") to one comprising all the dishes at once ("One of each, please.")
Thus a restaurant with five house specialties could post an exhaustive menu of platter combinations thereof:
Fudging the prices somewhat would make it just about impossible for one to tell easily what the best deal for the money would be.
Having made it through the entree, one could then work one's way through the combinations of the 31 flavors of ice cream offered.
Rather than the economic perspective they adopt, I prefer to think of it from a mathematical point of view. Consider S, the set of all n individual dishes they sell on the menu. The maximum variety of combination platters which could be assembled from these is the set of all subsets of S, known as the power set of S, P(S) and has 2n elements, ranging from an order of no dishes at all ("I'll just have a coffee, thanks.") to one comprising all the dishes at once ("One of each, please.")
Thus a restaurant with five house specialties could post an exhaustive menu of platter combinations thereof:
{}, {chile rellenos}, {elvis green chile fried chicken}, {chile rellenos,elvis green chile fried chicken}, {chicken flautas}, {chile rellenos,chicken flautas}, {elvis green chile fried chicken,chicken flautas}, {chile rellenos,elvis green chile fried chicken,chicken flautas}, {chuychanga}, {chile rellenos,chuychanga}, {elvis green chile fried chicken,chuychanga}, {chile rellenos,elvis green chile fried chicken,chuychanga}, {chicken flautas,chuychanga}, {chile rellenos,chicken flautas,chuychanga}, {elvis green chile fried chicken,chicken flautas,chuychanga}, {chile rellenos,elvis green chile fried chicken,chicken flautas,chuychanga}, {steak burrito}, {chile rellenos,steak burrito}, {elvis green chile fried chicken,steak burrito}, {chile rellenos,elvis green chile fried chicken,steak burrito}, {chicken flautas,steak burrito}, {chile rellenos,chicken flautas,steak burrito}, {elvis green chile fried chicken,chicken flautas,steak burrito}, {chile rellenos,elvis green chile fried chicken,chicken flautas,steak burrito}, {chuychanga,steak burrito}, {chile rellenos,chuychanga,steak burrito}, {elvis green chile fried chicken,chuychanga,steak burrito}, {chile rellenos,elvis green chile fried chicken,chuychanga,steak burrito}, {chicken flautas,chuychanga,steak burrito}, {chile rellenos,chicken flautas,chuychanga,steak burrito}, {elvis green chile fried chicken,chicken flautas,chuychanga,steak burrito}, {chile rellenos,elvis green chile fried chicken,chicken flautas,chuychanga,steak burrito}
Fudging the prices somewhat would make it just about impossible for one to tell easily what the best deal for the money would be.
Having made it through the entree, one could then work one's way through the combinations of the 31 flavors of ice cream offered.
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