treatment suggesteddecision subject_id level message 1 2 1 2 "It is more likely that a black ball came from Urn B, and 2/3 of the other teams have made this same choice. " 1 2 2 2 Go with the majority 1 2 3 2 I recieved a black and a bunch of teams picked black as well 1 2 4 1 2 5 "More black balls in B, therefore higher chance to be in B " 1 2 6 0 the balls are replaced right? so previous teams' choices shouldn't have an effect on ours right? 1 2 7 2 "It is likely the first two teams drew black because it is the majority, and the third team drew red by a 33% chance. It is in our best interest to choose B, especially since we got a black ball too " 1 2 8 2 "Since 2 out of 3 of the previous teams chose urn B, and our draw corresponds to that choice, I'd say that urn b is a good bet. " 1 2 9 SImply going on probability here. 1 2 10 1 2 11 I'm predicting urn B since it has a higher chance of being the true one. 1 2 12 1 2 13 2 "Its definitely B, both teams before us chose B, which means they probably drew black balls. If team 2 had drawn a white ball, then they would have definitely chosen urn A not B. So pick B " 1 2 14 "Given that theodds are in the favor of Urn B, I'm okay with going with it. " 1 2 15 3 "The first team definitely saw a black ball, they went in blind and chose B The second team must have also saw a black ball, and corroborated with what team 1 saw, the 3rd team saw a white ball, which contradicted what the previous team saw It is possible that the 2nd team saw white, but just went along with team 1 so, I would say, out of 4 draws, there's certainly 1 black, 1 maybe black, and 1 white our draw is a black one I am pretty confident that we should vote on urn B " 1 2 16 Seems like Urn B is more likely 1 2 17 1 2 18 2 more blacks than whites. 1 2 19 2 "2/3 chance that black ball comes from urn B 2/3 of the teams above got a black ball, i'm guess ing (2/3 thought it was urn b) " 1 2 20 2 1-B 2-B 3-A . Drew Black. Im pretty sure its B 1 2 21 This is confusing 1 2 22 1 2 23 1 2 24 2 The previous teams have a 2/3 choice of B 1 2 25 2 obviously a higher chance that the black ball is come from B and given that the first 2 teams also have black balls 1 2 26 1 "its a 66% chance that it came from urn b, and the choices of our predecessors don't matter... " 1 2 27 I don't know this is all probability so this is a guess 1 2 28 2 3 blackballs are draw 1 2 29 2 makes more sense that that it is urn B from the probability that a black ball was chosen and that the teams before us mostly chose urn B 1 2 30 1 2 31 1 2 32 1 2 33 0 50/50 not entirely sure 1 2 34 1 2 35 let's play it safe 1 2 36 2 "It looks very likely that it's Urn B. Assuming everyone has gone with the most likely choice, then both team 1 and team 2 must have seen a black ball (while team 3 saw a white one), and we saw a black ball. Urn B has more black balls. " 1 2 37 1 2 38 2 I'm pretty sure its urn B since there's a lot of black draws. 1 2 39 1 2 40 2 "The chance that this comes from Urn A is possible, but pretty low. (8/27) So let's go with B with probability (19/27) " 1 2 41 2 i think that it is urn b because there is a greater possiblity that the ball came from that urn. 1 2 42 0 its a guessing game 1 2 43 2 the chances that black ball comes from B is 2/3 plus 2 teams already selected B 1 2 44 2 I said b because we are trying for a black and urn b has 2/3 black balls (therefore greater prob of getting black) 1 2 45 1 2 46 2 "Teams 1 and 2 probably saw a black ball, and team 3 a white ball 3 blacks and 1 white is much more likely for urn b " 1 2 47 were more likely to get it right if we choose this urn but i guess it could also be urn A soo i feel like this round is really just a guess 1 2 48 2 Higher joint probability that the ball came from Urn B. 1 2 49 1 2 50 1 2 51 0 "randomly choose my selection. i will choose B, u select A and computer will take decison randomly on behalf of us " 1 2 52 2 probably B since 2/3 teams below chose B 1 2 53 2 "2 out of 3 teams chose