You can put more than one order on a set. For example, regarding salsas from the set **{**mild**,** medium**,** hot**}**:

- mild
**<** medium **<** hot, where **<** means the predicate “is less spicy than”
- medium
**≻** hot **≻** mild, where **x****≻y** means the predicate “She prefers **x** to **y**”.

One could launch off into defining **≻ᵢ**’s for every **ᵢ** of the population. (This is the kind of thing one needs to do in talking about Arrow’s Theorem.) That’s when notation begins to suck.

### Like this:

Like Loading...

*Related*

Tags: Arrow's Theorem, mathematics, order theory, orders, preferences, salsa, sets, transitivity

This entry was posted on December 5, 2011 at 4:35 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.

## Leave a Reply