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rwallace comments on Open Thread: March 2010 - Less Wrong
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This was in my drafts folder but due to the lackluster performance of my latest few posts I decided it doesn't deserve to be a top level post. As such, I am making it a comment here. It also does not answer the question being asked so it probably wouldn't have made the cut even if my last few posts been voted to +20 and promoted... but whatever. :P
Perceived Change
Once, I was dealing a game of poker for some friends. After dealing some but not all of the cards I cut the deck and continued dealing. This irritated them a great deal because I altered the order of the deck because some players would not receive the cards they were supposed to be dealt. One of the friends happened to be majoring in Mathematics and understood probability as much as anyone else at the table. Even he thought what I did was wrong.
I explained that the cut didn’t matter because everyone still has the same odds of receiving any particular card from the deck. His retort was that it did matter because the card he was going to get is now near the middle of the deck. Instead of that particular random card he will get a different particular random card. As such, I should not have cut the deck.
During the ensuing arguments I found myself constantly presented with the following point: The fact of the game is that he would have received a certain card and now he will receive a different card. Shouldn’t this matter? People seem to hold grudges when someone swaps random chances of an outcome and the swap changes who wins.
The problem with this objection is illustrated if I secretly cut the cards. If they have no reason to believe I cut the deck, they wouldn’t complain. Furthermore, it is completely impossible to perceive the change by studying before and after states of the probabilities. More clearly, if I put the cards under the table and threatened to cut the cards, my friends would have no way of knowing whether or not I cut the deck. This implies that the change itself is not the sole cause of complaint. The change must be accompanied with the knowledge that something was changed.
The big catch is that the change itself isn’t actually necessary at all. If I simply tell my friends that I cut the cards when they were not looking they will be just as upset. They have perceived a change in the situation. In reality, every card is in exactly the same position and they will be dealt what they think they should have been dealt. But now even that has changed. Now they actually think the exact opposite. Even though nothing about the deck has been changed, they now think that the cards being dealt to them are the wrong cards.
What is this? There has to be some label for this, but I don’t know what it is or what the next step in this observation should be. Something is seriously, obviously wrong. What is it?
Edit to add:
The underlying problem here is not that they were worried about me cheating. The specific scenario and the arguments that followed from that scenario were such that cheating wasn't really a valid excuse for their objections.
It's a side effect.
Yes, they were being irrational in this case. But the heuristics they were using are there for good reason. Suppose they had money coming to them and you swooped in and took it away before it could reach them, they would be rational to object, right? That's why those heuristics are there. In practice the trigger conditions for these things are not specified with unlimited precision, and pure but interruptible random number generators are not common in real life, so the trigger conditions harmlessly spill over to this case. But the upshot is that they were irrational as a side effect of usually rational heuristics.
So, when I pester them for a rational reason, why do they keep giving an answer that is irrational for this situation?
I can understand your answer if the scenario was more like:
"Hey! Don't do that!"
"But it doesn't matter. See?"
"Oh. Well, okay. But don't do it anyway because..."
And then they mention your heuristic. They didn't do anything like this. They explicitly understood that nothing was changing in the probabilities and they explicitly understood that I was not cheating. And they were completely willing to defend their reaction in arguments. In their mind, their position was completely rational. I could not convince them that it was rational with math. Something else was the problem.
"Heuristics" is nifty, but I am not completely satisfied with that answer. Why would they have kept defending it when it was demonstrably wrong?
I suppose it is possible that they were completely unaware that they were using whatever heuristic they were using. Would that explain the behavior? Perhaps this is why they could not explain their position to me at the time of the arguments?
How would you describe this heuristic in a few sentences?
I suspect it starts with something like "in the context of a game or other competition, if my opponent does something unexpected, and I don't understand why, it's probably bad news for me", with an emotional response of suspicion. Then when your explanation is about why shuffling the cards is neutral rather than being about why you did something unexpected, it triggers an "if someone I'm suspicious of tries to convince me with logic rather than just assuring me that they're harmless, they're probably trying to get away with something" heuristic.
Also, most people seem to make the assumption, in cases like that, that they aren't going to be able to figure out what you're up to on the fly, so even flawless logic is unlikely to be accepted - the heuristic is "there must be a catch somewhere, even if I don't see it".
Because human beings often first have a reaction based on an evolved, unconscious heuristic, and only later form a conscious rationalization about it, which can end up looking irrational if you ask the right questions (e.g. the standard reactions to the incest thought experiment there). So, yes, they were probably unaware of the heuristic they were actually using.
I'd suppose that the heuristic is along the lines of the following: Say there's an agreed-upon fair procedure for deciding who gets something, and then someone changes that procedure, and someone other than you ends up benefiting. Then it's unfair, and what's yours has probably been taken.
Given that rigorous probability theory didn't emerge until the later stages of human civilization, there's not much room for an additional heuristic saying "unless it doesn't change the odds" to have evolved; indeed, all of the agreed-upon random ways of selecting things (that I've ever heard of) work by obvious symmetry of chances rather than by abstract equality of odds†, and most of the times someone intentionally changed the process, they were probably in fact hoping to cheat the odds.
† Thought experiment: we have to decide a binary disagreement by chance, and instead of flipping a coin or playing Rock-Paper-Scissors, I suggest we do the following: First, you roll a 6-sided die, and if it's a 1 or 2 you win. Otherwise, I roll a 12-sided die, and if it's 1 through 9 I win, and if it's 10 through 12 you win.
Now compute the odds (50-50, unless I made a dumb mistake), and then actually try it (in real life) with non-negligible stakes. I predict that you'll feel slightly more uneasy about the experience than you would be flipping a coin.
Everything else you've said makes sense, but I think the heuristic here is way off. Firstly, they object before the results have been produced, so the benefit is unknown. Second, the assumption of an agreed upon procedure is only really valid in the poker example. Other examples don't have such an agreement and seem to display the same behavior. Finally, the change to the produce could be by a disinterested party with no possible personal gain to be had. I suspect that the reaction would stay the same.
So, whatever heuristic may be at fault here, it doesn't seem to be the one you are focusing on. The fact that my friends didn't say, "You're cheating" or "You broke the rules" is more evidence against this being the heuristic. I am open to the idea of a heuristic being behind this. I am also open to the idea that my friends may not be aware of the heuristic or its implications. But I don't see how anything is pointing toward the heuristic you have suggested.
Hmm... 1/3 I win outright... 2/3 enters a second roll where I win 1/4 of the time. Is that...
1/3 + 2/3 * 1/4 =
1/3 + 2/12 =
4/12 + 2/12 =
6/12 =
1/2
Seems right to me. And I don't suspect to feel uneasy about such an experience at all since the odds are the same. If someone offered me a scenario and I didn't have the math prepared I would work out the math and decide if it is fair.
If I do the contest and you start winning every single time I might start getting nervous. But I would do the same thing regardless of the dice/coin combos we were using.
I would actually feel safer using the dice because I found that I can strongly influence flipping a fair quarter in my favor without much effort.