B, i like the odds " 1 2 54 1 "Since we have black ball, the likelihood to get a black ball in Urn B is greater. " 1 2 55 2 "i took a networks class and from what i remember...if each team sees a private draw, we can assume that each of the previous teams saw a clack ball. since urn b has a 2/3 chance of having a black ball, its a higher probability that it came from urn b. " 1 2 56 1 2 57 playing the odds 1 2 58 1 "since the private draw is black, urn b is more likely to be the true urn. " 1 2 59 2 2 out of 3 chose urn B so odds are in that favor 1 2 60 I am choosing Urn B just becuase there is a 2/3 chance that it is from Urn B 1 2 61 1 2 62 2 "If 2/3 of the previous decisons are team B, makes me believe they both had black. If team 3 had white, then they may be inclined to choose A. Since we had black, it only furthers my decision for B " 1 2 63 2 "URN B GOT MORE PROB OF GETTING BLACK, AND ALSO MORE PREDECESSOR TEAM CHOOSE B " 1 1 64 if we decide to go with the same one we should be okay if we coincide with the same answer we should win let's go with your choice 1 2 65 1 1 66 2 Even though it is againt the 2/3 odds if more people chose A before us they likely got the correct color 1 2 67 1 2 68 0 Urn B has another black ball available 1 2 69 1 2 70 1 Going on percentages i believe it is likely that it is from urn b 1 2 71 1 "The ball picked was black, right? So, there's a greater chance that it came from urn B than urn A " 1 2 72 1 It would be foolish not to choose the urn with the greater proportion of black balls. 1 1 73 2 "I'm not sure. If the other teams chose A, they might have gotten a white ball and only one team got the black ball. If we combine our results that is a 2/5 black which is about 1/3 like urn A " 1 1 74 1 2 75 1 2 76 3 This was a common question in Networks (econ class) only the first two choices matter 1st person got black since he chose B 2nd person got white b/c otherwise would def choose B so ours is B that 2/3 black 1 2 77 0 "seems pretty likely its from B, especially since a lot teams before picked A, indicating that they got white balls " 1 2 78 1 since we got a black ball id say that it was urn b i dont really get how the other teams picks affect this one 1 2 79 0 "idk, just a guess " 1 1 80 2 3 out of 4 previous teams are picking A so that is more likely they probably decide to pick A because see a white ball drawn 1 2 81 1 it doesnt matter what the other teams found there is still a higher probability that a black ball is chosen from the urb B therefore i would choose b 1 1 82 2 Most people must have seen a white draw for there to be predominatley A being chosen. 1 2 83 1 2 84 1 "I don't see how the previous draws affect anything. We got black, it's 2/3 chance from B, 1/3 chance from A unless I'm completely confused. " 1 2 85 1 there is a 66.7% chance that the ball is black. i'm not sure how the previous draws would affect our guess 1 1 86 2 Only because 3 teams chose A 1 2 87 1 1 88 2 "3 white balls in a row from the black urn is only a (1/3)times(1/3) times (1/3) chance - therefore, very low. I suspect that people chose urn A if they got a white ball " 1 2 89 1 1 90 2 "Based on our ball it seems it should be B, but all of the other teams choosing A leads me to believe they may have gotten 3 white balls. Although the last few could have been influenced by the first... so I'm not exactly sure, but I'm picking A. " 1 2 91 1 2 92 idk guess 1 2 93 3 "Well, from our observations it seems that we would be choosing Urn B. However, if we look at previous guesses, a desire may be made to choose Urn A from belieivng that other people must be drawing white balls. We have to consider the fact that other teams are also being influenced by previous decisions. For example, team 4 may have drawn a black ball and wanted to choose Urn B, but didn't in order to match the previous people. Therefore, I still think we should choose Urn B. " 1 2 94 1 "the chosen ball is black. there is a 2/3 chance that a black ball came