Asking for reassurance: a Bayesian interpretation
June 9, 2011 25 Comments
Bayesianism gives us a prescription for how we should update our beliefs about the world as we encounter new evidence. Roughly speaking, when you encounter new evidence (E), you should increase your confidence in a hypothesis H only if that evidence would’ve been more likely to occur in a world where H was true than in a world in which H was false — that is, if P(E|H) > P(E|not-H).
I think this is indisputably correct. What I’ve been less sure about is whether Bayesianism tends to lead to conclusions that we wouldn’t have arrived at anyway just through common sense. I mean, isn’t this how we react to evidence intuitively? Does knowing about Bayes’ rule actually improve our reasoning in everyday life?
As of yesterday, I can say: yes, it does.
I was complaining to a friend about people who ask questions like, “Do you think I’m pretty?” or “Do you really like me?” My argument was that I understood the impulse to seek reassurance if you’re feeling insecure, but I didn’t think it was useful to actually ask such a question, since the person’s just going to tell you “yes” no matter what, and you’re not going to get any new information from it. (And you’re going to make yourself look bad by asking.)
My friend made the valid point that even if everyone always responds “Yes,” some people are better at lying than others, so if the person’s reply sounds unconvincing, that’s a telltale sign that that they don’t genuinely like you/ think you’re pretty. “Okay, that’s true,” I replied. “But if they reply ‘yes’ and it sounds convincing, then you haven’t learned any new information, because you have no way of knowing whether he’s telling the truth or whether he’s just a good liar.”
But then I thought about Bayes’ rule and realized I was wrong — even a convincing-sounding “yes” gives you some new information. In this case, H = “He thinks I’m pretty” and E = “He gave a convincing-sounding ‘yes’ to my question.” And I think it’s safe to assume that it’s easier to sound convincing if you believe what you’re saying than if you don’t, which means that P(E | H) > P(E | not-H). So a proper Bayesian reasoner encountering E should increase her credence in H.
(Of course, there’s always the risk, as with Heisenberg’s Uncertainty Principle, that the process of measuring something will actually change it. So if you ask “Do you like me?” enough, the true answer might shift from “yes” to “no”…)
Shakespeare’s Uncertainty Principle: You cannot simultaneously know both someone’s true feelings for you and their true identity.
Love it.
And the corollary of Pyramus-Thisbe statistics for the Puck Exclusion Principle: Your love may be in equilibrium but but you’ll never be able to have more than negligible mutual interaction.
Whenever I’m on the receiving end of questions like that, I freeze up, not because I’m bad at lying but because I’m bad at telling the truth in a convincing way. I’m always afraid I’ll say something like “Well, to *me* you are!” which is true and yet very un-reassuring. Then, once I’ve frozen up, any answer I croak out will sound like a lousey lie. Best not to ask me.
But, yes, you’re pretty!
I have the same problem of sounding like I’m lying when I’m afraid people are going to suspect me of lying (even when I’m telling the truth!). But still, I’d say the problem is probably worse when you really ARE lying.
Old Jewish joke: You told me you were leaving so I’d think you’re leaving, but you really are leaving, so why did you lie?
Oh good, I thought it was just me who did this! Although, I actually can lie more convincingly than I can tell the truth in situations like this, and I think I figured out the reason is something like, if someone is trying to get me to reassure them about something silly, I’m actually thinking “Well, the answer is yes, but that’s a silly question.” And so it comes off as not being genuine. In the rare cases I feel compelled to lie, it’s not for a “silly” reason, so I actually care that they believe me, so I come off as truthful.
I’ve discovered the ‘would you gain any new information by my answer?’ response, and its close analogue, the ‘what guy in my situation wouldn’t answer yes?’ usually aren’t the best routes to take – but they don’t go as badly as one would think either.
Good for you! I wish more people would answer that way, to help discourage this silly practice.
The question may not be “Do you find me pretty?” but may be “Do you think that I am a good painter?” It’s a rare person who is not insecure about *something* and wishes to be complimented on it in order to increase their self-worth. So at some point we all fish for that compliment – it just depends on how subtly we do it so this silly practice will continue in some form, probably forever.
“What do you think of my hypothesis?” 😉
Interesting conundrum! I agree that the questioner does learn something about your attitude even though your behavior is constrained by politeness. This is an issue many psychologists had wrong in the past, assuming that one causal hypothesis ought to be completely discounted given evidence for an alternative [ Morris, M. W., & Larrick, R. P. (1995). When one cause casts doubt on another: A normative analysis of discounting in causal attribution. Psychological Review, 102, 331-355].
