Question

Problem 4: (Prospect theory explanation for the Common Ratio Effect): A famous experimental violation of EU is the finding by Kahneman and Tversky that most people preferred $3000 with certainty over an 80% chance of $4000, but preferred a 20% chance of $4000 over a 25% chance of $3000. Using the probability weight w(?) = (1 − ?)? + ?? for the probability of the best outcome of a lottery and the weight w(?) = (1 − ?)(1 − ?) + ?? for the probability of the worst outcome of a lottery, and setting

? = 0.80, ? = 0.10, show that prospect theory explains this classical demonstration of the common ratio effect. Use the weight ?(?) = 1 for a lottery that offers a single outcome with probability ? = 1. Assume a simple linear value function of the form ?(?) = ?.

Answer 1

a) The statement is a mere observation of facts, but there is no hypothesis test performed to conclude that Hardees' fried chicken is favoured over Kentucky fried chicken.

b) The statement does not prove or disprove the claim, as there has been no hypothesis test performed. Moreover, the samples are not random samples. Based on convinience sample, the result concluded is biased.

c) The statement is wrong in a way, that median salary denotes the middle value in the salary data set, whereas, mean is the average of salary of the professor in the data set. A median cannot be rounded of into a mean. In any case, the median to be equal to mean, the distribution of salary has to be perfectly symmetrical.

d) The probability is a subjective one, where the author uses his own judgement to come up with the value. There is no formula used to calcualate the probbaility.