from urn B. Hence, I am choosing urn B which has higher probability. The other teams might have had different private draws and hence chose differently. I will, however, consider your explanation before submitting my final decision. " 1 2 95 higher probability i dont know 1 2 96 1 The draw was a black ball so it must be urn B. 1 2 97 1 "If the other teams are mostly going with A, and we have a black ball, I think our best choice is B. " 1 2 98 Urn B has the most black balls 1 1 99 2 "The first team saw black, so they chose the black urn\ however the second team saw white, so they chose the white urn so did the third team. because they chose the white urn it is almost definitely the white urn, A " 1 1 100 2 "since 3 of the teams before us chose A, we might assume that they got a white ball. we may have just gotten a black ball by chance from urn A " 1 1 101 2 "Okay so the teams before us chose A more frequently, which means they private draw must have been white, with one black. We got a black one, but since its a 50% chance that both urns could be the true urn, we can attribute ours to simple probability Thus, we have a 75% chance of it being A More frequency-better chance it comes from one urn than the other " 1 2 102 1 2 103 1 2 104 1 1 105 2 "Since three out of four teams chose A, I think it is highly possibly we are seeing the ball from A " 1 1 106 2 "Given that we were shown a black ball, there is a 2/3 chance that it is in B. However, the other teams chose A, which means that they were given a white ball, meaning that there is a greater chance of A " 2 2 1 2 A black ball is more likely to have come from Urn B. Not enough teams have gone before us to be affected by the fact that 3/5 of them selected A 2 1 2 Not sure 2 2 3 2 seems reasonable to pick urn b with all these blacks 2 2 4 2 2 5 1 More blacks in urn B so I choose B 2 2 6 more likely to be B once again i think. 2 1 7 Majority is still A so we are better off choosing that 2 2 8 2 "this is a tough one, but based on our draw, B is a good choice. Also, 2 out of 5 other teams chose B " 2 2 9 "Again, probability. " 2 1 10 "3 of the 5 previous teams have said A, do you think that could mean that it's A? " 2 2 11 I'm not totally sure about this. 2 1 12 2 2 13 "Its a tough call, but i'd guess b just cause ours was black " 2 2 14 Odds are for Urn B 2 2 15 "team 1 saw black team 2 saw white, for sure team 3 saw white for sure, since it could be influenced by either team 1 or 2, but chose to go with white team 4 saw black team 5 saw white team 5 has 2 guaranteed black before it, and 2 guaranteed white before it, but chose white, so probably got white our draw is black, there's 3 white, 2 black before us I'd say its 50 50, let's go with black, urn B since we're sure about what we saw " 2 2 16 0 "if there are 3 draws of black ball, 2 of them should be from B, so I'm going with B. " 2 1 17 2 2 18 either one 2 2 19 2 50-50 odds that its a or b... 3bs 3as 2 2 20 "B,A,A,B,A- Black, it could be either " 2 1 21 It's a 50/50 chance 2 1 22 2 2 23 2 1 24 2/3 chance of A chosen before 2 1 25 2 "Since there are more A than B choices that woyuld suggest the urn with the higher probability for white balls, but we drew a black ball, so i'ts even but I'm going to go with A " 2 1 26 2 "the majority of the teams so far picked A, so I'm gonna go ahead and say we got a black ball based on a 1/3 chance " 2 2 27 0 I have no clue. 2 2 28 2 1 29 2 Most of the teams ahead of us chose urn A. 2 2 30 2 2 31 2 2 32 2 2 33 pretty sure 2 1 34 2 2 35 2 2 36 It looks like both are equally likely. 2 1 37 2 2 38 2 "Three black balls, three white balls were observed It's a 50 50, I'll go with what we saw, urn B " 2 1 39 "probably A, even though the draw is B because at least three teams got a draw of a white ball. " 2 2 40 2 "There is exactly a 50% chance of either one, so I will go with B since we got a black ball. " 2 1 41 2 "i think that it could be urn A even though the ball is black given the decisions that the previous teams have made, where 3 of the 5 teams chose A most likely because they got white balls. " 2 2 42 2 2 43 2 3 teams went for A and 2 for B it seems that there's an equal chance but B contains 2 black balls... 