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.
To venture a guess: their true objection was probably “you didn’t follow the rules for dealing cards”. And, to be fair to your friends, those rules were designed to defend honest players against card sharps, which makes violations Bayesian grounds to suspect you of cheating.
No, this wasn’t their true objection. I have a near flawless reputation for being honest and the arguments that ensued had nothing to do with stacking the deck. If I were a dispassionate third party dealing the game they would have objected just as strongly.
I initially had a second example as such:
Assume my friend and I each purchased a lottery ticket. As the winning number was about to be announced, we willing traded tickets. If I won, I would not be surprised to be asked to share the winnings because, after all, he chose the winning ticket.
It seems as though some personal attachment is created with the specific random object. Once that object is “taken,” there is an associated sense of loss.
Your reputation doesn’t matter. Once the rules are changed, you are on a slippery slope of changing rules. The game slowly ceases to be poker.
When I am playing chess, I demand that the white moves first. When I find myself as the black, knowing that the opponent had whites the last game and it is now my turn to make the first move, I rather change places or rotate the chessboard than play the first move with the blacks, although it would not change my chances of winning. (I don’t remember the standard openings, so I wouldn’t be confused by the change of colors. And even if I were, this would be the same for the opponent.)
Rules are rules in order to be respected. They are often a lot arbitrary, but you shouldn’t change any arbitrary rule during the game without prior consent of the others, even if it provably has no effect to the winning odds.
I think this is a fairly useful heuristic. Usually, when a player tries to change the rules, he has some reason, and usually, the reason is to increase his own chances of winning. Even if you opponent doesn’t see any profit which you can get from changing the rules, he may suppose that there is one. Maybe you remember somehow that there are better or worse cards in the middle of the pack. Or you are trying to test their attention. Or you want to make more important changes of rules later, and wanted to have a precedent for doing that. These possibilities are quite realistic in gambling, and therefore is is considered a bad manner to change the rules in any way during the game.
I don’t know how to respond to this. I feel like I have addressed all of these points elsewhere in the comments.
A summary:
The poker game is an example. There are more examples involving things with less obvious rules.
My reputation matters in the sense that they know wasn’t trying to cheat. As such, when pestered for an answer they are not secretly thinking, “Cheater.” This should imply that they are avoiding the cheater-heuristic or are unaware that they are using the cheater-heuristic.
I confronted my friends and asked for a reasonable answer. Heuristics were not offered. No one complained about broken rules or cheating. They complained that they were not going to get their card.
It seems to be a problem with ownership. If this sense of ownership is based on a heuristic meant to detect cheaters or suspicious situations… okay, I can buy that. But why would someone who knows all of the probabilities involved refuse to admit that cutting the deck doesn’t matter? Pride?
One more thing of note: They argued against the abstract scenario. This scenario assumed no cheating and no funny business. They still thought it mattered.
Personally, I think this is a larger issue than catching cheaters. People seemed somewhat attached to the anti-cheating heuristic. Would it be worth me typing up an addendum addressing that point in full?
If this sense of ownership is based on a heuristic meant to detect cheaters or suspicious situations… okay, I can buy that. But why would someone who knows all of the probabilities involved refuse to admit that cutting the deck doesn’t matter? Pride? … People seemed somewhat attached to the anti-cheating heuristic.
The System 1 suspicion-detector would be less effective if System 2 could override it, since System 2 can be manipulated.
(Another possibility may be loss aversion, making any change unattractive that guarantees a different outcome without changing the expected value. (I see hugh already mentioned this.) A third, seemingly less likely, possibility is intuitive ‘belief’ in the agency of the cards, which is somehow being undesirably thwarted by changing the ritual.)
I really don’t know. Unusual mental architecture, like high reflectivity or ‘stronger’ deliberative relative to non-deliberative motivation? Low paranoia? High trust in logical argument?
People seemed somewhat attached to the anti-cheating heuristic. Would it be worth me typing up an addendum addressing that point in full?
Depends, of course, on what exactly you would say and how much unpleasant the writing is for you.
My reputation matters in the sense that they know wasn’t trying to cheat. As such, when pestered for an answer they are not secretly thinking, “Cheater.” This should imply that they are avoiding the cheater-heuristic or are unaware that they are using the cheater-heuristic.
I would say that they impement the rule-changing-heuristic, which is not automatically thought of as an instance of the cheater-heuristic, even if it evolved from it. Changing the rules makes people feeling unsafe, people who do it without good reason are considered dangerous, but not automatically cheaters.
EDIT: And also, from your description it seems that you have deliberately broken a rule without giving any reason for that. It is suspicious.
I would say that they impement the rule-changing-heuristic, which is not automatically thought of as an instance of the cheater-heuristic, even if it evolved from it. Changing the rules makes people feeling unsafe, people who do it without good reason are considered dangerous, but not automatically cheaters.
This behavior is repeated in scenarios where the rules are not being changed or there aren’t “rules” in the sense of a game and its rules. These examples are significantly fuzzier which is why I chose the poker example.
The lottery ticket example is the first that comes to mind.
EDIT: And also, from your description it seems that you have deliberately broken a rule without giving any reason for that. It is suspicious.
Why wouldn’t the complaint then take the form of, “You broke the rules! Stop it!”?
Why wouldn’t the complaint then take the form of, “You broke the rules! Stop it!”?
Because people aren’t good at telling their actual reason for disagreement. I suspect that they are aware that the particular rule is arbitrary and doesn’t influence the game, and almost everybody agrees that blindly following the rules is not a good idea. So “you broke the rules” doesn’t sound as a good justification. “You have influenced the outcome”, on the other hand, does sound like a good justification, even if it is irrelevant.
