3
$\begingroup$

I've been thinking about preferences alot recently and have been specifically thinking about the reflexivity requirement.

That is: $$x \succsim x$$

Though this is apparent and obvious, I have been wondering why this is a required condition for rationality and if its possible to have a preference relation that is complete but non-reflexive.

Is it possible?

$\endgroup$
  • $\begingroup$ Interesting. Would it be too limiting to express this as "I feel worse-off if I have to give up a unit widget in exchange for the exact same unit widget?" $\endgroup$ – heh Nov 28 '19 at 15:52
  • $\begingroup$ @heh reflexivity states an object is at least as good as itself. What im asking is that what if $x \succsim x$ is not true? Does this mean that if presented with this item $x$ you would not consume it on its own? $\endgroup$ – EconJohn Nov 28 '19 at 15:56
  • $\begingroup$ If you took the inverse of reflexivity logically - using your words - it would be that "An object is worse than itself". This seems to be a different concept than whether one would prefer the object "on its own", no? Not trying to be pedantic - this is an interesting question and I just want to clarify what you are asking. $\endgroup$ – heh Nov 28 '19 at 16:08
  • $\begingroup$ @heh no worries! Im just as confused. I think completeness may be violated but not transitivity. In anycase im not sure $\endgroup$ – EconJohn Nov 28 '19 at 16:12
  • $\begingroup$ I'm not confident enough to post this as an answer, but I think you lose transitivity. Consider: $y \succ x \prec x$. $\endgroup$ – heh Nov 28 '19 at 16:19
3
$\begingroup$

Rationality requires the following:

Completeness

For all $x, y \in X$, either $x \succsim y$ or $y \succsim x$ or both.

Transitivity

For all $x, y, z \in X$, if $x \succsim y$ and $y \succsim z$, then $x \succsim z$.

Also note that if $x=y$ then completeness implies that $x\succsim x$. So reflexive preferences follow from completeness. So I would say Completeness and Transitivity are required for rationality. Reflexive preferences just follow from complete preferences.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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