2 2 44 1 "since there is proportionally more black balls in B, theres likely a greater chance our urn is B " 2 1 45 2 It might be A since three teams chose A before us 2 1 46 "Team 1 probably drew a black ball, as they have no information Team 2 must have drawn white, if they chose A despite team 1's decision to choose black Team 3 probably drew white as well, as the previous teams decisions are split so they decide on their own team 4 must have drawn black, as them drawing white would be totally agains ttheir choice to choose B It's 50-50 " 2 2 47 2 2 48 Higher joint probability that the ball came from urn B. 2 2 49 2 2 50 1 more black balls in urn B 2 2 51 0 "randomly choose my selection. i will choose B, u select A and computer will take decison randomly on behalf of us " 2 1 52 "I think it it is A but not very sure... it could be B since the information is 50 50 but if you look at the first 3 choices, it seems to indicate A. " 2 1 53 0 i really dont know 2 2 54 1 The likelihood to get a black ball in urn B is higher. 2 2 55 2 "based on the previous teams responses, we can assume that they saw black, then white, white, black, white each team is acting on their private draw. since there are three whites and they chose urn A. There are currently 2 private draws of black and votes for urn B. we should go with what our private draw was and which urn is associated with the highest probability " 2 1 56 2 2 57 1 it's black so i'm going with B 2 2 58 2 1 59 2 well this sucks 50-50 chance on this one 2 2 60 1 I am choosing Urn B because there is a higher probability of it being drawn from there. 2 1 61 2 1 62 2 "ratioo of white toblack is most likely 3:2, so i picked urn A " 2 2 63 2 "COMBINE BOTH THE OTHER TEAM AND PROB OF THE URN, I THINK IS B " 2 2 64 1 we should go with the draw that is given to us we must agree on these in order to win 2 2 65 most likely 2 1 66 2 "It is logical that the people before us chose the urn with the 2/3 liklihood of being correct, I believe we should follow their decision " 2 2 67 2 2 68 0 urn b is the only one with another black ball available 2 2 69 2 2 70 1 i believe ours came from B 2 2 71 1 "The ball picked was black. There are two black balls in urn B and only one black ball in urn A. Therefore, there's a 2/3 chance the ball came from urn B and a 1/3 chance it came from urn A. " 2 2 72 2 1 73 2 "If choosing A means a white ball was drawn and choosing B means a black ball was drawn, then there is a 1/3 black ball to 2/3 white ball which is the same as urn A " 2 1 74 3 It seems the other teams saw more white balls though it is possible the third and the fourth team actuall saw black balls but they had to make a random choince. 2 2 75 2 2 76 3 1st person had to choose a White 2nd person had to choose a black the rest we cannot say since the previous decisions may cloud there judgment i say B since 2/3 of the signals we know about are black' 2 2 77 2 1 78 2 since more of the teams before us chose a i think it is urn a even though we got black i think they all came from the same urn so if more a's got chosen before i think its a 2 2 79 0 just a guess 2 1 80 2 "there are 5 teams before us and 4 of them choose A, so i am confident that it is A most of them must see a white ball from A " 2 2 81 1 there is still a higher chance that the black ball is chosen (2/3 versus 1/3) therefore i would still choose B it doesnt matter what the other teams chose 2 1 82 2 It seems that most people saw a white ball in their private draw. 2 2 83 2 2 84 1 "2/3 chance that black ball is from B, 1/3 chance from A " 2 2 85 1 I think it would be the best to stick with urn B since the probability is in favor of that. 2 1 86 2 4 out of 5 say A 2 1 87 2 1 88 2 "I assume teams chose urn A if they drew white. The chance