150. Mutual & Common Knowledge | THUNK
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- Опубликовано: 10 фев 2025
- Mutual & common knowledge: because simulating someone else simulating you is confusing...perhaps usefully so....
Links for the Curious
A spreadsheet tabulating the results of the 2/3rds game after 2 weeks: l.facebook.com...
Common Knowledge & Aumann's Agreement Theorem, by Scott Aaronson - www.scottaaron...
Common Knowledge (Vanderschraaf & Sillari, 2014) - plato.stanford...
The Psychology of Common Knowledge & Coordination (Thomas et al, 2014) - dash.harvard.e...
Bystander "Apathy" (Latane & Darley, 1969) - greatergood.be...
The logic of indirect speech (Pinker et al, 2008) - stevenpinker.c...
This channel is so underrated!
JaCk JF very true
Fun video!
I think we can compute an upper bound estimate dependent on the amount of recursion we assume the average guesser will do. If we assume that the population of guessers only chooses between 1 and 100 without dependence on others (0th degree as in 2/3^0) then our 2/3 guess should have an upper limit of 0.66 * 100 and a lower limit of 1. Assuming a guesser of first degree (2/3 ^1 of the average) we can draw upper and lower bounds since a first degree guesser will guess 1
First Guess: 33.33
Second Guess: 22.22
Knowing that everyone knows that everyone knows, doesn't really help me in establishing a baseline at all. Knowing everyone knows, depending on the person, may illicit randomness or other clever behavior which makes predicting their numbers futile. So I can only go with numerical average of 50 as my starting point yielding 33.3. Hmm. But since the point is to get to 2/3rds of most people's answers, that puts guess #2 at 22.2. I have very little confidence in my solution however...there's a reason I'm not a game theorist. Great Episode!
If everyone guesses "1" we can all win, because then the answer would be 2/3 which you can round up to 1
07:01 I explicitly want the answer to be 33.
07:29 Does 33 sound good to anyone..?
We had 33 yesterday.
33 - I misunderstood the question the first time bbecause I'm a moron.
Second choice - 100, so I force the average up and give the majority of other commentors a chance for victory
But what if I guess zero to drive the average down? Checkmate!Edit: meant 1, because I think he said 1-100.
This is an excellent video, thanks!
Thanks for watching! ;)
So, i wanna point out that the game has referring has appear in Alice in Borderland (series / manga) but also reminds me the idea that Edgar Allan Poe makes on one of his stories, where a boy can play papper - rock - sicssors and gain to the others guessing the level of common knowledge of his opponent
14 (after video). explanation: I was familiar with the game and the concept behind it prior to the video, though seeing the video and re-thinking on all these knowledge regression levels made me realize I might have underestimated the prevalence of these key demographics:
a. trolls, getting the game but refusing to play it to win
b. people who didn't get the game
c. people who got the game but who were more pessimistic (and rightly so) about group a+b.
the last group was the major reason for my change I believe, and why I upped my bet from 7 to 14.
I don't have much else to get a hold of, except different orders of thinking: if people assume 40 is the average, then most people will guess around 30. But people probably guess that that's the 2/3rds value, and so maybe the majority will actually guess 2/3rds of _that_, or 20. So really it's how many people do I think will sit in the first order guess, second order guess, etc. It also depends on what I think other people thing the first order value is (2/3rds of 50, the average of random numbers between 1 and 100? 2/3rds of 33, the average value between 0 and 66, where 66 is the actual upper bound of what's capable?)
I assume this approaches some limit, something cheeky. These kinds of recursively constructed things usually do that.
I guess, 25?
EDIT: Got to the end of the video, sounds like I was sort of on the right track from the start. Maybe more because I'm second guessing myself than because of any different approaches, I'll guess 20.
1st: 33
2nd: approaching 0 (in an ideal scenario)
depending on how many iterations you think others will go down, you answer will change.
i think most will only go down 2 or 3 levels, this makes the mean around 18 ish.
my guess 12
since i think the number of people guessing 1, and the number of people guessing higher numbers like 69 42 and 100 will roughly even it out so you can ignore the outliers.
Your videos are so good!
I was thinking if the initial question might be a good way to generate a true random number?