The lottery ticked example is a valid argument, which is easily explained by attachment to random objects and which can’t be explained by rule-changing heuristic. However, rule-fixing sentiments certainly exist and I am not sure which play stronger role in the poker scenario. My intuition was that the poker scenario was more akin to, say, playing tennis in non-white clothes in the old times when it was demanded, or missing the obligatory bow before the match in judo.
Now, I am not sure which of these effects is more important in the poker scenario, and moreover I don’t see by which experiment we can discriminate between the explanation.
But this isn’t a rule of the game—it’s an implementation issue. The game is the same so long as cards are randomly selected without replacement from a deck of the appropriate sort.
That the game has the same structure either way is recognized only at a more abstract mental level than the level that the negative reaction comes from; in most people, I suspect the abstract level isn’t ‘strong enough’ here to override the more concrete/non-inferential/sphexish level.
The ideal decision algorithm used in the game remains the same, but people don’t look at it this way. It is a rule, since it is how they have learned the game.
I’m not sure our guesses (I presume you have not tested the lottery ticket swap experimentally) are actually in conflict. My thesis was not “they think you’re cheating”, but simply, straightforwardly “they object to any alteration of the dealing rules”, and they might do so for the wrong reason—even though, in their defense, valid reasons exist.
Your thesis, being narrow, is definitely of interest, though. I’m trying to think of cases where my thesis, interpreted naturally, would imply the opposite state of objection to yours. Poor shuffling (rule-stickler objects, my-cardist doesn’t) might work, but a lot of people don’t attend closely to whether cards are well-shuffled, stickler or not.
(Incidentally, If you had made a top-level post, I would want to see this kind of prediction-based elimination of alternative hypotheses.
EDIT: Wow, this turned into a ramble. I didn’t have time to proof it so I apologize if it doesn’t make sense.
I’m not sure our guesses (I presume you have not tested the lottery ticket swap experimentally) are actually in conflict. My thesis was not “they think you’re cheating”, but simply, straightforwardly “they object to any alteration of the dealing rules”, and they might do so for the wrong reason—even though, in their defense, valid reasons exist.
Okay, yeah, that makes sense. My instinct is pointing me in the other direction namely because I have the (self perceived) benefit of knowing which friends of mine were objecting. Of note, no one openly accused me of cheating or anything like that. If I accidently dropped the deck on the floor or knocked it over the complaints would remain. The specific complaint, which I specifically asked for, is that their card was put into the middle of the deck.
(By the way, I do not think that claiming arrival at a valid complaint via the wrong reason is offering much defense for my friends.)
Your thesis, being narrow, is definitely of interest, though. I’m trying to think of cases where my thesis, interpreted naturally, would imply the opposite state of objection to yours. Poor shuffling (rule-stickler objects, my-cardist doesn’t) might work, but a lot of people don’t attend closely to whether cards are well-shuffled, stickler or not.
Any pseudo random event where people can (a) predict the undisclosed particular random object and (b) someone can voluntarily preempt that prediction and change the result tends to receive the same behavior.
(I presume you have not tested the lottery ticket swap experimentally)
I have not tested it in the sense that I sought to eliminate any form of weird contamination. But I have lots of anecdotal evidence. One such, very true, story:
My grandfather once won at bingo and was offered to choose a prize from a series of stuffed animals. Each animal was accompanied by an envelope containing some amount of cash. Amongst the animals were a turtle and a rhinoceros. Traditionally, he would always choose the turtle because he likes turtles but this time he picked the rhinoceros because my father happens to like rhinos. The turtle contained more money than the rhino and my dad got to hear about how he lost my grandfather money.
Granted, there are a handful of obvious holes in this particular story. The list includes:
My grandfather could have merely used it as an excuse to jab his son-in-law in the ribs (very likely)
My grandfather was lying (not likely)
The bingo organizers knew that rhinos were chosen more often than turtles (not likely)
My grandfather wasn’t very good at probability (likely, considering he was playing bingo)
Etc.
More stories like this have taught me to never muck with pseudo random variables whose outcomes effect things people care about even if the math behind the mucking doesn’t change anything. People who had a lottery ticket and traded it for a different equal chance will get extremely depressed because they actually “had a shot at winning.” These people could completely understand the probabilities involved, but somehow this doesn’t help them avoid the “what if” depression that tells them they shouldn’t have traded tickets.
People do this all the time involving things like when they left for work. Decades ago, my mother-in-law put her sister on a bus and the sister died when the bus crashed. “What if?” has dogged her ever since. The connection between the random chance of that particular bus crashing on that particular day is associated with her completely independent choice to put her sister on the bus. While they are mathematically independent, it doesn’t change the fact that her choice mattered. For some reason, people take this mattering and do things with it that makes no sense.
This topic can branch out into really weird places when viewed this way. The classic problem of someone holding 10 people hostage and telling you to kill 1 or all 10 die matches the pattern with a moral choice instead of random chance. When asking if it is more moral to kill 1 or let the 10 die people will argue that refusing to kill an innocent will result in 9 more people dying than needed. The decision matters and this mattering reflects on the moral value of each choice. Whether this is correct or not seems to be in debate and it is only loosely relevant for this particular topic. I am eagerly looking for the eventual answer to the question, “Are these events related?” But to get there I need to understand the simple scenario, which is the one presented by my original comment.
(Incidentally, If you had made a top-level post, I would want to see this kind of prediction-based elimination of alternative hypotheses.
I am having trouble understanding this. Can you say it again with different words?