of getting 4 whites from Urn B is very low therefore I believe it is urn A. Even though we drew a black, it's still greater probability that it is A " 2 2 89 2 1 90 0 "Again, really not sure on this one. It's a toss-up for me. " 2 2 91 3 "team 1 probably saw a white ball. team 2 probably saw a black ball. everything after that i think is bogus - information cascade effect. if we see black, we should go with B " 2 1 92 i think its A 2 1 93 3 "Even though we drew a black ball, feel that for 80% of people to have chosen A, this may indicate that white is the majority. However, I'm not sure at all, due to previous people also being influenced by previous decisions. We know that the first decision is not based off of previous decisions, therefore we can assume that the first person drew a white ball. The second person contrasted the first person so we can assume they went by their ball and chosen B. The third person was going off of a balanced group where half of the people had chosen whtie and half of the people had chosen black, therefore their decision is valid too. After that it was based on how people analyzed it somewhat. I believe the fourth person would still have stayed with what they got so I think A is better. " 2 1 94 2 "I am going with the previous teams on this one. I am not sure at all what is the right way to think about it now. If you have a better explanation, I will go with you. " 2 2 95 2 2 96 1 The result was a black ball so it has to be urn B. 2 2 97 I think we have a better chance selecting urn B. 2 2 98 1 "Even though th teams before mostly picked A, I don't think that should have a bearing on the choice here; B still has the higher statistical probability of having a black ball " 2 1 99 2 "The first team saw white so they chose A, but the second team saw black so they chose B. However, the third team saw white so they chose A, as did the next team Logically, the true urn is urn A " 2 1 100 2 "since most teams before us have chosen A, we may assume that most of them got the white ball from their drawing. using probability, it's more likely that we got a black by with 1/3 chance than the previous teams getting a white ball from urn B with much lower probability " 2 1 101 2 "Frequency of a is greater than B, thus, it's a good chance its urn A because although we picked black 4 whites to two blacks shows a 2 to 1 ratio meaning that for everty 3 balls, 2 are white and one is black this reflects the probabilty of urn A " 2 2 102 2 1 103 2 1 104 2 1 105 2 1 106 3 1 1 2 "A white ball is more likely to be from Urn A, and 2/3 of the previous teams have selected this urn as well " 3 1 2 3 1 3 2 got a white so i would assume to play the probablity game here 3 1 4 im going with high probability 3 1 5 More white in A so therefore I choose A 3 1 6 2 just using probability to make an educated guess here. 3 1 7 2 We received a white ball and the majority is on our side so we should choose A 3 1 8 2 2 out of 3 previous teams chose A and our draw corresponds to A as well. 3 1 9 3 1 10 3 1 11 2 "I'm assuming urn A has a higher chance than B, looking at the previous draws. " 3 2 12 3 1 13 2 "Its definitley, A, the only one who didnt draw a white ball was the 1st person, pick it] " 3 1 14 odds are for urb a 3 1 15 2 "same logic,,, lets go with A since majority came out as white " 3 1 16 0 "If you always choose A for a white draw, and B for a black draw, there's a 2/3 chance that you'll get it right. I don't think you can increase the probably of right guesses beyond 2/3? " 3 1 17 0 I think there is always an equal chance of getting A or B 3 1 18 3 1 19 2 3as 1 b as have higher prob of being white 3 1 20 2 "B,A,A- White. Its prob A " 3 1 21 I like these odds 3 1 22 3 1 23 3 1 24 2 current ball is white. previous teams chose A 2/3. 