Irreverent Demystifiers
Did I kick the hornet’s nest?
Responding to comments about my ambiguity aversion article
After my article “What is ambiguity aversion?” was published, I received several grumpy comments from people doggedly defending their choice behavior. Implying that mathy folk can behave irrationally is akin to kicking a hornet’s nest.
I owe those comments a response, so let me address the main flavors here:
Comment: You can’t call it irrational and leave it at that!
Response: I absolutely agree. I’m not leaving it at that. Rest assured that this is just one post in a very long series. Being cooped up at home made me daydream about the 5 years of my life devoted to experimental/behavioral economics and neuroeconomics (those lush grad school lawns!) and inspired me to dust off those topics. This article is not trying to stuff all 5 years into a single post — plenty of others to follow!
Comment: Calling my choice “irrational” isn’t nice. I’m offended.
Response: The word “irrational” is not intended as a slur here… there’s a formal definition of rationality in economics and the A&D choice deviates from it. In fact, you’ll be relieved to know that “irrational” is not the same thing as “suboptimal” — irrationality is sometimes more optimal than rationality. If this idea gets your blood pumping, you might just fall in love with the field of experimental/behavioral economics! That’s pretty much what the entire field is about and it offers you decades of tasty research to chew on. Also, this article demonstrates just one of many ways you could be irrational. There are so many more!
Comment: You forgot risk aversion and expected utility theory.
Response: No, those are impossible to forget. But you’re right that I probably should have written about them before putting out this article. Mea culpa. Stay tuned, I’ve got half of it in draft already. While you’re Googling angrily in the meantime, be careful to avoid the rookie mistake of confusing risk with ambiguity. Risk aversion does not explain ambiguity aversion, but you’ll have to be patient with me while I polish up the article explaining why that’s true.
Comment: People choose A&D to hedge their bets.
Response: No, please check the game rules again. An early typo made it sound like you get two shots at $100 (you only get one!) but that was fixed before the bulk of the poll votes came in. We still see A&D as the favorite choice. (In a setting that allows two shots, you were smart to notice hedging opportunities, but hedging is not enough to explain the results. There’s still the problem of B&C’s unpopularity, since B&C offers hedging opportunities too. If the behavior were only about hedging, why the disparity?)
Comment: It’s a two-player game, so the Nash equilibrium…
Response: Nope, it’s a one-player game. You’re not playing against me since I’m not trying to win or keep the $100 for myself, I’m trying to run a little gameshow in my imaginary living room. But fear not, we can game theory up a storm together on future topics.
Comment: You’re trying to trick me.
Response: Aw, I would never. I’m nice. ❤
Comment: No, seriously, you’re trying to trick me.
Response: You do bring up a pretty relevant methodology point.
In experimental economics, it’s very important that the experimenter never tricks the participant. If we say the bucket has 3 colors of golf balls in it, that’s what it has in it. If we say those ball colors are determined at the beginning of the game, we won’t do a sleight of hand switcheroo on you. We also don’t keep any money we “save” if you don’t win, so we’re not playing against you.
We’re not trying to induce aberrant behavior, we’re trying to reveal existing behavior. So it goes against our best interest to trick anyone into doing something other than what they’d do in similar situations in the wild. (That the participant might be surprised in hindsight by what they chose is another matter.)
In the lab, we go to great lengths to explain (verbally and on the consent form) that what the participant sees is what the participant gets. What they choose is up to them. The payoffs are real and there’s no trickery. Since experimental economics is the tradition I was trained in, I’m not trying to trick you either. But I’m not surprised that you’re assuming I am.
Our tradition struggles with participants whose trust has been polluted by other fields where trickery is part of the fun. (I’m not pointing any fingers, nope, not at all, I wouldn’t dare to accuse any, ahem, social psychology labs of lying to participants.) In the end, experimental economics labs end up bleeding a lot of budget to repair that broken trust (for example by doing practice rounds followed by real cash put in the participant’s hand if they win).
So, fair enough.
Comment: [Insert comment about variance reduction here.]
Response: Er, no, variance is not defined without a distribution. You’ll have to go Bayesian to proceed with this train of thought, which brings me to…
Comment: [Insert Bayesian comment here.]
Response: Bayesian buddies, are you struggling to clamber over our language barrier here? To map the things behavioral economists are calling risk vs uncertainty onto your lingo:
Objective risk involves probability calculations with “objective” priors. If the word “objective” enrages the epistemological nitpickers among you, replace it with the word “spoonfed.” These are priors either dictated to you by someone (the decision-maker in charge, the professor assigning your homework, tradition, etc.) or perhaps they’re priors everyone would generally agree on (e.g. treating coins as fair and moving along without bickering).
Subjective risk involves probability calculations with priors you have to choose.
Ambiguity involves feeling like you’re powerless to come up with priors/assumptions in the first place. The cordon separating ambiguity from subjective risk for a given situation varies from person to person. In the article, the “economist” character never faces ambiguity aversion in the Ellsberg setting because they’re trained to think* in a way that leapfrogs ambiguity and goes straight to subjective risk. That’s not because they’re immune to ambiguity aversion but rather because they don’t see the Ellsberg setting as ambiguous.
*Economists are taught to apply the Principle of Indifference. If we’re blessed with professors who make us practice, many of us learn to do it near-instinctively. Thanks Jacob Tan for writing up an explanation of what that is so that I don’t have to.
Perhaps you’d find it useful to think of the phenomenon of ambiguity aversion in terms of a sort of distress the decision-maker feels when forced to come up with a prior. I’m not talking about the distress of picking parameters to plug into a conjugate prior, I’m talking about coming up with assumptions covering the entire setup. Students double-majoring in Bayesian statistics and behavioral economics could probably squeeze a thesis out of attempts to quantify subcategories of ambiguity through the difficulty of prior elicitation…
Comment: It’s just a thought experiment; people wouldn’t choose A&D if there were real money involved.
Response: Great instinct, but no. My undergrad advisor and favorite prof was John List. Lovely guy in every way, but a tyrant on one topic: unrealistic experimental setup. Which makes sense, since he’s the fellow who pioneered the use of field experiments in economics. John’s voice still lives in my head, “If it’s a thought experiment, it doesn’t count, take it to the lab. But you’re not done yet! If it’s a lab experiment, it doesn’t count, take it to the field (the real world). Always study choice behavior with real rewards in realistic settings.” Thanks to field experimenters like John, most of the pillars of modern decision theory — including this one — have been fully replicated in the real world with real money. (Before you ask, yes, it did occur to them to vary the reward amounts.)
And now for something completely different…
Thanks for reading! If you had fun here and you’re curious about AI, here’s a beginner-friendly intro I made for your amusement:
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