# Symmetric and asymmetric preferences

I encountered a question where it was given that the consumers had asymmetric preferences. I couldn't find the definition of the term in any of the microeconomics book available to me.

Can anybody explain the terms and the difference between symmetric and asymmetric preferences? Please!

• That is odd phrasing. I would normally interpret this phrasing to mean that not all of the consumers have the same preference. But that seems like it usually does not need to be stated as an assumption.... It would probably help to give the full context.
– usul
May 5 '15 at 18:50

It is just a strict preference relation, an asymmetric (generic) relation $\succ$ is such that $a \succ b \implies \lnot b \succ a$. With respect to symmetric preferences there are not really pure symmetric ones in consumer theory at least, the only symmetric relation is total indifference ~ over the whole choice set. Clearly a ~b implies b ~a. A typical $\succeq$ preference relation is the union of an asymmetric and symmetric part.

• in my experience the term "antisymmetric" is usually used for this. "asymmetric" could be another way of referring to that, but it could also mean something entirely different (e.g. preferences built out of utility functions that put much more weight on deviations from one side of a threshold than the other). Maybe some more context in the question could clarify. May 5 '15 at 15:09
• @nominallyrigid No, anti-symmetry is something different and means that $a\succ b$ and $b\succ a$ imply that $a=b$. May 28 '18 at 10:46