3 1 25 2 "Three whites in a row, Urn A " 3 1 26 2 "Our draw seems to coincide with the majority, so I say urn A " 3 1 27 0 I have no clue. 3 1 28 3 1 29 2 Gotta be A since most teams ahead of us also chose A and we see a white ball. 3 1 30 3 2 31 3 1 32 3 1 33 0 not entirely sure on this one 3 1 34 3 1 35 3 1 36 2 "Since it's a white ball, and presumably two out of the first three teams saw a white ball, the chances are very good that it's going to be urn A. " 3 1 37 3 1 38 2 "should be white, we see a lot of white balls. " 3 1 39 2 "Team 2 did not go along with Team 1 because they also saw a white, and Team 3 probably saw white as well, or else they wouldn't have gone with team 2. Since we see white also, it's probably from A. " 3 1 40 A seems most likely. 3 1 41 "similar to the decision in the 1 round, i think that the ball is from urn A because of the higher probability. " 3 1 42 3 1 43 2 2 teams already selected A seems they got white balls as well 3 1 44 "since there is proportionally more white balls in A, theres likely a greater chance our urn is A " 3 1 45 2 "It is more likely for a white ball to have come from Urn A And two teams before us have chosen A, so we should go with A " 3 1 46 "draws are almost purely based on the individual ball draw, as the disparity of information in the teams previous theirs indicates 3 white balls to 1 black ball, basically " 3 2 47 3 1 48 2 Higher joint probability that the ball came from Urn A. 3 1 49 3 1 50 Greater no. of white balls in A 3 2 51 0 "randomly choose my selection. i will choose B, u select A and computer will take decison randomly on behalf of us " 3 1 52 2 2/3 teams before choose A too so they probably got the white ball as well. 3 1 53 2 "We got white, two other teams chose white. i like A " 3 1 54 2 "The likelihood to draw a white ball in urn A is higher than urn B. In addtion, Team 2 and Team 3 all picked urn A. " 3 1 55 2 "ok, so based on our private draw we would assume urn A. we are currently in an information cascade (since the 2 previous teams before us also entered A we can assume that they also had private draws of white. Therefore we should also pick A. " 3 1 56 2 "I'm choosing this based on the other teams and our draw. Also, I think I forgot to press enter for the last message... So for the last one, I made that decision based on the other teams draws not ours. " 3 1 57 2 "I'm choosing A because it is a white ball, and 2/3 of the other teams chose A " 3 1 58 3 1 59 2 same as the first 3/4 were white so definitely urn A is the smatr choice 3 1 60 3 1 61 3 1 62 2 Makes sense based on previous draws. Or does it..... 3 1 63 2 MORE TEAM AND MORE PROB FOR URN A 3 1 64 1 must stay with the urn that is draw and always pick the same one as a team if we don't pick the same one we will not win 3 1 65 3 2 66 2 Follow majority. Despite whatever we drew there there is more data. 3 1 67 3 1 68 1 urn a has a greater chance of containing a white ball 3 1 69 3 1 70 0 Based on percentages and what the other teams chose i believe ours is from urn a 3 1 71 1 "Urn A contains two white balls and urn B contains one. Therefore, there's a 2/3 chance the ball came from urn A. " 3 1 72 3 2 73 2 This is the same scenario as the first one except flip flopped at which point I would change my answer to B. 3 1 74 0 team 1 and team 4 drew black balls and team 3 and team 5 drew white. therefore it is a 50/50 chance. 3 2 75 3 2 76 3 "1st ball was def black we cant say for 2nd draw if white, the 2nd persons signals could be black or white and he could choose B) i say guess black] " 3 1 77 3 2 78 3 1 79 0 just a guess 3 2 80 2 4 teams before us and 3 of them picked B so I would pick B 3 1 81 1 "it doesnt matter the order of sequence of the other teams i would still choose A since the probability of choosing a white ball is twice that of a black ball (2/3 vs. 1/3) therefore, i would still choose A " 3 2 82 2 "Hard to say, still though most people seem to have seen a black ball. " 3 2 83 3 1 84 3 1 85 1 I went with A because the chances it came from A are more likely that B. 3 1 86 3 2 87 3 2 88 2 "It appears from previous teams choices that 3 of the 4 balls were black. Therefore, even though we drew a white ball, it's more likely that our urn is B " 3 1 89 3 2 90 2 I guess I'm really easily influenced by what people have picked beforehand. 