But they dont learn that much and they risk changing your attitude for the worse. Thats a more accurate response but probably not one that would make them feel better!
Yes/no questions are so black and white. A grayscale answer would be, “You’re an 8,” which brings us to fuzzy logic.
http://en.wikipedia.org/wiki/Fuzzy_logic#Comparison_to_probability
Unfortunately, since the culturally expected answer is total certainly (100%, or “a 10”), this type of response usually doesn’t work out so well either: the implication is that there must be *some*body you have in mind that’s prettier than the asker. In particularly exceptional circumstances they may even interrogate you about who that prettier person is. (As you can probably tell, I’m speaking from personal experience.)
Umm, Emmanuelle Chriqui.
Can’t help it
A good post about Bayesian reasoning. However, the Heisenberg Uncertainty Principle is not the same as the observer effect. Some observable quantities which seem compatible at usual human scales turn out not to be compatible at the quantum level. It’s really a property of mathematics, and has nothing to do with interference from a measurement process. HyperPhysics has a good visual depiction of why uncertainty exists between position and momentum, which is the canonical example of the uncertainty principle (although those are far from the only pair of incompatible observables).
Good point. I thought there was something fishy about that analogy, but I decided to make a joke about it instead of verifying the physics 🙂
Actually, I think that Julia is technically correct. While it is certainly true that the uncertainty principle is a consequence of mathematics (non-commuting operators), the Heisenberg uncertainty principle is enforced by the fact that a measurement corresponds to coupling to a continuum in a _particular_ basis, which introduces noise in the “other quadrature”/non-commuting observable. In other words, the mathematical argument about commutation relations is _equivalent_ (given the other laws of quantum mechanics) to the more naive “measurement back-action” story typically told to, and by, lay-people.
The fact that “am I pretty?” is not a quantum-limited measurement is an entirely different story 🙂
I think there’s a subtle distinction here. Incompatible observables don’t have simultaneous eigenstates, so if you’re in the position eigenstate, you’re not in the momentum eigenstate. Making the measurement is what gets you into the position eigenstate, which means there’s uncertainty in momentum because the eigenstates can’t exist simultaneously. To me, that doesn’t seem to be quite the same as saying the measurement is the direct cause of the uncertainty. Perhaps these two ways of thinking about it are equivalent, though, and I just prefer the former because of people who take the latter to imply ridiculous pseudo-philosophical ideas like “The Secret.” (I’m not saying that Julia did anything like this, though; I just think the idea that measuring something changes it could have been presented without the Heisenberg reference.)
Hmmm, interesting way of looking at that question. I, too, have trouble telling the truth in a convincing way.
It seems to reduce to a form of “absence of evidence IS evidence of absence” (http://lesswrong.com/lw/ih/absence_of_evidence_is_evidence_of_absence/), if you interpret convincing “yes, you’re pretty” as absence of evidence of homeliness.
I’d say that’s another great example of this principle, definitely. Although the funny thing in this case is that most people intuitively know that absence of evidence is evidence of absence.
It’s usually when someone doesn’t want to admit they’re wrong that they resort to “Well just because you haven’t found X doesn’t mean it doesn’t exist!”
Suppose you take the Color Perception Test and don’t see the patterns. That’s either evidence that you’re colorblind, or that there are no patterns and the test is a scam.
A lot of cranks think they proved Einstein wrong, and don’t consider the possibility that they’re the ones who screwed up.
On the subject of using Bayes’ rule in daily life, I’ve never figured out how I feel about the “Heat Wave in X Seen as Evidence of Global Warming” news stories which seem to appear on a regular schedule*.
My first impulse is to be irritated (this is usually my first impulse; I’m pretty cranky). There are lots of cities, counties, and states out there, twelve months in the year, and so even in the absence of global warming we’ll be continuously setting temperature records somewhere sometime.
But thinking it through some more, surely global warming makes it more likely that any given temperature record is set, and stories like this therefore ought to make me revise my belief in global warming, whatever it is, upwards.
But on the other hand, it seems plausible that newspapers report records but not lack of records (“Temperature About the Same as You’d Expect” – not a publishable news story), so I would be wrong to update my belief based on the headlines.
*I suppose its questionable whether this really qualifies as “daily life.”
Revise your belief by the Bayes factor: B = P(E|H) / P(E|not-H). If newspapers are slightly more likely to report temperature records if global warming is true, then such reports should slightly increase your belief in global warming.