# 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.

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 $$x : y$$.
• I have seen this colon notation in other papers, too, but I think $(y|x)$ is even more common. No need to be ashamed. Feb 8 '21 at 23:00