Thank you! And judging from the distribution of answers, probably not...unless some numbers are significantly more random than others...;)
1 was my first guess since at ever iteration, we'll all choose a decrease by 2/3 the random average. So 33 -> 22 -> 15 -> 10 -> 7 -> 5 -> 3 -> 2 -> 1. However, in just the 2 step case it ought to be around just 22
Initial guess: 33
Second guess: 17
(After enough iterations: 1)
as of 4-20-20 there were 156 entries with a combined sum of 3989. the average answer was 26. two-thirds of the average is 17.
only one person guessed correctly; Humberto Ramos Costa
42 is the answer.
u serious? or u just joking?
Dude! Such a good video!
First Option: 23
Second Option: Still 23 Jajajaj
Cool video!
33.3
I'm assuming a pretty even spread on every other guess, and apparently 33.3 is ~2/3rd's of 50. I guess that makes sense, since it's about 1/3rd of 100
second guess:
22
since everybody else is clever enough to base their guess on the average of the entire spread, except they should know that too, so:
third guess:
I don't know, I never handled the recursive "I know that you know..." stuff all that well.
I heard in an interview that this will be the topic of Pinker's next book
0:43 Since I love to play entirely outside the rules and simply play to please myself, I choose 99.141.
8:43 Again, since I'm used to being outside the rules and playing to confuse , I guess 11.11. Whey-Haw!
The speculation about nerds is interesting, though I sort of wonder because in the modern landscape, "nerds" don't necessarily have science or math backgrounds, but your average Whovian or Star Wars nerd seems to have similar problems. But it made me think about the general perception that nerds have trouble reading social cues, and now I'm wondering if maybe it's a "chicken or egg" scenario.
5
"Obviously," even before the video, after enough iterations, one gets to 1.
The video had no effect on my answer, checking a few of the other comments though, I'm tempted to change to something around 21-23.
23 both times, I was already aware that I know and that everyone knows that I know and that everyone knows that everyone knows and bla bla bla.
The thing is: who's gonna make the spreadsheet with the results? :D
0 (best scenario)
15 (more realistic, my guess)
22, just going down one level. What an interesting video though!
22
Edit: 2nd guess: 11.
I originally figured most people would take 2/3 of 50, which is 33.
Now I think there will be a bunch of people who put 1, and a bunch at 33, 22, etc. and maybe some other outliers, and some people messing with the system and putting 100.
Guessing that:
40% say 1
30% say 33
20% say 22, etc. we get:
(.4*1+.3*33+.2*22+.05*17+.05*40)*2/3 is around 11
22: most people will guess 33, because they expect the mean to be about 50, and 2/3 of 50 is 33. So, if most people guess 33, then the mean will actually be closer to 33. 2/3 of 33 is 22.
Alternatively, other people could think like this, as well. This would bring the mean down from 33. Maybe 20 or 18 would be more appropriate. Let's see how the video goes...
I still think my original guess was good. You see, at each step in that common knowledge recursion, fewer and fewer people follow it a step further. So, people with really low guesses will outweigh people with high guesses, lowering the expected average from 22, but not too far.
Final guess: 19
This is not common knowledge but the answer is definitely 42, I know Josh know but Josh doesn't know that we know. This gap shall be filled with intellectual and nerdy reading.
Initial guess: 37.5
Let's see how this video plays out,
Second guess: Well if everyone knows that everyone else is going to try and guess this then X% are going to try and be contrarian and pick a deliberately obscure number to throw out other guesses. Y% probably won't think about the problem that long and will pick something fairly instinctive, whether that number be personally important to them or just generally nice round numbers. Z% probably thought of other strategies in response to this common knowledge.
So now I need to work out what percentage of the viewers of this video will fall into each category...Z sticks out though because I don't know how many different possible outcomes I haven't thought of...how would I work that out...(visions of fractals)
THIS RABBIT HOLE GOES TOO DEEP! ABANDON SHIP! (heavy splash and frantic, receding paddling sounds)
1.
Second guess 2/3
1. Because everyone will keep guessing smaller and smaller numbers
First guess: 20
Second guess: 22
I keep my previous guess after watch the video.
