Trading Money for Something Else

Last week I focused on the opinion-based / subjective view of comparing alternatives. In a previous post I also discussed multi-criteria optimization and the idea that you can balance different criteria to identify a mathematical “best” option. In this article I will bridge the gap using the idea of conversion factors for the same fundamental quantity (feet to meters) and extending it to work in other situations.

In school we learn about conversion factors and their mathematical definitions. If you are from the USA, you learn there are 12 inches in a foot, 3 feet in a yard, 5280 feet in a mile, and maybe 2.54 centimeters to an inch. In other countries you learn there are 100 centimeters in a meter and 1000 meters in a kilometer. If you are an engineer or in the sciences, you will also learn interesting things like digital scales do not actually measure mass directly, but instead they measure the force you are applying on them (newtons is one unit of force) and that number is converted into an estimate of your mass (pounds).

So, our first observation is that sometimes our conversion factors are given by a definition. For example, 12 inches in a foot. Other times we have conversion factors of convenience. For example, the true way to measure mass directly is to apply a known force to something and measure how fast it accelerates. But instead we usually measure weight since it is much easier to do. This is the foot-in-the-door to extending conversion factors much more broadly.

We accept that weight is equivalent to mass because we have a way to convert between them. But what about the subtitle of this post? How many dollars is a life worth? Like many things, context matters. One easy-to-navigate context is an individual choosing how to spend their limited charity dollars. How could I use that money to have the maximum benefit? Towards that end, GiveWell describes their technique to convert money given to a charity into an estimate of how many lives would be saved.

The fundamental idea is really quite simple. A conversion factor says if you take X of one thing, you can exchange it for Y of another. If I donate about $5000 to the right charity, they can take that money and save one life. If I take $5000 and trade it for a vacation, that will not result in one life saved, but it should produce some amount of happiness / memories / etc. And that is the premise of using money as your universal equivalent. If I can compare money to something else, I can convert two “something elses” to money and compare them to each other. Would I personally prefer to have a specific vacation that costs $5000 or to save one life?

This concept of converting things which are different fundamental quantities is the underpinning of multi-criteria optimization. Feet convert to miles by definition. Money converts to lives saved or experiences had through the possibility of an exchange of that money for the thing in question. Every time you buy something, you are (hopefully) making two observations about the conversion factor

• According to the market, I can convert this many dollars for that thing in question.

• According to my judgement, I would rather have that thing in question than this many dollars.

This continues to build on the theme of understanding situations in the context of a decision. Money means very little separate from the things it can be traded for. We could instead use lives saved, or a number of legos as our universal unit of measure. By just converting all your alternatives into the same units, you can see which is “more.”

One important caveat: context matters. I’m repeating myself… but if you miss just little bits of context, you will get entirely wrong answers. When I taught engineering economics, the fundamental goal was for students to understand the time-value of money. A dollar today is worth more than a dollar tomorrow, because a dollar today can do something useful before you get it back tomorrow. Students would often claim that their personal interest rate was 0% because many banks offer virtually no interest, and most people have some money in a bank account. What they had missed is they don’t put money in the bank to get the 0% interest, they do so because having a sure thing of a certain amount of money being safe and available is worth missing out on interest.