Question

2. T he set of alternatives is Z-\a,b,c,d,e,f,gj. It has been observed that, when the available alternatives were a, e and f Bill chose a. We express this by saying that the observation was ( {a, e, Л.a) . The following is a list of observations concerning Bill: (a) Assuming that Bill's preferences did not change during the observation period, is Bill's behavior rationalizable by a complete and transitive preference relation? Explain your answer. (b) Suppose that Bill is not indifferent between any two alternatives. If he had been faced with a choice from the set fa,b,e. f?, what would he have chosen? [Warning: tricky question!]

Answer 1

(a) to check for completeness we need to observe whether the observations are establishing relationship between each and every element or not.

transitivity can be understood through an example: when a is preferred over b, and b is preferred over c then a should be preferred over c. In the case of preference relation it can also be seen as is a is chosen over b then b can't be chosen over a in other set of observation.

(a) to check for completeness we need to observe whether the observations are establishing relationship between each and every element or not. transitivity can be understood through an example: when a is preferred over b, and b is preferred over c then a should be preferred over c. In the case of preference relation it can also be seen as is a is chosen over b then b can't be chosen over a in other set of observation. (a) We have a set of alternatives z = {a, b, c, d, e, f, g} Given: When the available alternatives were a, e and f Bill chose a. i.e. ({a, e, f}, a) So we can say that a > e (a is preferred over e and f) a > f we have some other, observations, we have to check whether his behaviour is rational? i.e. whether preference relations are complete and transitive or not? (i) ({a, d,

(b) for this, we have to observe previous observations