# Preference notation by agent $i$

I want to say that the preferences of agent 1 on a consumption set $$X$$ are the same as agent 2's and the inverse of agent 3's (hence 2's is also the inverse of 3's). How would I do this using the ≽ notation, or alternatively any other notation?

• What do you mean by "inverse"? That 3's ranking of elements in $X$ is exactly opposite of 2's? Or simply that 3's preference is different from 2's? May 14 at 4:01

For all pairs $$x,x' \in X$$ we have $$x \preceq_1 x' \Longleftrightarrow x \preceq_2 x'$$ and $$x \preceq_1 x' \Longleftrightarrow x \succeq_3 x'.$$