How to Make Big Decisions

This post continues the series on “Making Better Decisions,” which started here and discussed the dangers of intuition here and here. We last discussed how using the wrong way to decide can make you vulnerable to manipulation here.

Big decisions, such as buying a new car or hiring a new coworker, are hard because you need to carefully balance many aspects (or dimensions). As we saw in the last post, it is tempting to rely on some criterion that promises to make comparisons easier. As we also saw, many such “methods” are flawed because decisions made following them will be inconsistent. That is, they will depend on whether other, irrelevant options (which you will not take anyway) are offered or not. And that makes you vulnerable to manipulation.

What to do, then? Actually, decision theory has a solution for this problem. There is a powerful result in decision theory, originally proven by Nobel Prize winner Kenneth Arrow, which shows the only way to make consistent decisions. And, although this result does have a mathematical proof, the idea is actually simple.

If you evaluate an option (e.g., a car model, a potential apartment to rent, a job candidate) depending on comparisons to other options, you are in trouble. If your method asks to find out how many other candidates have less experience or have worse college grades than the one you are looking at, that evaluation will jump around when a new candidate shows up or a previous one drops. The only way to avoid this is to pin down an evaluation for every option that only depends on the characteristics of that option. An easy way to do that is to build the evaluation as an actual number using only those characteristics but taking into account your personal tradeoffs.

Building Utility Values

Let’s make it concrete. Suppose you are looking for a new apartment to rent. Take the list of potential apartments from the previous post, which includes the four dimensions that (in this example) you care about:

• Apartment A: 900 sq. ft. $3,000, 40 min, elevator
• Apartment B: 800 sq. ft, $2,500, 1 h, no elevator
• Apartment C: 700 sq. ft. $2,000, 1.5 h, elevator
• Apartment D: 1,000 sq. ft., $5,000, 1 h, no elevator
• Apartment E: 400 sq. ft., $2,400, 30 min, no elevator

Think about tradeoffs. Suppose you decide 100 square feet more are worth $800 of rent. That is a tradeoff of 1 square foot for each $8. You can build your personal “utilities” (as they are called in economics and decision theory) by multiplying the square feet by 8 and subtracting the monthly rent (subtracting because paying more money is bad).

For the sake of the example, suppose that you also decide that 10 minutes less of commuting time are also worth $500 of rent. That is a tradeoff of 1 minute for each $50, so you multiply the commuting time in minutes by 50 and subtract it from your utilities (again, subtract because longer commuting is bad). Finally, suppose that having an elevator in the building is worth $1,000 in monthly rent to you. Then you add 1,000 to the utility of every apartment in your list if it has an elevator, and add nothing if not. That gives you a list of utilities.

• Apartment A: 8 x 900 – 3000 – 50 x 40 + 1000 = 3200
• Apartment B: 8 x 800 – 2500 – 50 x 60 = 900
• Apartment C: 8 x 700 – 2000 – 50 x 90 + 1000 = 100
• Apartment D: 8 x 1000 – 5000 – 50 x 60 = 0
• Apartment E: 8 x 400 – 2400 – 50 x 30 = –700

The numbers you are getting do not mean anything in themselves. Only their comparison is meaningful. If you now list the apartments in the order of the numbers, you get a ranking, from best to worst:

A is better than B; B is better than C; C is better than D; and D is better than E.

Or, with fewer words:

A, then B, then C, then D, then E.

This is a ranking, or, as economists and decision theorists like to call it, a preference. It tells you to choose A and, if A is not available, to go for B. And so on. And whether an apartment is better than another will never change if other apartments disappear from the list or new apartments are added to it, because those extra apartments do not change the utilities. Nobody can manipulate you to reverse the ranking of two options. If you use this way of constructing utilities to reach a preference, you cannot be manipulated, and you will always be consistent.

What Is Your Preference?

What the mathematical result of Arrow actually says is that any method that gives you a preference for all options you might face is consistent, and no other method is. So, if your method does not give you a preference, there is very good reason to say that it is not a good method. And if you want to be consistent, you need to find out a preference.

Decision-Making Essential Reads

Navigating the Landscape of Unintended Consequences

Who Is Rational—and How Irrational Are We?

And you see the problem.

You could have decided that 100 square feet are worth $900 or only $700. Or that the elevator is worth $2,000 or only $500. You would then have computed different utility numbers and possibly arrived at a different preference. Actually, the construction given here, where you try to come up with monetary tradeoffs for every dimension, is an example of Multi-attribute Utility Theory, which is the main decision method taught and used to make big decisions in management.

But that method also forces you to quantify exact, constant tradeoffs ($5 for each square foot), a property called “linearity.” In reality, you might have changing tradeoffs; for example, you might care a lot about size for apartments below 700 square feet, and not so much for larger ones—you already have enough space. For instance, you could have added the square root of the number of square feet, so going from 100 to 400 square feet (20 – 10 = 10) is worth the same as going from 400 to 900 square feet (30 – 20 = 10). The message is that any way to compute utilities will give you a preference and make you consistent, but there might be many different preferences. Which makes sense: After all, different people will probably have different preferences!

How do you find your preference, then? More on that in the next post.