(By the way, I do not think that claiming arrival at a valid complaint via the wrong reason is offering much defense for my friends.)
I’ll give you that one, with a caveat: if an algorithm consistently outputs correct data rather than incorrect, it’s a heuristic, not a bias. They lose points either way for failing to provide valid support for their complaint.
I have not tested it in the sense that I sought to eliminate any form of weird contamination. But I have lots of anecdotal evidence. One such, very true, story: [truncated for brevity]
Yes, those anecdotes constitute the sort of data I requested—your hypothesis now outranks mine in my sorting.
(Incidentally, If you had made a top-level post, I would want to see this kind of prediction-based elimination of alternative hypotheses.
I am having trouble understanding this. Can you say it again with different words?
When I read your initial comment, I felt that you had proposed an overly complicated explanation based on the amount of evidence you presented for it. I felt so based on the fact that I could immediately arrive at a simpler (and more plausible by my prior) explanation which your evidence did not refute. It is impressive, although not necessary, when you can anticipate my plausible hypothesis and present falsifying evidence; it is sufficient, as you have done, to test both hypotheses fairly against additional data when additional hypotheses appear.
Ah, okay. That makes more sense. I am still experimenting with the amount of predictive counter-arguing to use. In the past I have attempted to so by adding examples that would address the potential objections. This hasn’t been terribly successful. I have also directly addressed the points and people still brought them up… so I am pondering how to fix the problem.
But, anyway. The topic at hand still interests me. I assume there is a term for this that matches the behavior. I could come up with some fancy technical definition (perceived present ownership of a potential future ownership) but it seems dumb to make up a term when there is one lurking around somewhere. And the idea of labeling it an ownership problem didn’t really occur to me until my conversation with you… so maybe I am answering my own question slowly?
Something like “ownership” seems right, as well as the loss aversion issue. Somehow, this seemingly-irrational behavior seems perfectly natural to me (and I’m familiar with similar complaints about the order of cards coming out). If you look at it from the standpoint of causality and counterfactuals, I think it will snap into place...
Suppose that Tim was waiting for the king of hearts to complete his royal flush, and was about to be dealt that card. Then, you cut the deck, putting the king of hearts in the middle of the deck. Therefore, you caused him to not get the king of hearts; if your cutting of the deck were surgically removed, he would have had a straight flush.
Presumably, your rejoinder would be that this scenario is just as likely as the one where he would not have gotten the king of hearts but your cutting of the deck gave it to him. But note that in this situation the other players have just as much reason to complain that you caused Tim to win!
Of course, any of them is as likely to have been benefited or hurt by this cut, assuming a uniform distribution of cards, and shuffling is not more or less “random” than shuffling plus cutting.
A digression: But hopefully at this point, you’ll realize the difference between the frequentist and Bayesian instincts in this situation. The frequentist would charitably assume that the shuffle guarantees a uniform distribution, so that the cards each have the same probability of appearing on any particular draw. The Bayesian will symmetrically note that shuffling makes everyone involved assign the same probability to each card appearing on any particular draw, due to their ignorance of which ones are more likely. But this only works because everyone involved grants that shuffling has this property. You could imagine someone who payed attention to the shuffle and knew exactly which card was going to come up, and then was duly annoyed when you unexpectedly cut the deck. Given that such a person is possible in principle, there actually is a fact about which card each person ‘would have’ gotten under a standard method, and so you really did change something by cutting the deck.
A digression: But hopefully at this point, you’ll realize the difference between the frequentist and Bayesian instincts in this situation. [...]
Yep. This really is a digression which is why I hadn’t brought up another interesting example with the same group of friends:
One of my friends dealt hearts in a manner of giving each player a pack of three cards, the next player a pack of three cards and so on. The amount of cards being dealt were the same but we all complained that this actually affected the game because shuffling isn’t truly random and it was mucking with the odds.
We didn’t do any tests on the subject because we really just wanted the annoying kid to stop dealing weird. But, now that I think about it, it should be relatively easy to test...
Also related, I have learned a few magic tricks in my time. I understand that shuffling is a tricksy business. Plenty of more amusing stories are lurking about. This one is marginally related:
At a poker game with friends of friends there was one player who shuffled by cutting the cards. No riffles, no complicated cuts, just take a chunk from the top and put it on the bottom. Me and the mathematician friend from my first example told him to knock it off and shuffle the cards. He tried to convince us he was randomizing the deck. We told him to knock it off and shuffle the cards. He obliged while claiming that it really doesn’t matter.
This example is a counterpoint to the original. Here is someone claiming that it doesn’t matter when the math says it most certainly does. The aforementioned cheater-heuristic would have prevented this player from doing something Bad. I honestly have no idea if he was just lying to us or was completely clueless but I couldn’t help but be extremely suspicious when he ended up winning first place later that night.
On a tangent, myself and friends always pick the initial draw of cards using no particular method when playing Munchkin, to emphasize that we aren’t supposed to be taking this very seriously. I favor snatching a card off the deck just as someone else was reaching for it.
When you deal Texas Hold’em, do you “burn” cards in the traditional way? Neither I nor most of my friends think that those cards are special, but it’s part of the rules of the game. Altering them, even without [suspicion of] malicious intent breaks a ritual associated with the game.
While in this instance, the ritual doesn’t protect the integrity of the game, rituals can be very important in getting into and enjoying activities. Humans are badly wired, and Less Wrong readers work hard to control our irrationalities. One arena in which I see less need for that is when our superstitious and pattern-seeking behaviors let us enjoy things more. I have a ritual for making coffee. I enjoy coffee without it, but I can reach a near-euphoric state with it. Faulty wiring, but I see no harm in taking advantage of it.
