Cognitive Daily


Here’s a task that four-year-olds can do but three-year-olds have some trouble with. Imagine Sally in the picture below is playing with a ball. She puts the ball in the box and goes to the kitchen to get a drink. While she’s gone, Bill takes the ball out of the box and puts it in the bucket. When Sally returns, where does she look for the ball?


Most three-year-olds will say Sally would look in the bucket, apparently failing to realize that Sally doesn’t know anything about what Bill did while she was gone. Some researchers have explained this phenomenon by speculating that young children haven’t yet formed a theory of mind; they don’t understand that other people can have thoughts independent of their own.

But Susan Birch and Paul Bloom believe they have found a scenario where adults make a similar error.

Consider this:


This is Sally. She finishes playing with the ball and puts it in the box. Then she goes outside to play. While Sally is outside playing, her sister Denise moves the ball to another container. Then, Denise rearranges the containers in the room until they look like the picture below.


When Sally returns, she wants to play with the ball again. What are the chances Sally will look first for her ball in each of the above containers?

Here is how the adults given this test responded, as you might expect:


Another group of adults was shown the same set of pictures, but with a key difference in the text. this time they were told that “Denise moves the ball to the bucket.” The remainder of the instructions were the same. Now look at the results:


This time significantly more people said Sally would look for the ball in the bucket — despite the fact that Sally had the same information in each scenario. Birch and Bloom call this phenomenon the curse of knowledge — now that they know the ball is in the bucket, even adult respondents are more likely to say Sally will look there for it.

Birch and Bloom are careful to point out that this study doesn’t disprove the notion that three-year-olds are unable to take the perspective of others, but it does make it clear that other factors are in play. And it’s possible that, rather than being unable to understand the thoughts of others, younger children are simply more susceptible to the curse of knowledge.

Birch, S.A.J., & Bloom, P. (2007). The curse of knowledge in reasoning about false beliefs. Psychological Science, 18(5), 382-386.


  1. #1 Frac
    September 20, 2007

    Might 3 year olds be pre-disposed to think the adult “in the other room” is standing where they can see them? Wouldn’t that frequently be their experience with parents? Just curious. Perhaps it’s a simple matter of poor phrasing.

    This also reminds me of a study showing children of a certain age earnestly trying to get into toy cars that clearly wouldn’t fit them (such as one that they were just holding in their hand). Apparently the part of their brain that makes comparative size estimates doesn’t develop until well into the toddler stage.

  2. #2 Ayelet
    September 20, 2007

    Maybe I’m missing something, but I think what might be at play here is the fact that the bucket is now where the box used to be – and thus, when Sally returns, she’s going to automatically go by location, and look for where she put the ball, rather than in which container. Kind of like how we automatically reach for something we expect to be there, and end up grasping air.

    I would have an easier time with the curse of knowledge explanation if the story had referred to – well, any other container, really.

  3. #3 bonni
    September 20, 2007

    Yes, I thought the same thing about the bucket in the second example. I’ve seen my children do this many times. They remember the “last place they saw it” and go to that location. The container may or may not make a difference.

    An example might be that a child takes their shoes off and leaves them on the floor (they’re supposed to put them away, but that’s another discussion). Then they later take off their jumper (sweater) and throw that on the floor, too, right on top of the shoes.

    When I later say, “Where are your shoes?” they’ll go to the exact spot, but look very puzzled to see there are no shoes where they left them. It never seems to occur to them to move the jumper. (Maybe my kids are just weird, though, I admit I haven’t done a lot of empirical studies on them).

    Hence my belief that Sally will look in the bucket before the box. It’s not that I know where it is. It’s that I’ve seen the whole “but I saw it here” game too many times. 😉

  4. #4 Justin
    September 20, 2007

    I’m worried that the presence of a probability judgment might be an issue. The adults have to give a probability estimate which is only subject to the constraint that the box should be more probable than the bucket, which should be less probable than the vase or basket. But since that’s a weak constraint, and people are generally bad with probability, you might think priming effects (or something similar) would alter the probability assigned to looking in the bucket, without necessarily altering the ordering of the probabilities (i.e. they still say the bucket is less probable than the box, but more probable than the vase/basket).

    But that’s might be a different cognitive error than the one the children make. After all, the children think that it’s more probable that Sally looks in the bucket than in the box. They don’t just move a probability a little bit, but actually take the less probable option to be the more probable one. That’s a significant difference in kind.

  5. #5 gallstones
    September 21, 2007

    If I were Sally, my first response upon returning to the room would be to remark on the rearrangement. Then go look in the box, then get very annoyed.

