Friday, July 15, 2011

I'm angry so I'm not angry

Rose and Colin are in a relationship.  Because they are good game theorists, they think of it as a repeated game.  Rose is in charge of the rows, of course, and Colin has the columns.  (That's just how game theorists roll).

In particular, it's Colin's job to take out the trash every day.  Now, Rose understands that she can incentivize good behavior by punishing him sufficiently for any deviations from doing his job.  But let's say there's some essential noise.  The probability of remembering to take out the trash on any given day is not 100%. Colin could put more effort into remembering, but it would be prohibitively costly to actually remember all the time.  In fact it is socially optimal for him to just remember most of the time.  Rose knows this, and she sets up her punishments to incentivize the optimal probability of taking out the trash.

Now, here is the first odd thing that comes with being game theorists, with full awareness of what's going on here.  Rose knows she is incentivizing optimal behavior.  When Colin forgets to take out the trash, that's actually optimal behavior.  But Rose must still punish him, even though they both know he's done nothing wrong, because that's what keeps Colin from doing something wrong in the future.  

Let me be clear that because these are game theorists -- or just rational people more generally -- Rose and Colin understand that behavior should be evaluated for optimality not based on what actually happens after the fact, but rather on what was expected to happen beforehand.  If Colin accepts a bet on a coinflip, heads +$10, tails -$5, Rose will be happy with him.  To get angry at him when he happens to lose makes no sense, because the actual realization of the coin flip is not tied to Colin's behavior in any way.

So in this household, Rose (bless her heart) is not actually angry with Colin when he forgets to take out the trash.  She is not bothered by a bad realization of a random variable, so long as he is drawing from the right urn.  She is not angry, not even for a moment, when he drops a glass.  It happens to the best of us...the probability of breakage will always be nonzero.  Sometimes the situation just sucks, she is fond of saying.

But here's the second odd thing that comes out.  I said before that Rose "punishes" Colin when he forgets the trash.  But I didn't say how.  Even for economonomic types, there isn't lots of money and goods flying back and forth in the household.  More likely, if Colin does something bad, he is punished with Disapproval.  He likes Rose, you see, and he doesn't like it when Rose is upset with him.

And so we come to it.  Do you see the problem here?  Rose is supposed to punish Colin with anger, even though she isn't actually angry with him because she knows she is incentivizing ex ante good behavior, and the ex ante criterion is the correct way to evaluate behavior. (absent incomplete information, which we are ignoring today).

This is a huge problem for Rose and Colin.  Now, if Colin didn't really know what was up, possibly Rose could pretend to be angry. But since they're both game theorists, it is common knowledge that she isn't really angry.  Uh-oh.

But what actually happens?  I mean, if Rose can't credibly threaten to punish Colin, then he won't actually behave the way she wants him to, and then she'll actually be angry with him, but if she's going to actually be angry with him, then he'll do what he's supposed to, but then...

That's something for you to chew on.

For Further Thinking

So emotion-based punishments only work to the extent that your emotions are correlated with the states of the world in which you'd like to punish.  Being "in control" of your emotions normally means being able to damp them down, but what about amping them up?  It could be a useful ability, and there's information you can learn that will do its best to kill it.  Installment #643 of Information Is Not Always Good.


I do want to be explicit that there's nothing fundamentally inconsistent about having preferences over the state of the world, and therefore emotions that are tied to the realizations of random variables.  But how angry can Rose be about the simple fact that the trash is inside versus outside, versus the fact that Colin failed to take it out even though he was supposed to?  It's the latter that she's supposed to use as a lever, and it's the latter that she cannot use as a lever.  Furthermore, while we might like to believe that it should be "enough" to make her preferences over states of the world known to Colin, who cares about her, the reality is that they will always have different preferences even once they take each other's preferences into account, and there will always be bargaining going on in the relationship, to trade off between them.


So long as we're here, it goes even farther.  Picking the right urn is itself a meta-process, and on some level we're all just trying to do our best in this world, according to preferences we're all just as entitled to as anyone else.  I don't want to get too meta today, but I actually have a hard time getting angry about any behavior at all.  (Nor am I good at faking it).  This is mostly a good thing, I think, but it isn't without its drawbacks.  And while I think it's beneficial to me overall, it's not at all clear that it would be socially optimal for everyone to be like that.  Social approval and disapproval is an enormous part of what holds our society together.  I'll leave it at that for now.


  1. Exogen(e)ous CombustionJuly 15, 2011 at 1:33 PM

    To beat anyone else to it: I imagine you were so busy writing this post, you forgot to take out the trash.

  2. EC, I'm sure I'll find out tomorrow what I've forgotten today :)

  3. Rose could always call upon some external enforcer to carry out the punishment, but that might be too extreme.

  4. Tony, unfortunately I'm not up on my dr who, but...I'm sure that would make sense if I were :)

    There's still plenty that can be done in-house without whipping out the checkbooks...but disapproval would seem to be the most automatic, customizable, low-friction solution so maybe it's bad news when it breaks.

  5. The way it works in my house is that I know Jenn (my wife) isn't actually angry with me THIS time for forgetting to take out the trash, but when she reminds me that I didn't take it out (showing disapproval she doesn't really feel) she is letting me know that if I forget too often she WILL be angry.

  6. Smart, Robert. As you suggest, one possible solution to this problem: if we can observe the history of behavior, then over time we come to know with probability 1 whether the optimal probability is being used, and then we can just make the punishment conditional on truly bad behavior. Of course seeing the history is reasonable in the context of a relationship. The only caveat to be aware of is that when punishing at a later date, you know more information but also require more patience from the person you're punishing. If they don't care enough about the future, the threat of future punishment for bad behavior now may not be enough to motivate a stream of good behavior.

    More to come.