When you deal Texas Hold’em, do you “burn” cards in the traditional way? Neither I nor most of my friends think that those cards are special, but it’s part of the rules of the game. Altering them, even without (suspicion of) malicious intent breaks a ritual associated with the game.
We didn’t until the people on TV did it. The ritual was only important in the sense that this is how they were predicting which card they were going to get. Their point was based entirely on the fact that the card they were going to get is not the card they ended up getting.
As a reminder to the ongoing conversation, we had arguments about the topic. They didn’t say, “Do it because you are supposed to do it!” They said, “Don’t change the card I am supposed to get!”
One arena in which I see less need for that is when our superstitious and pattern-seeking behaviors let us enjoy things more. I have a ritual for making coffee. I enjoy coffee without it, but I can reach a near-euphoric state with it. Faulty wiring, but I see no harm in taking advantage of it.
Sure, but this isn’t one of those cases. In this case, they are complaining for no good reason. Well, I guess I haven’t found a good reason for their reaction. The consensus in the replies here seems to be that their reaction was wrong.
I am not trying to say you shouldn’t enjoy your coffee rituals.
RobinZ ventured a guess that their true objection was not their stated objection; I stated it poorly, but I was offering the same hypothesis with a different true objection—that you were disrupting the flow of the game.
I’m not entirely sure if this makes sense, partially because there is no reason to disguise unhappiness with an unusual order of game play. From what you’ve said, your friends worked to convince you that their objection was really about which cards were being dealt, and in this instance I think we can believe them. My fallacy was probably one of projection, in that I would have objected in the same instance, but for different reasons. I was also trying to defend their point of view as much as possible, so I was trying to find a rational explanation for it.
I suspect that the real problem is related to the certainty effect. In this case, though no probabilities were altered, there was a new “what-if” introduced into the situation. Now, if they lose (or rather, when all but one of you lose) they will likely retrace the situation and think that if you hadn’t cut the deck, they could have won. Which is true, of course, but irrelevant, since it also could have gone the other way. However, the same thought process doesn’t occur on winning; people aren’t inclined to analyze their successes in the say way that they analyze their failures, even if they are both random events. The negative emotion associated with feeling like a victory is stolen would be enough to preemptively object and prevent that from occurring in the first place.
However, even if what I said above is true, I don’t think it really addresses the problem of adjusting their map to match the territory. That’s another question entirely.
I agree with your comment and this part especially:
However, the same thought process doesn’t occur on winning; people aren’t inclined to analyze their successes in the say way that they analyze their failures, even if they are both random events.
Very true. I see a lot of behavior that matches this. This would be an excellent source of the complaint if it happened after they lost. My friends complained before they even picked up their cards.
Rather than focusing on any Bayesian evidence for cheating, let’s think like evolution for a second: how do you want your organism to react when someone else’s voluntary action changes who receives a prize? Do you want the organism to react, on a gut level, as if the action could have just as easily swung the balance in their favor as against them? Or do you want them to cry foul if they’re in a social position to do so?
Your friends’ response could come directly out of that adaptation, whatever rationalizations they make for it afterwards. I’d expect to see the same reaction in experiments with chimps.
How do you want your organism to react when someone else’s voluntary action changes who receives a prize?
I want my organism to be able to tell the difference between a cheater and someone making irrelevant changes to a deck of cards. I assume this was a rhetorical question.
Evolution is great but I want more than that. I want to know why. I want to know why my friends feel that way but I didn’t when the roles were reversed. The answer is not “because I knew more math.” Have I just evolved differently?
I want to know what other areas are affected by this. I want to know how to predict whatever caused this reaction in my friends before it happens in me. “Evolution” doesn’t help me do that. I cannot think like evolution.
As much as, “You could have been cheating” is a great response—and “They are conditioned to respond to this situation as if you were cheating” is a better response—these friends know the probabilities are the same and know I wasn’t cheating. And they still react this way because… why?
I suppose this comment is a bit snippier than it needs to be. I don’t understand how your answer is an answer. I also don’t know much about evolution. If I learned more about evolution would I be less confused?
It might be because people conceive a loss more severely than a gain. There might be an evolutionary explanation for that. Because of that they would conceive their “lossed” card which they already thought would be theirs more severely than the card the “gained” after the cut. While you on the other hand might already be trained to think about it differently.
Based on my friends, the care/don’t care dichotomy cuts orthogonally to the math/no math dichotomy. Most people, whether good or bad at math, can understand that the chances are the same. It’s some other independent aspect of your brain that determines whether it intensely matters to you to do things “the right way” or if you can accept the symmetry of the situation. I hereby nominate some OCD-like explanation. I’d be interested in seeing whether OCD correlated with your friends’ behavior.
As a data point, I am not OCD and don’t care if you cut the deck.
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.
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.
An important element of it being fair for you to cut the deck in the middle of dealing, which your friends may not trust, is that you do so in ignorance of who it will help and who it will hinder. By cutting the deck, you have explicitly made and acted on a choice (it is far less obvious when you choose not to cut the deck, the default expected action), and this causes your friends to worry that the choice may have been optimized for interests other than their own.
As you note, regular poker and poker with an extra cut mid-deal are completely isomorphic. In a professional game you would obviously care, because the formality of the shuffle and deal are part of a tradition to instill trust that the deck isn’t rigged. For a casual game, where it is assumed no one is cheating, then, unless you’re a stickler for tradition, who cares? Your friends are wrong. We have two different pointers pointing to the same thing, and they are complaining because the pointers aren’t the same, even though all that matters is what those pointers point to. It would be like complaining if you tried to change the name of Poker to Wallaboo mid-deal.
