The Certain Equivalent (Decisions 2)

The Certain Equivalent allows us to better understand complex preferences by making 100% certain outcomes feel equivalent to very different outcomes.

Remember, when considering the favorability of a variety of outcomes, the outcome that you want the most is the one with the highest utility. In contrast, the outcome you would expect to be least satisfied with is the outcome with the lowest utility.

The real purpose of assigning utility to different outcomes isn't to rank them from best to worst. It's to arrive at a precise valuation of how much you prefer one outcome to another. This guides you in making complex decisions.

Let’s look at a relatively difficult decision that you might face. You are moving to a new city, and you have to choose your living situation. You’re currently considering three options:

  1. A rental house in the suburbs
  2. A downtown apartment
  3. A single room in a downtown apartment near your job

You are new in town and don’t really have a sense of what the traffic is like in this city. If the commute is long, you might not want to live in the suburbs. On the other hand — you’ve been thinking about starting a family, or at least dating. You might need extra space. And what’s the night life like in the city? What about the level of crime? And then — what about price? These three options are very different in price. You feel very confused, unsure, and anxious. You somehow feel like every choice would be a mistake. You keep hemming and hawing, your mind circling through the three options in a loop, seemingly preferring a different option every hour. You’re losing sleep.

The problem is that you are indeed confused, about both the relative utility of various outcomes, and the probabilistic risk associated with each outcome. It’s a complicated problem, and it’s normal to feel confused. But we’re going to learn the tools to dissolve that confusion. If you install these tools as habits of mind, then you’ll make similar decisions quickly and painlessly. You can, indeed, learn to be a decisive person.

But right now, as you toss and turn, unable to choose which living arrangement to go with, you’re still thinking in terms of feelings and generalities. So let’s try to nail some important things down with numbers.

Set aside the questions of starting a family and commuting, and just think about your ineffable, unquantifiable feelings toward the three options. What would your preference be if you could simply ignore all considerations like commute time, cost, crime, and future opportunities? You think that you prefer #1 to #2 to #3, all other things being equal.

Rental house > apartment > small room

If I simply ask you, how much more do you prefer the idea of a house to an apartment, you might be able to think of a number, but you will not feel very sure. But we are going to learn a trick that can help you feel much more sure about yourself.

Here is the trick: Imagine an evil realtor, such as David Youssef, offers you a choice. He shows you two boxes. In Box 1 are the keys to choice #2, the Apartment, your middle choice, free of charge. In Box 2 is a coin, which the realtor will flip. The evil realtor further tells you that if you get heads in the coinflip, you get the keys to choice #1, the Rental House, your most preferred choice. But if you get tails in the coinflip, you’ll get choice #3, the Small Room, your least preferred choice.

Now here’s the fun part: The realtor reveals that in this game, you control the fairness of the coin. The objective of the game is to adjust the fairness of the coin … until you feel emotionally indifferent between Box 1 and Box 2.

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If you choose 80%, that means 80% yields a “certain equivalent” between Box 1 and Box 2. In other words, from your perspective, the equivalent value of a certainty of getting B (the Apartment), is an 80% chance of getting A (the House) and a 20% chance of getting C (the Room). You are indifferent between the two boxes.

This is a subjective process; you go with whatever number feels like a neutral balance, whatever number makes you feel like you no longer prefer one box over the other. If 90% feels too high and 70% feels low, go with 80%. But that 80% will likely feel more true and reliable than if you hadn’t performed the coin-flip exercise.

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The concept of substituting the expected value of a sure thing for the expected value of a probabilistic balance of two other things will be used heavily going forward. You do not always need to envision a mental coin-flip, but you do need to be comfortable with the idea that a probabilistic scenario can have a certain equivalent. With a bit of practice, you may become so comfortable with the idea of framing the value of one option in terms of indifference between other options that you can just intuitively come up with numbers that feel right.

One bonus feature of the certain equivalent concept is that you can plug in very different-feeling outcomes for #1, #2 and #3. You may have felt very confused about your relative preferences for three possibilities, but the idea of finding an indifference point between them can almost magically clarify things for you.

For example, in subsequent lessons we will show that you can use the same tool to evaluate outcomes involving the relative crime rate, cost, and commute time of the options, and thereby express these very different-seeming possibilities in terms of certain equivalents. Then we can use the probability that we assigned to each certain equivalent to establish the relative utility of each option.

Your homework this week is to structure a decision that you’re facing in your life in terms of a certain equivalent between the middle-preferred option, and a weighted-coin flip between the most and least preferred option. Be prepared to discuss with your cohort. If you have trouble finding a consequential decision, choose an inconsequential one; or, for the coward’s way out, simply consider a hypothetical change in job, college major, or living situation.

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