3 2 91 2 "team 1 probbaly saw black, team 2 probably saw black. if we see white, lets still go with B " 3 2 92 3 2 93 2 "We know that the first person would stick to what ball they drew, therefore it can be decided to be B. The second person would have no reason to follow the first person since its just one statistic so they are probably accurate too. The third person needed a reason to deviate so they were definitely A. The last person probably would have stayed with what they got so I think it was B, regardless of our drawing. " 3 2 94 3 1 95 3 1 96 0 The result was white so it has to be from urn A. The other teams except for team 3 is just plain wrong. 3 1 97 1 "I think since we are drawing a white ball, our best chance is to select from urn A. " 3 1 98 3 2 99 2 "The first two groups saw black, so they chose B. However, the third team saw white so they chose A. But the next team after that saw black so they chose B Logically, the true urn is urn B " 3 2 100 2 "we can assume that team 1 got the black ball, team 2 probably also got the black ball, and team 3 probably got the white ball. probability wise, it's more likely that its from urn B " 3 2 101 2 "The first team must have seen a black ball and chose B second team probably got black as well so chose B third team probably got white and decided to go with A 4th team got black again and went with B Thus if we assume all the choices before are rational then the choices are more black than white thus B MUST be the rationally right answer as in if you don't pick B, it would be quite irrational" 3 1 102 3 1 103 3 1 104 3 2 105 3 2 106 4 1 1 A white ball is more likely to be from A. There havent been enough teams before us to make anything of their choices. 4 2 2 2 The majority of balls drawn is likely to be black 4 2 3 2 def go with majority on this one. 4 2 4 hopefully this is trick one 4 1 5 1 More whites in urn A so I choose A 4 2 6 2 3 out 4 previous teams chose B. this gives B a slightly higher chance for us even if the ball was white. 4 2 7 2 "Even though we would choose A from probability, the majority of the choices are still urn B, thus indicating that we probably happened to pick the only white ball " 4 2 8 2 "since the previous teams overwhelmingly chose B, i'd go with B as ours. They obviously had reason to pick B " 4 1 9 1 Entirely based on probability. 4 2 10 2 based on the 3 black guesses before ours 4 2 11 2 "Looking at the previous teams' draws, there is a larger chance that they draw from the true urn B, although our draw was white " 4 1 12 i am not sure 4 2 13 2 its most likely cause 3 black balls have been drawn vs. 2 white balls 4 1 14 4 2 15 2 "team 1 definitely saw black team 2 saw black team 3 definitely saw white team 4 definitely saw black we saw white, but its 3 against 2, I'm pretty sure urn B is more likely than urn A " 4 1 16 "Again, if you always go with A for white and B for black, the probably of getting it right is 67%, but if you go with A for black and B for white, the probabability becomes 67*(1.3)+33*(1.3)+67*(1/3), which is below 67% " 4 2 17 4 2 18 2 go with the majority? 4 2 19 2 more bs than as...doesnt matter what our team got... still a greater # of bs than as 4 2 20 2 B- There are more B's than A's 4 2 21 So chill 4 2 22 4 1 23 4 2 24 2 Just cause there were lots of Bs chosen before 4 2 25 2 "even though we have a white, for the first 5 there are still more black decisions " 4 2 26 2 more previous teams got B... 4 1 27 0 I have no clue. 4 1 28 4 2 29 2 most of the people put B before us. 4 1 30 4 2 31 2 Seems black ball comes out more in this urn we should choose B 4 1 32 4 1 33 ? 