There are rules for the game that are perceived as fair.
If one participant goes changing the rules in the middle of the game this 1) makes rule changing acceptable in the game, 2) forces other players to analyze the current (and future changes) to the game to ensure they are fair.
Cutting the deck probably doesn’t affect the probability distribution (unless you shuffled the deck in a “funny” way). Allowing it makes a case for allowing the next changes in the rules too. Thus you can end up analyzing a new game rather than having fun playing poker.
For a casual game, where it is assumed no one is cheating, then, unless you’re a stickler for tradition, who cares? Your friends are wrong.
Sure, but the “wrong” in this case couldn’t be shown to my friends. They perfectly understood probability. The problem wasn’t in the math. So where were they wrong?
Another way of saying this:
The territory said one thing
Their map said another thing
Their map understood probability
Where did their map go wrong?
The answer has nothing to do with me cheating and has nothing to do with misunderstanding probability. There is some other problem here and I don’t know what it is.
An argument isomorphic to yours can be used to demonstrate that spousal cheating is okay as long as there are no consequences and the spouse doesn’t know. Maybe your concept of “valid objection” is overly narrow?
Rearranging the cards in a deck has no statistical consequence. Cheating on your spouse significantly alters the odds of certain things happening.
If you add the restriction that there are no consequences, there wouldn’t really be much point in doing it because its not like you get sex as a result. That would be a consequence.
The idea that something immoral shouldn’t be immoral if no one catches you and nothing bad happens as a result is an open problem as far as I know. Most people don’t like such an idea but I hear the debate surface from time to time. (Usually by people trying to convince themselves that whatever they just did wasn’t wrong.)
In addition, cutting a deck of cards does have an obvious effect. There is no statistical consequence but obviously you are not going to get the card you were originally going to be dealt.
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.
To venture a guess: their true objection was probably “you didn’t follow the rules for dealing cards”. And, to be fair to your friends, those rules were designed to defend honest players against card sharps, which makes violations Bayesian grounds to suspect you of cheating.
No, this wasn’t their true objection. I have a near flawless reputation for being honest and the arguments that ensued had nothing to do with stacking the deck. If I were a dispassionate third party dealing the game they would have objected just as strongly.
I initially had a second example as such:
It seems as though some personal attachment is created with the specific random object. Once that object is “taken,” there is an associated sense of loss.
Your reputation doesn’t matter. Once the rules are changed, you are on a slippery slope of changing rules. The game slowly ceases to be poker.
When I am playing chess, I demand that the white moves first. When I find myself as the black, knowing that the opponent had whites the last game and it is now my turn to make the first move, I rather change places or rotate the chessboard than play the first move with the blacks, although it would not change my chances of winning. (I don’t remember the standard openings, so I wouldn’t be confused by the change of colors. And even if I were, this would be the same for the opponent.)
Rules are rules in order to be respected. They are often a lot arbitrary, but you shouldn’t change any arbitrary rule during the game without prior consent of the others, even if it provably has no effect to the winning odds.
I think this is a fairly useful heuristic. Usually, when a player tries to change the rules, he has some reason, and usually, the reason is to increase his own chances of winning. Even if you opponent doesn’t see any profit which you can get from changing the rules, he may suppose that there is one. Maybe you remember somehow that there are better or worse cards in the middle of the pack. Or you are trying to test their attention. Or you want to make more important changes of rules later, and wanted to have a precedent for doing that. These possibilities are quite realistic in gambling, and therefore is is considered a bad manner to change the rules in any way during the game.
I don’t know how to respond to this. I feel like I have addressed all of these points elsewhere in the comments.
A summary:
The poker game is an example. There are more examples involving things with less obvious rules.
My reputation matters in the sense that they know wasn’t trying to cheat. As such, when pestered for an answer they are not secretly thinking, “Cheater.” This should imply that they are avoiding the cheater-heuristic or are unaware that they are using the cheater-heuristic.
I confronted my friends and asked for a reasonable answer. Heuristics were not offered. No one complained about broken rules or cheating. They complained that they were not going to get their card.
It seems to be a problem with ownership. If this sense of ownership is based on a heuristic meant to detect cheaters or suspicious situations… okay, I can buy that. But why would someone who knows all of the probabilities involved refuse to admit that cutting the deck doesn’t matter? Pride?
One more thing of note: They argued against the abstract scenario. This scenario assumed no cheating and no funny business. They still thought it mattered.
Personally, I think this is a larger issue than catching cheaters. People seemed somewhat attached to the anti-cheating heuristic. Would it be worth me typing up an addendum addressing that point in full?
The System 1 suspicion-detector would be less effective if System 2 could override it, since System 2 can be manipulated.
(Another possibility may be loss aversion, making any change unattractive that guarantees a different outcome without changing the expected value. (I see hugh already mentioned this.) A third, seemingly less likely, possibility is intuitive ‘belief’ in the agency of the cards, which is somehow being undesirably thwarted by changing the ritual.)
Why can I override mine? What makes me different from my friends? The answer isn’t knowledge of math or probabilities.
I really don’t know. Unusual mental architecture, like high reflectivity or ‘stronger’ deliberative relative to non-deliberative motivation? Low paranoia? High trust in logical argument?
Depends, of course, on what exactly you would say and how much unpleasant the writing is for you.
I would say that they impement the rule-changing-heuristic, which is not automatically thought of as an instance of the cheater-heuristic, even if it evolved from it. Changing the rules makes people feeling unsafe, people who do it without good reason are considered dangerous, but not automatically cheaters.
