Decision Skills
What is Ambiguity Aversion?
Part 2 of 3 — The differences between risk, uncertainty, and ambiguity
Did you choose A&C, A&D, B&C, or B&D in the rationality quiz?
(No idea what I’m talking about? That’s probably because you got here without first reading Part 1 (a 3 min quiz), so please do that before going any further. You’re going to need to know what those X&X things mean for the rest to make sense.)
I put up a barrier of cute pets from the internet so you don’t accidentally see the spoilers below. Scroll past them when you’ve finished reading Part 1.
What do most people choose?
If you’re like most people, you chose the perennial favorite: A&D.
Alas, if that’s true, it means you didn’t choose rationally! Yup, most people don’t, so there’s no need to feel bad. You’re in good company. All kinds of irrational decision-making is wired into our species and takes a lot of training to overcome.
What’s your result?
- A&C — Rational, especially if you like the color pink (or think I do).
- B&D — Rational, especially if you dislike the color pink (or think I do).
- Flipping a coin twice — Rational, especially if you’re a trained economist.
- A&D — Irrational but popular. Science thinks it knows why people do this.
- B&C — Irrational and science doesn’t understand you. :(
The majority of my readers are data science professionals and/or senior data leaders. While the quiz was running yesterday, I was amused to receive a bunch of comments like, “Too easy, give us something harder!” (Such bravado! My fingers itched to do a post on the overconfidence effect.)
If rational decision-making is so easy, why did three quarters of you mathy folks get it wrong?
Perhaps it’s not so easy after all and the data science curriculum isn’t the one that immunizes you from your human foibles. Maybe data scientists could stand to learn a thing or two from behavioral economists and psychologists…
Irrational decision-making
Someday I’ll write an article that zooms in on how economists define rationality (and introduce you to the four axioms of Von Neumann–Morgenstern rationality… mmmm, fancy) but for now, let’s keep it simple:
One way (among others) that a decision can be irrational is inconsistency, which is something the overwhelmingly popular A&D answer suffers from.
Get out your scalpels and prepare to dissect! We’ll do a little proof by rational cases.
Rational case #1: What the behavioral economist does
My undergraduate major in economics qualifies me for membership in that most coldblooded of groups — economists. Part of the training of a baby experimental/behavioral economist is to be beaten with a stick until we learn to take a rational approach to decisions like this one. So which answer do we prefer after our brainwashin- er, I mean, training has successfully taken root?
We. Don’t. Care.
The completely rational mind shouldn’t have any kind of preference here. We feel total, brazen, belligerent indifference when presented with these options. All four X&X combos are identical.
An economist is trained to look at the options and collapse the probabilities down. We ask, “While we know there are 30 white balls, what do we know about the distribution of yellow and pink among the remaining 60?”
Best answer: nothing.
Fact: I’ve given you no info about that in the setup and you’d have to know me pre-e-e-etty well to have info about my relative love of pink versus yellow. If you think you know which color I prefer, that’s you showing your biases.
So, as far as a trained economist is concerned, there’s:
- No info to suggest there’s more pink than yellow.
- No info to suggest there’s more yellow than pink.
That means there’s no reason to treat yellow and pink differently when we run the numbers, so here’s what’s most consistent with the contents of the economist’s head at the moment:
- 30 white
- 30 pink
- 30 yellow
Try running the numbers yourself to get the solution if you like:
Gamble A: 30 good vs 60 bad balls
Gamble B: 30 good vs 60 bad balls
Gamble C: 60 good vs 30 bad balls
Gamble D: 60 good vs 30 bad balls
This makes all bundles (A&C, A&D, B&C, B&D) equally attractive to an economist, who is then forced pick arbitrarily (or with a coin toss) to ease the pain of such profound indifference.
Rational case #2: What the fan of pink does
If you can’t muster total apathy and you like the act of picking a racehorse just for the fun of it, let’s suppose you like the color pink and you want to bet on there being more pink than yellow. (You’ll get a similar answer if you’re afflicted with the bias that I’d put more pink than yellow in the bucket for some strange reason.)
We’ll imagine the most gentle case—instead of equal yellow-pink odds, let’s start there and make a single yellow ball switch allegiances instead. The balance is now tipped minimally in favor of pink.
In your head at the moment:
- 30 white
- 31 pink
- 29 yellow
Gamble A: 30 good vs 60 bad balls
Gamble B: 29 good vs 61 bad balls
Gamble C: 61 good vs 29 bad balls
Gamble D: 60 good vs 30 bad balls
Since you’ll be playing Game 1 (A vs B) OR Game 2 (C vs D) but not both, there’s no benefit to trying to hedge your bets. If you want the $100, you’d be after gambles more good balls than bad. That means your only reasonable combo would be A&C.
Now try the extreme all-pink case:
- 30 white
- 60 pink
- 0 yellow
Gamble A: 30 good vs 60 bad balls
Gamble B: 0 good vs 90 bad balls
Gamble C: 90 good vs 0 bad balls
Gamble D: 60 good vs 30 bad balls
Again, it’s got to be A&C. Anything else makes no sense!
