5 Intuitive Question 2 15 pts Consider the following situati

5. Intuitive Question 2 (15 pts) Consider the following situation: I prefer baseball to basketba I am indifferent between hockey and golf I prefer basketball to golf. I prefer baseball to tennis. I prefer football to basketball I prefer baseball to skiing. I prefer hockey to tennis I am indifferent between tennis and skiing. . I prefer football to golf. I prefer baseball to football. I prefer basketball to tennis. (a) What sport(s) do I prefer the most? What sport(s) do I prefer the least? (b) Are my preferences above rational? Explain.

Solution

Based on the above information the preference of my sports will be as follows, with first being the most preferred sport and last being the least preferred sport:

Baseball

Football

Basketball

Hockey/Golf

Tennis/ Skiing

Hence,

Basketball is the most preferred sport

Tennis and Skiing are the least preferred sport

(b) A preference is said to be rational if preference ordering if it is complete. There is no pair wise or cyclical ranking and it is consistent and continuity. In the above case we are clearly able to identify the preference sequence without contradiction hence it is a rational preference