A Simple Model

Feb 28, 2026 I was thinking about this while on a car ride to the post office. I was getting my first adult passport and my sister asked me if we brought a necessary document. I, without looking since I felt sure about its presence, said yes. We then went to the post office and everything went smoothly.

On the car ride there (~ $10$ min), I thought about a simple model. I had two actions: Nothing or Check. If I did Nothing when the document was in the car then I would lose 1 util (enormous). But if I did Check (i.e. check the file) and the document wasn’t in the car, I would lose c utils.

If the document was present & I did Nothing, then I would gain $0$ utils. However, if the document wasn’t present and I did Check then I would receive $g$ utils (gratitude). In this model, it wouldn’t make sense to “randomize” my actions since it’s not like this happens every day and I have a particular frequency of how often I do Nothing.

Payoff Matrix

Actions/States	$Present$	$Not$ $Present$
$N(othing)$	$0$	$-1$
$Check$	$-c$	$g$

Therefore, I prefer to Check if my belief (a probability $p \in [0,1]$) of the document actually being present satisfies $p < \frac{g+1}{c+g+1}$. Remember, $c$ is the cost of me checking when the document is in fact present, $1$ is the cost of that I forgot the document, and $g$ is the gratitude I receive if I did check and see the document was missing. Intuitively, $c$ must be a lot smaller than $1$ e.g. $c=0.1$. If $g$ were set to be $1$, this means that the magnitude of my happiness is the same as my potential distress. My model would imply that I would need to have a high level of certainty ($>95\%$) to safely do Nothing.

Okay, so this is a pretty stupid model, but I was satisfied due to the following observation. I felt so averse to considering a strategy where I randomized (setting a frequency among multiple trials) between doing nothing or something. However, I had no issue with picking a probability to represent my belief about the presence of the document in the car. Isn’t that so cool? Within a model of choice, the Bayesian and Frequentist philosophy towards what a probability is are very much present.