  6. #6 Magnus
    September 21, 2007

    Hrrr, those diagrams tell u absolutely nothing! There is maybe an increase from 23 to 33 percent, but how do I know if that is staticicly sigificant? If u don’t gonna tell how big the groups were, it’s better to write nothing at all…

    Besides, the study is stupid anyway. Off course more people are gonna choose the bucket if it is mentioned in the text, than if it is not. The study shows nothing, this blogg-post about it shows even less 😛

  7. #7 Dave Munger
    September 21, 2007


    The diagrams don’t tell you whether the data is significant, but they certainly tell you something: they show the general pattern of responses.

    We know it’s significant because the authors report preps of .95.

    Your claim that “Of course more people are gonna choose the bucket if it is mentioned in the text” is not necessarily true: In the first scenario (with only a box and a bucket) they do not.

    The point of the study is that tests on children such as my first example don’t necessarily show that children don’t understand the thoughts of others.

  8. #8 Ben
    September 21, 2007

    I think the diagrams are unfortunate because the bucket gets moved to the same physical location as the box. It seems feasible that an adult would go back to the same physical location that they left the ball, or at least they believe they would. It would be interesting to replicate this test in real life to see what the actual responses are. I’d want to make sure to have a 3rd variance setup where the bucket still has the ball but is not moved to the same location as the box. Interesting theories, though…

  9. #9 Dave Munger
    September 21, 2007

    It seems feasible that an adult would go back to the same physical location that they left the ball, or at least they believe they would.

    Sure it does, and that’s why people say there’s a 23 percent chance that Sally would search there when they don’t know where the ball is. But what’s interesting is that when they *do* know where the ball is, that pollutes their estimate, and they increase their prediction of whether Sally will search there — even though there’s no difference at all from Sally’s perspective.

  10. #10 Scotty B
    September 21, 2007

    This is obviously because the bucket is blue, just like the box. Oh, and Sally needs glasses.


  11. #11 ES
    September 21, 2007

    I might do the same thing since they might not remember the box but just the location and so go to the bucket. To test whether it’s not the location that they are remembering they should do another 1 and this time not put the bucket where the box used to be.

    Please say how many people took part in the study next time if you are going to put graphs like that up.

  12. #12 Dave Munger
    September 21, 2007

    ES — Normally I do, however the authors didn’t report N for each condition. There were three conditions with a total of 155 participants, so I’m assuming around 50 in each condition.

  13. #13 Tony Jeremiah
    September 21, 2007

    The same type of reasoning has been observed for Piagetian tasks. For example, most 4-5 year olds are observed to have problems with abstract versions of the three-mountain task (which parallels a theory-of-mind/perspective taking task). However, when researchers used more concrete versions of the task (e.g., the use of everyday objects that children rather than adults understand) these same children are capable of doing the task. Much of their reasoning is strongly dependent on concrete experiences. So basically, if you make the task simpler (more concrete) for a child’s world, children will display thinking similar to that of adults.

    The underlying logic for this study is the same but opposite–if you make the task more complicated (abstract) for adults, then you’ll see performance that parallels a child’s thought. In this instance, though, I think the results are a combination of a task more taxing on the memory system (i.e., there are many elements to pay attention to) which makes it easier for semantic priming factors to influence the results.

    Actually, this particular study reminds me of one conducted by Loftus, where changing the wording of a question influences the type of responses one gets. In that study, participants watched a video of an accident and were then asked to approximate how fast the vehicles were going. The mean guess for speed increased for participants when only one word in the question was changed to either contacted, hit, bumped, collided, or smashed. For this study, it seems that the results can be explained by a difference in using the word “container” vs. “bucket”. The former word primes one to pay attention to all of the containers; the latter primes one to pay attention to one container (i.e., the bucket).

    So rather than a “curse of knowledge” explanation, it seems an Occam’s razor explanation would be that the study’s result is due to a confound of using leading questions as Loftus might suggest.

  14. #14 metzgerm
    September 21, 2007

    It seems like the authors must understand that many adults will choose the bucket because it is in the same place the box used to be–in the first case ~20% do. It is rational to think that Sally will go to the box and it is rational to think that Sally will go to the old location (now the bucket). And adults must make the choice as to which of these rational actions they think Sally will do first.

    I would guess that in each set-up the people choosing the bucket would say they chose it because it was in the correct location (a rational reason), but then why do more people make this choice in the second set-up? This suggests that adults know that Sally didn’t see the ball being moved, but they will sometimes incorrectly use that information (perhaps subconsciously) if they are faced with two rational choices with no clear answer–or perhaps they chose only based on their knowledge of the true location and rationalize this decision by the idea that it is in the same location.

    So this could really be an explanation of how decision making is not always directed by rational thought, although we will usually use rational thought to explain our decisions.

