Context effect demonstrations

In each of the following demonstrations, an inductively rational observer will select the option that has a greater relative desirability value, which, in turn, is computed using Equation ??. We turn first to Luce’s classic thought experiment. In the frog legs example, the reversal in preferences is anecdotally explained by the diner originally forming a low opinion of the restaurant’s chef, given the paucity of choices on the menu, deciding to pick the safe salmon over a possibly burnt steak. However, the waiter’s presenting frog legs as the daily special suddenly raises the diner’s opinion of the chef’s abilities, causing him to favor steak. This intuition maps very easily into our framework of choice selection, wherein the diner’s partial menu observations o1 = {steak, salmon} and o2 = {steak, salmon, frog legs} are associated with two separate contexts c1 and c2 of observing the menu X . Bad experiences related to ordering steak in menus typically observed under context c1 (interpretable as ‘cheap restaurants’) may be encoded by defining the vector m = {1, 0, 0, 0} for c1 and good experiences ordering steak off menues observed in context c2 (interpretable as ‘upscale restaurants’) as m = {0, 1, 0, 0} for c2. Then, by definition, p(r|salmon, c1) > p(r|steak, c1), while p(r|salmon, c2) < p(r|steak, c2). Assume these probability pairs, obtained through the diner’s past experiences in restaurants to be {a, 1− a} and {1− b, b} respectively. When the waiter first offers the diner a choice between steak or salmon, the diner computes relative desirabilities using (??), where the only context for the observation is {salmon, steak}. Hence, the relative desirabilities of steak and salmon are computed over a single context, and are simply R(salmon) = 0.7, R(steak) = 0.3. When the diner is next presented with the possibility of ordering frog legs, he now has two possible contexts to evaluate the desirability of his menu options: {salmon, steak} and {salmon, steak, frog legs}. Based on the sequence of his history of experience with both contexts, the diner will have some posterior belief p(c) = {p, 1− p} on the two contexts. Then, the relative desirability of salmon, after