Question

Problem 4. Chloe likes to read Latin American fiction: Fuentes, Vargas Llosa, Garcia Marquez, Carbajal, you name it. Though she prefers longer novels than shorter ones, she sometimes has trouble telling books apart. In particular, she is indifferent between any two novels that have the same number of pages. But she also is indifferent between two novels when the difference in the number of pages is greater than ten (> 10) and less than twenty (< 20).
(a) Is Chloe’s strict preference relation complete and transitive? Explain or give a counterexample.

(b) Is Chloe’s indifference relation complete and transitive? Explain or give a counterexample.

(c) Is Chloe’s weak preference relation complete and transitive? Explain or give a counterexample

Answer 1

Answer 4(a): Chloe’s strict preference relation is transitive but not complete. This is because, Chloe’s preferences are movable and can be adaptive to the change in the situation, however, there are huge gaps in her preferences, such as Chloe has trouble telling the books apart, which means that she lacks the judgement capability and therefore, stays confused with her own decision , as to whether she likes to read a particular volume of book or not.

Answer (b): Chloe’s indifference preference relation is transitive and almost complete. This is because, when Chloe has the option to choose between two novels of the same size, she is indifferent to it, and can choose either of them. Therefore, the transformation is possible and the inference is complete.

Answer (C): Chloe’s weak preference relation is transitive but not complete. This is because, Chloe’s preferences are movable and can be adaptive to the change in the situation, however, there are huge gaps in her preferences, such as what is Chloe’s preference when the difference in the number of pages is less than 10 or when it is greater than 20. In order to be a complete preference, all these gaps should be answered.