Assume that a restaurant has N dishes on its menu that are rated from worst to best, 1 to N (according to your personal preferences). You, however, don't know the ratings of the dishes, and when you try a new dish, all you learn is whether it is the best (highest rated) dish you have tried so far, or not. Each time you eat a meal at the restaurant you either order a new dish or you order the best dish you have tried so far. Your goal is to maximize the average total ratings of the dishes you eat in M meals (where M is less than or equal to N).
The average total ratings in a sequence of meals that includes n "new" dishes and b "best so far" dishes can be no higher than the average total ratings in the sequence having all n "new" dishes followed by all b "best so far" dishes. Thus a successful strategy requires you to order some number of new dishes and thereafter only order the best dish so far. The problem then reduces to the following:
Given N (dishes on the menu) and M <= N (meals to be eaten at the restaurant), how many new dishes D should you try before switching to ordering the best of them for all the remaining (M–D) meals, in order to maximize the average total ratings of the dishes consumed?
Now, I realize that this problem exists more as a form of intellectual masturbation than as a serious question, but it is nonetheless indicative of the fundamental problems of the modern form of economic analysis. In the first place, it assumes that human preferences are fixed and unchanging. In the second place, it assumes that the end result is the only thing that has value.
For example, no dish is the “best” dish, for “best” is merely a term of value, and is only indicative of a subjective value preference. Furthermore, subjective value preferences are fluid and subject to change. What dish is the best on one occasion may not be the best on a different occasion, simply because what you want changes over time. If you go into a restaurant on Monday and order their best burger, and go back Wednesday and order a chicken sandwich, you may find that you prefer the chicken to the burger on Wednesday simply because you were tired of burgers. The idea that one food option is always and forever is the best thing to eat is patently ludicrous. It’s almost as if these guys forget about the law of diminishing returns, which is literally a freshman concept. And yet their model is predicated on a false assumption that is not reflected in either the real world, or even the academic world.
Additionally, this analysis ignores alternative forms of value. When someone goes to a restaurant, one is not merely purchasing a meal, but service an atmosphere as well. One could also desire a little variety to their meals. As such, evaluating simply the content of the meal to find the best is short-sighted simply because it ignores that one component of every restaurant meal is the service, which varies by shift, not by dish. Also, those who desire variety will find that no one meal is the best simply because, as noted before, appetites and subjective values change.
At any rate, it’s no wonder that a lot of economists seem like over-educated morons. In their attempts to dazzle one another with their mathematical brilliance and technical proficiency, they often end up with mathematical models that do not reflect the real word and are often coldly inhuman. Now wonder their theories are worthless: they’re based on a world that (thankfully) doesn’t exist.