EDIT: And also, from your description it seems that you have deliberately broken a rule without giving any reason for that. It is suspicious.
This behavior is repeated in scenarios where the rules are not being changed or there aren’t “rules” in the sense of a game and its rules. These examples are significantly fuzzier which is why I chose the poker example.
The lottery ticket example is the first that comes to mind.
Why wouldn’t the complaint then take the form of, “You broke the rules! Stop it!”?
Because people aren’t good at telling their actual reason for disagreement. I suspect that they are aware that the particular rule is arbitrary and doesn’t influence the game, and almost everybody agrees that blindly following the rules is not a good idea. So “you broke the rules” doesn’t sound as a good justification. “You have influenced the outcome”, on the other hand, does sound like a good justification, even if it is irrelevant.
The lottery ticked example is a valid argument, which is easily explained by attachment to random objects and which can’t be explained by rule-changing heuristic. However, rule-fixing sentiments certainly exist and I am not sure which play stronger role in the poker scenario. My intuition was that the poker scenario was more akin to, say, playing tennis in non-white clothes in the old times when it was demanded, or missing the obligatory bow before the match in judo.
Now, I am not sure which of these effects is more important in the poker scenario, and moreover I don’t see by which experiment we can discriminate between the explanation.
This is the best synopsis of the “true rejection” article I have ever seen.
That works for me. I am not convinced that the rule-changing heuristic was the cause but I think you have defended your position adequately.
But this isn’t a rule of the game—it’s an implementation issue. The game is the same so long as cards are randomly selected without replacement from a deck of the appropriate sort.
(The first Google hit for “texas hold’em rules” in fact mentions burning cards.)
That the game has the same structure either way is recognized only at a more abstract mental level than the level that the negative reaction comes from; in most people, I suspect the abstract level isn’t ‘strong enough’ here to override the more concrete/non-inferential/sphexish level.
The ideal decision algorithm used in the game remains the same, but people don’t look at it this way. It is a rule, since it is how they have learned the game.
I’m not sure our guesses (I presume you have not tested the lottery ticket swap experimentally) are actually in conflict. My thesis was not “they think you’re cheating”, but simply, straightforwardly “they object to any alteration of the dealing rules”, and they might do so for the wrong reason—even though, in their defense, valid reasons exist.
Your thesis, being narrow, is definitely of interest, though. I’m trying to think of cases where my thesis, interpreted naturally, would imply the opposite state of objection to yours. Poor shuffling (rule-stickler objects, my-cardist doesn’t) might work, but a lot of people don’t attend closely to whether cards are well-shuffled, stickler or not.
(Incidentally, If you had made a top-level post, I would want to see this kind of prediction-based elimination of alternative hypotheses.
EDIT: Wow, this turned into a ramble. I didn’t have time to proof it so I apologize if it doesn’t make sense.
Okay, yeah, that makes sense. My instinct is pointing me in the other direction namely because I have the (self perceived) benefit of knowing which friends of mine were objecting. Of note, no one openly accused me of cheating or anything like that. If I accidently dropped the deck on the floor or knocked it over the complaints would remain. The specific complaint, which I specifically asked for, is that their card was put into the middle of the deck.
(By the way, I do not think that claiming arrival at a valid complaint via the wrong reason is offering much defense for my friends.)
Any pseudo random event where people can (a) predict the undisclosed particular random object and (b) someone can voluntarily preempt that prediction and change the result tends to receive the same behavior.
I have not tested it in the sense that I sought to eliminate any form of weird contamination. But I have lots of anecdotal evidence. One such, very true, story:
Granted, there are a handful of obvious holes in this particular story. The list includes:
My grandfather could have merely used it as an excuse to jab his son-in-law in the ribs (very likely)
My grandfather was lying (not likely)
The bingo organizers knew that rhinos were chosen more often than turtles (not likely)
My grandfather wasn’t very good at probability (likely, considering he was playing bingo)
Etc.
More stories like this have taught me to never muck with pseudo random variables whose outcomes effect things people care about even if the math behind the mucking doesn’t change anything. People who had a lottery ticket and traded it for a different equal chance will get extremely depressed because they actually “had a shot at winning.” These people could completely understand the probabilities involved, but somehow this doesn’t help them avoid the “what if” depression that tells them they shouldn’t have traded tickets.
People do this all the time involving things like when they left for work. Decades ago, my mother-in-law put her sister on a bus and the sister died when the bus crashed. “What if?” has dogged her ever since. The connection between the random chance of that particular bus crashing on that particular day is associated with her completely independent choice to put her sister on the bus. While they are mathematically independent, it doesn’t change the fact that her choice mattered. For some reason, people take this mattering and do things with it that makes no sense.
This topic can branch out into really weird places when viewed this way. The classic problem of someone holding 10 people hostage and telling you to kill 1 or all 10 die matches the pattern with a moral choice instead of random chance. When asking if it is more moral to kill 1 or let the 10 die people will argue that refusing to kill an innocent will result in 9 more people dying than needed. The decision matters and this mattering reflects on the moral value of each choice. Whether this is correct or not seems to be in debate and it is only loosely relevant for this particular topic. I am eagerly looking for the eventual answer to the question, “Are these events related?” But to get there I need to understand the simple scenario, which is the one presented by my original comment.
I am having trouble understanding this. Can you say it again with different words?
Have no fear—your comment is clear.
I’ll give you that one, with a caveat: if an algorithm consistently outputs correct data rather than incorrect, it’s a heuristic, not a bias. They lose points either way for failing to provide valid support for their complaint.
