Interpreting the Reference Outcome in Thaler (1985) 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.
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 $y$ &quot;back in the day&quot; when calculations were done by hand on paper. Then, I guess, people became lazy and $x \div y$ became $x : y$.