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On page 18 of Thaler 1985 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 the ':' implies $(X + \frac{\Delta X}{X})$. However, I don't how that fits into the overall problem stated in the paper.

Serkan
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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 $x : y$.

Bayesian
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  • 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 Feb 08 '21 at 18:59
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    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 Feb 08 '21 at 23:00