Yes, those anecdotes constitute the sort of data I requested—your hypothesis now outranks mine in my sorting.
When I read your initial comment, I felt that you had proposed an overly complicated explanation based on the amount of evidence you presented for it. I felt so based on the fact that I could immediately arrive at a simpler (and more plausible by my prior) explanation which your evidence did not refute. It is impressive, although not necessary, when you can anticipate my plausible hypothesis and present falsifying evidence; it is sufficient, as you have done, to test both hypotheses fairly against additional data when additional hypotheses appear.
Ah, okay. That makes more sense. I am still experimenting with the amount of predictive counter-arguing to use. In the past I have attempted to so by adding examples that would address the potential objections. This hasn’t been terribly successful. I have also directly addressed the points and people still brought them up… so I am pondering how to fix the problem.
But, anyway. The topic at hand still interests me. I assume there is a term for this that matches the behavior. I could come up with some fancy technical definition (perceived present ownership of a potential future ownership) but it seems dumb to make up a term when there is one lurking around somewhere. And the idea of labeling it an ownership problem didn’t really occur to me until my conversation with you… so maybe I am answering my own question slowly?
Something like “ownership” seems right, as well as the loss aversion issue. Somehow, this seemingly-irrational behavior seems perfectly natural to me (and I’m familiar with similar complaints about the order of cards coming out). If you look at it from the standpoint of causality and counterfactuals, I think it will snap into place...
Suppose that Tim was waiting for the king of hearts to complete his royal flush, and was about to be dealt that card. Then, you cut the deck, putting the king of hearts in the middle of the deck. Therefore, you caused him to not get the king of hearts; if your cutting of the deck were surgically removed, he would have had a straight flush.
Presumably, your rejoinder would be that this scenario is just as likely as the one where he would not have gotten the king of hearts but your cutting of the deck gave it to him. But note that in this situation the other players have just as much reason to complain that you caused Tim to win!
Of course, any of them is as likely to have been benefited or hurt by this cut, assuming a uniform distribution of cards, and shuffling is not more or less “random” than shuffling plus cutting.
A digression: But hopefully at this point, you’ll realize the difference between the frequentist and Bayesian instincts in this situation. The frequentist would charitably assume that the shuffle guarantees a uniform distribution, so that the cards each have the same probability of appearing on any particular draw. The Bayesian will symmetrically note that shuffling makes everyone involved assign the same probability to each card appearing on any particular draw, due to their ignorance of which ones are more likely. But this only works because everyone involved grants that shuffling has this property. You could imagine someone who payed attention to the shuffle and knew exactly which card was going to come up, and then was duly annoyed when you unexpectedly cut the deck. Given that such a person is possible in principle, there actually is a fact about which card each person ‘would have’ gotten under a standard method, and so you really did change something by cutting the deck.
Yep. This really is a digression which is why I hadn’t brought up another interesting example with the same group of friends:
We didn’t do any tests on the subject because we really just wanted the annoying kid to stop dealing weird. But, now that I think about it, it should be relatively easy to test...
Also related, I have learned a few magic tricks in my time. I understand that shuffling is a tricksy business. Plenty of more amusing stories are lurking about. This one is marginally related:
This example is a counterpoint to the original. Here is someone claiming that it doesn’t matter when the math says it most certainly does. The aforementioned cheater-heuristic would have prevented this player from doing something Bad. I honestly have no idea if he was just lying to us or was completely clueless but I couldn’t help but be extremely suspicious when he ended up winning first place later that night.
On a tangent, myself and friends always pick the initial draw of cards using no particular method when playing Munchkin, to emphasize that we aren’t supposed to be taking this very seriously. I favor snatching a card off the deck just as someone else was reaching for it.
When you deal Texas Hold’em, do you “burn” cards in the traditional way? Neither I nor most of my friends think that those cards are special, but it’s part of the rules of the game. Altering them, even without [suspicion of] malicious intent breaks a ritual associated with the game.
While in this instance, the ritual doesn’t protect the integrity of the game, rituals can be very important in getting into and enjoying activities. Humans are badly wired, and Less Wrong readers work hard to control our irrationalities. One arena in which I see less need for that is when our superstitious and pattern-seeking behaviors let us enjoy things more. I have a ritual for making coffee. I enjoy coffee without it, but I can reach a near-euphoric state with it. Faulty wiring, but I see no harm in taking advantage of it.
We didn’t until the people on TV did it. The ritual was only important in the sense that this is how they were predicting which card they were going to get. Their point was based entirely on the fact that the card they were going to get is not the card they ended up getting.
As a reminder to the ongoing conversation, we had arguments about the topic. They didn’t say, “Do it because you are supposed to do it!” They said, “Don’t change the card I am supposed to get!”
Sure, but this isn’t one of those cases. In this case, they are complaining for no good reason. Well, I guess I haven’t found a good reason for their reaction. The consensus in the replies here seems to be that their reaction was wrong.
I am not trying to say you shouldn’t enjoy your coffee rituals.
RobinZ ventured a guess that their true objection was not their stated objection; I stated it poorly, but I was offering the same hypothesis with a different true objection—that you were disrupting the flow of the game.
I’m not entirely sure if this makes sense, partially because there is no reason to disguise unhappiness with an unusual order of game play. From what you’ve said, your friends worked to convince you that their objection was really about which cards were being dealt, and in this instance I think we can believe them. My fallacy was probably one of projection, in that I would have objected in the same instance, but for different reasons. I was also trying to defend their point of view as much as possible, so I was trying to find a rational explanation for it.
