<p>For all pairs <span class="math-container">$x,x' \in X$</span> we have
<span class="math-container">$$
x \preceq_1 x' \Longleftrightarrow x \preceq_2 x'
$$</span>
and
<span class="math-container">$$
x \preceq_1 x' \Longleftrightarrow x \succeq_3 x'.
$$</span></p>

CC BY-SA 4.0
2022-05-14T04:13:04.687Z
2022-05-14T04:13:04.687Z
Giskard
<p>I want to say that the preferences of agent 1 on a consumption set <span class="math-container">$X$</span> 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?</p>

CC BY-SA 4.0
2022-05-14T04:01:02.790Z
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?
Herr K.
<mathematical-economics><preferences>
Preference notation by agent $i$
user41190
# Preference notation by agent $i$

(Asked by: username_0 on 2022-05-14)

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?

**Tags:** mathematical-economics, preferences
> **Comments:**
> **username_1**: 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?  

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## 1 answers

### Answer by username_2 on 2022-05-14. Score: 2 | Accepted answer

For all pairs $x,x' \in X$ we have
$$
x \preceq\_1 x' \Longleftrightarrow x \preceq\_2 x'
$$
and
$$
x \preceq\_1 x' \Longleftrightarrow x \succeq\_3 x'.
$$


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