Hmm I don't know what everyone will be choosing so let's look at the upper limit. If everyone else takes the maximum value off 100, then my upper limit should be (2/3)*100 = 67 (rounded). assuming everyone is aware of this upper limit and acts accordingly, the same line of reasoning applies to make a new upper limit of (2/3)*67=45. This also shows a trend where the upper limit to my answer is n_max=100*(2/3)^k with k the iteration number of this line of thought. Clearly, as k increases n goes to 0, only to be bounded by 1 since n >= 1, but answering n=1 is self defeating since then no-one will be right if everyone answers 1. Also, not everyone will be following this line of reasoning and some will potentially even go towards the k=1 answer, but still a number of people will be giving low (
Not changing it for the second guess. will the results be shared in the next video?
1.3
Edit: Still 1.3
I haven't thought about it much, I just did 2/3 of 2, since that's the smallest integer other than 1, but I'm not sure there is really any way to guess optimally.
20 (I know if everyone is rational and knows that everyone else is rational, etc., then everyone would put 0, but of course that's not the case. Guessing that's what he's gonna talk about)
Guess before video: 27.5 (If we think half of the people will guess 2/3 of 50, and the other half will go another level deep and do 2/3 of 33)
Guess after video: 10 (somewhere between the group which will go infinite and write '1' and other higher guess)
2/3 or 3. End: I cheated and just rolled to the comments lol. Thanks for the great video, and for making me want Chinese food :|
second guess: 2/3. If it's a valid number. If not, then 1 again.
Initial guess: 35
Second guess: 52
1. It's depressing how your videos never garner more than 1000 views. What gives?
First guess: 22
Second guess: 17
1st guess: 33
2nd guess: 22
Well, 22 would be my guess!
Initial : 24
After: 2
1?
It seems to me that I guessed almost correctly the first time (14) and I'm surprised because I read about this subject before and was thinking to go down even further because other people might have read about this too. fs.blog/2014/04/mental-model-complex-adaptive-systems/
Edit: why people chose 33 if it was common knowledge that you have to pick two thirds of the most common answer? Even if it wasn't common knowledge who would have even picked 99 or 100 because that's not even in the range of acceptable answers.
First guess: 0 (in this case all will win)
first guess: 20
second guess: 20
42?
First guess: 12
Second guess: still 12, there will always be a few comments who act ironic/illogical and say way to high numbers
And i'm curious now what the actual average is!
My guess is 22. The mostly likely mean value out of 100 should be 50 and 2/3 is 33, but everyone is guessing at 2/3 the mean value of the guessed numbers, so assuming most people stop at this point i took another 2/3 to match the new mean value given the conditions for guessing.
Edit: Alright I guess I was on the right track. But seeing how smart this audience is I'm gonna guess that the average is approaching zero as we all know that the other's know that to take another 2/3 to stay ahead of the curve. great video!
(2/3)^210 (comment number) * 100
First guess was 6 second 1
First guess: 8
Second Guess: Still 8 :)
33
Second guess: 2
20
Edit: I'd leave it unchanged.
Not a bad guess! Bang on the money for the first-round guessers (20.4 as of 2018-08-08 8:45 AM), & not far off the second round (13.2).
2nd guess 100, I know nobody knew I guess this.
so you didn't follow the directions. ur a genius
22
second guess: 1
73!
That's a lot higher than 100.
4.47011546151e105?
That's a lot of digits.
This is one of my favorite comments ever.
r/unexpectedfactorial
22 if no one into an infinite loop except me :p
2, and second guess still 2
1
Second guess: 1
65
With a 2nd of 30
12.8 (second)
That's a suspiciously good guess. ;)
6 and 44
33,3
13 second level
7 well 6.3334 ish
FIRST: 20
SECO: 12
These are remarkably close to the actual values! As of 2018-08-08 8:43 AM, they're 20.4 & 13.2!
THUNK yaiy, I am genius. Give me Nobel prize ... or something ... Pls.
First guess: 3
7 (before video)
70
90
25 / 33
first 2, second 2
22.2
1/2
10
30
3
50
40
27
15
96
17
congratz, you won
42
45
38
95
37
33
25
61
24
4
2
44
69