I suspect that the real problem is related to the certainty effect. In this case, though no probabilities were altered, there was a new “what-if” introduced into the situation. Now, if they lose (or rather, when all but one of you lose) they will likely retrace the situation and think that if you hadn’t cut the deck, they could have won. Which is true, of course, but irrelevant, since it also could have gone the other way. However, the same thought process doesn’t occur on winning; people aren’t inclined to analyze their successes in the say way that they analyze their failures, even if they are both random events. The negative emotion associated with feeling like a victory is stolen would be enough to preemptively object and prevent that from occurring in the first place.
However, even if what I said above is true, I don’t think it really addresses the problem of adjusting their map to match the territory. That’s another question entirely.
I agree with your comment and this part especially:
Very true. I see a lot of behavior that matches this. This would be an excellent source of the complaint if it happened after they lost. My friends complained before they even picked up their cards.
That’s what they say, I take it.
To modify RobinZ’s hypothesis:
Rather than focusing on any Bayesian evidence for cheating, let’s think like evolution for a second: how do you want your organism to react when someone else’s voluntary action changes who receives a prize? Do you want the organism to react, on a gut level, as if the action could have just as easily swung the balance in their favor as against them? Or do you want them to cry foul if they’re in a social position to do so?
Your friends’ response could come directly out of that adaptation, whatever rationalizations they make for it afterwards. I’d expect to see the same reaction in experiments with chimps.
I want my organism to be able to tell the difference between a cheater and someone making irrelevant changes to a deck of cards. I assume this was a rhetorical question.
Evolution is great but I want more than that. I want to know why. I want to know why my friends feel that way but I didn’t when the roles were reversed. The answer is not “because I knew more math.” Have I just evolved differently?
I want to know what other areas are affected by this. I want to know how to predict whatever caused this reaction in my friends before it happens in me. “Evolution” doesn’t help me do that. I cannot think like evolution.
As much as, “You could have been cheating” is a great response—and “They are conditioned to respond to this situation as if you were cheating” is a better response—these friends know the probabilities are the same and know I wasn’t cheating. And they still react this way because… why?
I suppose this comment is a bit snippier than it needs to be. I don’t understand how your answer is an answer. I also don’t know much about evolution. If I learned more about evolution would I be less confused?
It might be because people conceive a loss more severely than a gain. There might be an evolutionary explanation for that. Because of that they would conceive their “lossed” card which they already thought would be theirs more severely than the card the “gained” after the cut. While you on the other hand might already be trained to think about it differently.
Based on my friends, the care/don’t care dichotomy cuts orthogonally to the math/no math dichotomy. Most people, whether good or bad at math, can understand that the chances are the same. It’s some other independent aspect of your brain that determines whether it intensely matters to you to do things “the right way” or if you can accept the symmetry of the situation. I hereby nominate some OCD-like explanation. I’d be interested in seeing whether OCD correlated with your friends’ behavior.
As a data point, I am not OCD and don’t care if you cut the deck.
I am more likely to be considered OCD than any of my friends in the example. I don’t care if you cut the deck.
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.
An important element of it being fair for you to cut the deck in the middle of dealing, which your friends may not trust, is that you do so in ignorance of who it will help and who it will hinder. By cutting the deck, you have explicitly made and acted on a choice (it is far less obvious when you choose not to cut the deck, the default expected action), and this causes your friends to worry that the choice may have been optimized for interests other than their own.
I don’t think this is relevant. I responded in more detail to RobinZ’s comment.
As you note, regular poker and poker with an extra cut mid-deal are completely isomorphic. In a professional game you would obviously care, because the formality of the shuffle and deal are part of a tradition to instill trust that the deck isn’t rigged. For a casual game, where it is assumed no one is cheating, then, unless you’re a stickler for tradition, who cares? Your friends are wrong. We have two different pointers pointing to the same thing, and they are complaining because the pointers aren’t the same, even though all that matters is what those pointers point to. It would be like complaining if you tried to change the name of Poker to Wallaboo mid-deal.
There are rules for the game that are perceived as fair.
If one participant goes changing the rules in the middle of the game this 1) makes rule changing acceptable in the game, 2) forces other players to analyze the current (and future changes) to the game to ensure they are fair.
Cutting the deck probably doesn’t affect the probability distribution (unless you shuffled the deck in a “funny” way). Allowing it makes a case for allowing the next changes in the rules too. Thus you can end up analyzing a new game rather than having fun playing poker.
Sure, but the “wrong” in this case couldn’t be shown to my friends. They perfectly understood probability. The problem wasn’t in the math. So where were they wrong?
Another way of saying this:
The territory said one thing
Their map said another thing
Their map understood probability
Where did their map go wrong?
The answer has nothing to do with me cheating and has nothing to do with misunderstanding probability. There is some other problem here and I don’t know what it is.
An argument isomorphic to yours can be used to demonstrate that spousal cheating is okay as long as there are no consequences and the spouse doesn’t know. Maybe your concept of “valid objection” is overly narrow?
Rearranging the cards in a deck has no statistical consequence. Cheating on your spouse significantly alters the odds of certain things happening.
If you add the restriction that there are no consequences, there wouldn’t really be much point in doing it because its not like you get sex as a result. That would be a consequence.
The idea that something immoral shouldn’t be immoral if no one catches you and nothing bad happens as a result is an open problem as far as I know. Most people don’t like such an idea but I hear the debate surface from time to time. (Usually by people trying to convince themselves that whatever they just did wasn’t wrong.)
In addition, cutting a deck of cards does have an obvious effect. There is no statistical consequence but obviously you are not going to get the card you were originally going to be dealt.