<p>Complete but intransitive preferences are <strong>Cyclical Preferences</strong>.</p>
<p>An example of complete but intransitive preferences is in the game of &quot;rock, paper, scissors&quot;</p>
<p>In this case we can have
<span class="math-container">$$\textrm{Rock}\succ \textrm{Scissors} \textrm{ and Scissors}\succ \textrm{Paper}$$</span>
<strong>but not:</strong>
<span class="math-container">$$\textrm{Rock}\succ \textrm{Paper}$$</span></p>
<p>A classic example of Cyclical preferences in economic theory is the <a href="https://en.wikipedia.org/wiki/Condorcet_paradox" rel="nofollow noreferrer">Condorcet paradox
</a>.</p>
<p>I hope this helps</p>

CC BY-SA 4.0
2022-03-16T05:21:28.150Z
2022-03-16T05:21:28.150Z
EconJohn
<p>A preference is rational if it is complete <strong>and</strong> transitive. You need both properties satisfied for it to be rational. So an intratransitive and complete preference will still be irrational.</p>
<p>Indifference and strong preference on the other hand are relations derived from the preference relation itself.</p>
<p>The preference relation <span class="math-container">$\succcurlyeq$</span> itself says <span class="math-container">$x$</span> is <strong>at least as good</strong> as <span class="math-container">$y$</span>, where <span class="math-container">$x$</span> and <span class="math-container">$y$</span> are two alternatives available to a decision maker. Formally <span class="math-container">$x \succcurlyeq y$</span> .</p>
<p>Strong preference relation <span class="math-container">$x \succ y$</span> (read as <span class="math-container">$x$</span> is strictly preferred to <span class="math-container">$y$</span>), <span class="math-container">$\iff$</span> <span class="math-container">$x \succcurlyeq y$</span> and <strong>NOT</strong> <span class="math-container">$y \succcurlyeq x$</span>.</p>
<p>Indifference relation <span class="math-container">$x \sim y$</span> (read as x is indifferent to y) <span class="math-container">$\iff$</span> <span class="math-container">$x \succcurlyeq y$</span> and <span class="math-container">$y \succcurlyeq x$</span></p>

CC BY-SA 4.0
2022-03-15T13:57:50.373Z
2022-03-15T14:15:22.477Z
2022-03-15T14:15:22.477Z
Rumi
<p>I am trying to make sense of the following terminology and putting it into a table helps me keep concepts straight:
<a href="https://i.sstatic.net/7joR2.png" rel="noreferrer"><img src="https://i.sstatic.net/7joR2.png" alt="enter image description here" /></a></p>
<p>If I am understanding correctly, irrational behavior is describe as a preference relation that is both irrational and incomplete. Is that correct?  If so, what would you call a preference relation that is complete, yet intransitive?</p>
<p>Thank you,</p>

<microeconomics><preferences><rationality>
What would you call a preference relation that is intransitive yet complete?
Alejandro
# What would you call a preference relation that is intransitive yet complete?

(Asked by: username_0 on 2022-03-14)

I am trying to make sense of the following terminology and putting it into a table helps me keep concepts straight:
[![enter image description here](https://i.sstatic.net/7joR2.png)](https://i.sstatic.net/7joR2.png)

If I am understanding correctly, irrational behavior is describe as a preference relation that is both irrational and incomplete. Is that correct? If so, what would you call a preference relation that is complete, yet intransitive?

Thank you,

**Tags:** microeconomics, preferences, rationality

---

## 2 answers

### Answer by username_1 on 2022-03-16. Score: 2 | Accepted answer

Complete but intransitive preferences are **Cyclical Preferences**.

An example of complete but intransitive preferences is in the game of "rock, paper, scissors"

In this case we can have
$$\textrm{Rock}\succ \textrm{Scissors} \textrm{ and Scissors}\succ \textrm{Paper}$$
**but not:**
$$\textrm{Rock}\succ \textrm{Paper}$$

A classic example of Cyclical preferences in economic theory is the [Condorcet paradox](https://en.wikipedia.org/wiki/Condorcet_paradox).

I hope this helps


---

### Answer by username_2 on 2022-03-15. Score: 4

A preference is rational if it is complete **and** transitive. You need both properties satisfied for it to be rational. So an intratransitive and complete preference will still be irrational.

Indifference and strong preference on the other hand are relations derived from the preference relation itself.

The preference relation $\succcurlyeq$ itself says $x$ is **at least as good** as $y$, where $x$ and $y$ are two alternatives available to a decision maker. Formally $x \succcurlyeq y$ .

Strong preference relation $x \succ y$ (read as $x$ is strictly preferred to $y$), $\iff$ $x \succcurlyeq y$ and **NOT** $y \succcurlyeq x$.

Indifference relation $x \sim y$ (read as x is indifferent to y) $\iff$ $x \succcurlyeq y$ and $y \succcurlyeq x$


---

