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”.
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.
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.
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.
† 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.
Hmm… 1⁄3 I win outright… 2⁄3 enters a second roll where I win 1⁄4 of the time. Is that...
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.
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.