    If this conscious rationalization of the act is necessary, then I think that telling people that the ball was moved to the bucket and putting the bucket in a different location would not have the same effect–or it might actually lower the bucket to below 20%. In any case I’d like to see that experiment (suggested by several other comments), and also the reported explanations for the choice of container (including what that 5% that chose basket or vase were thinking).

  15. #15 zaphod
    September 21, 2007

    I always have a hard time with experiments like this proving much of anything, because of the sensitivity of the results to the wording of the scenarios and question. I also agree with other commenters that the colors and placement of the bucket and the box in the various scenarios may also skew the results. That being said, I still may be persuaded that the curse of knowledge is at play.

  16. #16 Rebecca
    September 22, 2007

    My first thought was, “How old is Sally?”

    If Sally is quite young, she might first look in the container that now is positioned where the box was — regardless of what that container is. If she’s older, she might look in the box first regardless of its new position.

    I’m not sure this study really proves anything about how adults think. The circumstances described in the story are too ambiguous.

  17. #17 Herb West
    September 22, 2007

    Dave, for this study to make sense you have to report data for all three conditions: ignorance, knowledge-plausible, and knowledge-implausible. As it currently stands your explanation makes no sense. You need to re-read the paper and revise your post.

    The standard deviations in this study were enormous. For example, in the condition in which the correct container was in the same location (knowledge-plausible) 34% of subjects chose same location with a standard deviation of 25%. Another example, in the condition in which the correct container was unspecified (ignorance condition) 23% thought Sally would look in the same location with a standard deviation of 22%. For the condition in which the correct container was basket/vase (knowledge-implausible) the percentage that chose basket was 6% with std dev of 16% and the percentage that chose vase was 3% with a std dev of 5%.

    The enormous standard deviations suggest to me that there were subpopulations within the subjects that gave distinctly different answers based on distinctly different reasoning. Therefore, pooling all the data together with this magnitude of standard deviations is probably not warranted.

  18. #18 Archana Raghuram
    September 23, 2007

    Something tells me there is something wrong with adult study, I can’t point to it though.

    If 30% adults said bucket, it just points to a lack of concentration or intelligence. If you have understood the question, you cannot get the answer wrong, isn’t it?

  19. #19 Zef
    September 24, 2007

    If anything, this is just proof of the ‘curse of word problems’! >:-)

  20. #20 Daryl McCullough
    September 24, 2007

    I have a hypothesis for the mechanism for how telling the adults where the ball is might make a difference. To answer the question, the subjects must consider what strategy Sally might follow. Three possible strategies might include: (1) choose randomly, (2) look in the container that the ball was in previously, or (3) look in the location where the ball was previously.

    The effect of telling people that Denise put the ball into the bucket is to suggest strategy (3) to them when they may have never thought of it before.

  21. #21 Crash
    November 8, 2007

    The study isn’t about Sally. Neither is it about the developing 3 year old mind. It is about the skew we place on rational analysis based upon what we know (or think we know).
    It is clear that we alter our story telling when we believe we are among others who share our knowledge and beliefs. What is indicated by the experiment is that we unjustifiably and unconscientiously alter our analysis of facts and unintentionally distort our ability to rationally predict out comes based upon our knowledge store.

  22. #22 Renee
    November 28, 2007

    The information is NOT the same. In case 1, the kids are characterized differently than in case 2. Sally and Denise are siblings, so if Denise puts the ball in the same location while moving the boxes, Sally may be more likely to look for it there than you would think if we get no information about Denise. In case one, where we don’t learning anything about the siblings at all, you would go to the default theory of mind which says to look in the box.

    In fact, this means that adults may have a better theory of mind than the psychologists designing the experiment!

  23. #23 Xanthir, FCD
    November 28, 2007

    Ooh, Daryl hits an interesting theory. It may not be that knowing the ball is in the basket actually changed the relative weight of different possibilities for some people, but rather that it introduced new possibilities entirely. This would result in different weightings, and thus possibly different answers, but not directly because of the (irrelevant) knowledge.

    I would like to see the experiment repeated, but with the order of the examples reversed. That way we can establish the “Sally thinks Denise purposely put the ball in the same location” hypothesis early on, and we can then be sure that it is present in the “Denise puts the ball in a random container” situation.

  24. #24 Samantha Vimes
    November 29, 2007

    Am I the only one who thinks that, in reality rather than theory, Sally would yell at Denise for moving everything around? Depending on how cooperative the siblings are, Sally might think Denise would leave it in the box(nice or lazy), move it to the bucket (nice, as it leaves the ball in the same place), or stick it in the vase (likely the worst of the containers to look for it in) or taken it away altogether.


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