-2
$\begingroup$

Give an example of preferences over a countable set in which the preferences cannot be represented by a utility function that returns only integers as values.

I know a utility function exist that represents preference over a countable set. I know a few types of preferences such as lexicographic, monotonic, quasi linear. I have always dealt with utility function assuming preferences are represented by that utility function. So how to solve this question?

Improve this question
$\endgroup$
4
  • $\begingroup$ What countable means? It can be finite countable? Or only infinite countable? $\endgroup$
    – Marcelo Gelati
    Apr 13, 2019 at 11:23
  • $\begingroup$ Both cases u can take $\endgroup$
    – panda
    Apr 13, 2019 at 11:25
  • $\begingroup$ I'll give you a tip first, and if you still can't solve the problem, comment later on. $\endgroup$
    – Marcelo Gelati
    Apr 13, 2019 at 11:26
  • $\begingroup$ Ok.thnx fr the tips in advance. $\endgroup$
    – panda
    Apr 13, 2019 at 11:27

1 Answer 1

Reset to default
2
$\begingroup$

There is a proposition that says:

If there is a function $u: X \rightarrow \mathbb{R}$ that represents the preference relation $\succsim$, then $\succsim$ is rational.

So, the contrapositive form of this statement is:

If $\succsim$ isn't rational, then all functions $u$ don't represent $\succsim$.

So, it's a good approach to create a preference relation that isn't rational, i.e., the preference must violate transitivity or completeness.

Improve this answer
$\endgroup$
1
  • $\begingroup$ Whatever your example is, it's probably wrong. The question assumes the relation is transitive and complete. $\endgroup$
    – Guilherme Jardim Duarte
    Feb 24, 2020 at 0:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.