Rational case #3: What the hater of pink does
If you want to bet on yellow or you’re convinced of my fondness for little duckies, the logic is the same, but now the only answer that makes sense is B&D.
Most people picked irrational option A&D… WAT?!
Despite all that, on the Twitter poll, we got nearly 65% of folks picking irrational option A&D. The choice of those two together makes no sense by the logic above.
A&D are inconsistent options (if A is better than B, then C should be better than D… in fact, the two sets are almost the same gamble — all we did was move the same pink balls over the line to the other side):
Gamble A: W good, rest bad
Gamble B: Y good, rest bad
Gamble C: W+P good, rest bad
Gamble D: Y+P good, rest bad
That symmetry is gorgeous… If you bet on yellow in gamble B, rationality suggests you should still do it in gamble D. But people don’t. Despite the fact that A&D wouldn’t make sense together if you were working with the same bucket twice, despite the fact that the choice is irrational and inconsistent, people still like it best.
The Ellsberg Paradox
Yes, indeedy, it’s a paradox! In fact, it’s called the Ellsberg Paradox, named for the decision theorist Daniel Ellsberg who came up with the little game we just played while he was working on his 1962 PhD thesis at Harvard — a fact that his Wikipedia page barely mentions in its excitement over his other claim to fame: leaking the Pentagon Papers (yes, the ones you’ve heard of in the context of Nixon, the Watergate scandal, and all that jazz).
But what does it mean?
Most economists’ answer to the puzzle involves the introduction of a new concept called “ambiguity aversion” to explain this weird choice pattern.
Let’s look at it like Ellsberg looked at it. What do options A&D have in common? What might have drawn you to them?
If you didn’t collapse the numbers of pink and yellow like we did and kept working with unknowns all the way through, here’s what’s in your head:
- 30 white
- ?? pink
- ?? yellow
Try running the numbers yourself to get the solution if you like:
Gamble A: 30 good vs 60 bad balls
Gamble B: ?? good vs ?? bad balls
Gamble C: ?? good vs ?? bad balls
Gamble D: 60 good vs 30 bad balls
Here be dragons! It’s the great unknown!! Oh no. Let’s stick with something safe and pick the known gambles over the ones where the state of the universe is ambiguous…
“Risk” means the probabilities are known. “Ambiguity” means they’re not.
What is ambiguity aversion?
To put the theory simply: ambiguity hurts the human animal. We don’t like it. We’re willing to make suboptimal choices to avoid it.
When things are risky, it’s not so bad. Ambiguity scares us much more.
Risk is something we can handle if we’re not too grumpy about making a probability calculation or two, but ambiguity really gets to us. Ambiguity causes a different discomfort than risk. A more primal one. (“What?!” I hear you asking, “Aren’t risk, uncertainty, and ambiguity the same thing? Aren’t they synonyms?” Mais non, not if you’re a behavioral economist.)
In basic terms:
- “Risk” refers to decisions where you know the probabilities explicitly. (A and D)
- “Ambiguity” refers to decisions where you have no idea and your decision-making gets stuck. (B and C)
- “Uncertainty” — could refer to either, depending on which field and decade you grew up in.*
When you plug in the concept of ambiguity aversion into the behavioral paradox, everything makes perfect sense. If you picked A&D, the popular theory proposed by Ellsberg in the 60s and refined by economists since then says that it was those question marks that stopped you in your tracks.
Psychologists think humans are hardwired to find ambiguity painful.
You didn’t want to deal with the pain of that ambiguity, so you picked the options that seemed easier to get a handle on… even if they were irrational and inconsistent. That’s a pretty good adaptation for a creature that lives on the savannah — be careful with that dark patch of tall grass… you never know what’s lurking there, so it might be best to avoid it. If possible, stick to the sunny patches where you can at least see what gambles you’re getting into.
Relevance to COVID-19
Perhaps you see where I’m going with this and why I was inspired to scribble about this specific topic at a time when all the headlines are pandemic-flavored… One of the emotional drains of the early days of COVID-19 is all the ambiguity we suddenly have to navigate. If you believe the economic theory about ambiguity aversion and you’re feeling down because so little is known about the new dangers the media warns you about daily, you have an explanation for at least one of the lurking stressors eating at you.
Watch this space for a link to an article I’m working on about what you can do to cope better with your ambiguity aversion, but for now, I hope you get a little bit of comfort from understanding that it’s quite normal to feel extra pain from ambiguity. At the very least, if here must be dragons, they now have a name.
For my decision-making guide to COVID-19, see this link.
If here must be dragons, at least now they have a name.
Part 3 is for the excessively interested
If you want to get into the academic nitty gritty of what the word uncertainty means, here’s the link.
[P.S. For those who *must* know which color I prefer after all, here’s the reveal… This cat is indifferent between pink and yellow. Ha! That’s why I picked them for the example. Ellsberg’s original used the colors black (my favorite), white, and red.]
About those comments
After this article was published, I received several grumpy comments from people doggedly defending their choice behavior. (Calling mathy folk irrational is akin to kicking a hornet’s nest.) You can find my responses here.
And now for something completely different…
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