<p>The two notations you refer to have nothing to do with each other.</p>
<p>In Thaler's paper an outcome <span class="math-container">$(y:x)$</span> means that outcome <span class="math-container">$y$</span> realized while the agent expected to get outcome <span class="math-container">$x$</span>. It refers to the idea that a reference point (<span class="math-container">$x$</span>) matters when an actual outcome (<span class="math-container">$y$</span>) is evaluated.</p>
<p>The other post refers to a mathematical notational convention used in some parts of the world. Here, <span class="math-container">$:$</span> is a mathematical operation, division. The historical reason for this is that <span class="math-container">$\frac{x}{y}=x/y$</span> was sometimes written as <span class="math-container">$x \div y$</span> for longer expressions <span class="math-container">$x$</span> and <span class="math-container">$y$</span> &quot;back in the day&quot; when calculations were done by hand on paper. Then, I guess, people became lazy and <span class="math-container">$x \div y$</span> became <span class="math-container">$x : y$</span>.</p>

CC BY-SA 4.0
2021-02-08T18:59:57.080Z
Oh! Thank you for this. It makes sense. Would you care to inform me on whether this is standard notation for Expected vs Realized outcomes in Utility Theory in general? Or is this something he defines in his original paper? As of now I am a bit ashamed that I didnt know this, and now I want to know whether I skipped something important!
Serkan
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2021-02-08T23:00:04.203Z
I have seen this colon notation in other papers, too, but I think $(y|x)$ is even more common. No need to be ashamed.
Bayesian
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2021-02-08T17:47:53.553Z
2021-02-08T17:47:53.553Z
Bayesian
<p>On page 18 of  <a href="https://pubsonline.informs.org/doi/abs/10.1287/mksc.1070.0330" rel="nofollow noreferrer">Thaler 1985</a> on Value-functions <span class="math-container">$V(\cdot)$</span>, he makes an example about an individual expecting some outcome <span class="math-container">$X$</span>, who instead obtains <span class="math-container">$(X + \Delta X)$</span> which he then defines as the reference outcome <span class="math-container">$(X + \Delta X:X)$</span>.</p>
<p>How is the ':' interpreted in this case?</p>
<p>In this <a href="https://math.stackexchange.com/questions/1628537/what-does-the-colon-stand-for-in-this-equation">post</a> the ':' implies <span class="math-container">$(X + \frac{\Delta X}{X})$</span>. However, I don't how that fits into the overall problem stated in the paper.</p>

<utility>
Interpreting the Reference Outcome in Thaler (1985)
Serkan
# Interpreting the Reference Outcome in Thaler (1985)

(Asked by: username_0 on 2021-02-08)

On page 18 of [Thaler 1985](https://pubsonline.informs.org/doi/abs/10.1287/mksc.1070.0330) on Value-functions $V(\cdot)$, he makes an example about an individual expecting some outcome $X$, who instead obtains $(X + \Delta X)$ which he then defines as the reference outcome $(X + \Delta X:X)$.

How is the ':' interpreted in this case?

In this [post](https://math.stackexchange.com/questions/1628537/what-does-the-colon-stand-for-in-this-equation) the ':' implies $(X + \frac{\Delta X}{X})$. However, I don't how that fits into the overall problem stated in the paper.

**Tags:** utility


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## 1 answers

### Answer by username_1 on 2021-02-08. Score: 3 | Accepted answer

The two notations you refer to have nothing to do with each other.

In Thaler's paper an outcome $(y:x)$ means that outcome $y$ realized while the agent expected to get outcome $x$. It refers to the idea that a reference point ($x$) matters when an actual outcome ($y$) is evaluated.

The other post refers to a mathematical notational convention used in some parts of the world. Here, $:$ is a mathematical operation, division. The historical reason for this is that $\frac{x}{y}=x/y$ was sometimes written as $x \div y$ for longer expressions $x$ and $y$ "back in the day" when calculations were done by hand on paper. Then, I guess, people became lazy and $x \div y$ became $x : y$.

> **Comments:**
> **username_0**: Oh! Thank you for this. It makes sense. Would you care to inform me on whether this is standard notation for Expected vs Realized outcomes in Utility Theory in general? Or is this something he defines in his original paper? As of now I am a bit ashamed that I didnt know this, and now I want to know whether I skipped something important!  
> **username_1**: I have seen this colon notation in other papers, too, but I think $(y|x)$ is even more common. No need to be ashamed.  

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