4 1 34 4 1 35 4 2 36 2 "Assuming everyone goes with the most likely urn for their draw, then we have three black balls and two white ones (including ours), which still makes B a little bit more likely than A (but not by much). " 4 2 37 2 "the first two teams probably saw black, so they chose B. The third team probably saw white, so they chose A. The fourth team saw black again so they chose B. It is probably urn B " 4 2 38 2 "more likely to be from urn B, there's more black balls " 4 1 39 4 2 40 2 "There is a small chance that this could be A, but it is not that likely. " 4 2 41 2 "even though we got a white ball, which has a higher probablity that it came from urn A, looking at the other team's decisions, 3 of the 4 chose B. " 4 1 42 1 higher prob its from A 4 2 43 2 3 teams chose B it is highly possible that they got black balls 4 1 44 This ones tricky. Most of our peers said B but our drawing leads me to think its possible A (b/c we have white and theres more white balls in A). I'm going to only have a 50% confidence. 4 2 45 2 "A majority of the previous teams chose B so their test ball may have been black, we should go with their decisions. " 4 2 46 "Team 4's choice is irrelevant, because they could be influecned by 1 and 2 Team 3 drew a white " 4 1 47 better chance that it is A but could be either i guess 4 1 48 0 Higher joint probability that the ball came from urn A. 4 1 49 4 1 50 greater odds of having white ball in A 4 2 51 0 "randomly choose my selection. i will choose B, u select A and computer will take decison randomly on behalf of us " 4 2 52 2 "most people chose B, so black ball is probably showing up more often " 4 1 53 1 more white balls in A 4 1 54 1 I think previous teams' decision should not affect the ball drawn from other team. The likelihood to get a white ball is higher in urn A 4 1 55 1 "the colors drawn were black, black, white, black. because there is no information cascade we should pick the urn based on our private draw " 4 2 56 Based on the other teams draws...not our probablity draw. 4 2 57 2 "even though white would most likely be from A, I'm going with B because 3/4 of the other teams chose B and therefore probably picked black balls " 4 2 58 1 "we better pick the same urn. if we have different urn, lets go with urs " 4 2 59 2 slight edge to urn B 4 1 60 4 2 61 4 2 62 2 4 1 63 0 "COMBINE WITH THE OTHER TEAM'S ANSWER, URN A GOT MORE PROB IN THIS CASE " 4 1 64 2/3 is always better than 1/3 pick A it was drawn we must pick the same number in order to win 4 1 65 4 1 66 I am totally confident it is A. 100% I determined 3/3 correct on the last set 4 1 67 4 1 68 urn a has more white balls 4 1 69 4 1 70 the first one must have been black based on odds i think it is more likely ours is from a 4 1 71 0 No idea. Just guessing.... 4 1 72 4 1 73 2 "With these proportions we have, 3 white and 1 black which is closer to urn A " 4 1 74 3 team 2 and 4 definitely drew a white. team 1 drew a black. it is not clear which team 3 drew. still higher chance for Urn A. 4 1 75 4 1 76 3 "Common type of question in econ class Networks"""" dominant strategy was to base answer of 1st and 2nd draw in addition to your private draw 2/3 signals were white so i say A " 4 1 77 2 more teams before picked A 4 1 78 2 since more chose a they probably saw white balls and so did we so they are more likely to be coming from urn a since there are more white balls in that urn 4 1 79 0 just a guess 4 1 80 2 we see white ball 2 out of 3 teams before us also pick A hence A has a good chance from my previous 3 rounds it is always correct to follow the previous trend 4 1 81 2 i would go with what the other teams went with in the past also it seems like A has the higher probability anyway of getting a white ball 4 1 82 Don't be an idiot 4 1 83 4 1 84 2 "White is more likely to come from A, also other earlier teams picked A more often " 4 1 85 1 I'm just sticking with the probability that if it is white it is more likely to come from urn A and if it is black it is more likely to come from urn B 4 1 86 4 1 87 4 1 88 2 "3 teams before us seem to have picked white, and we picked white. Urn A is our best probability " 4 2 89 4 1 90 2 Most chose A and our ball was white 4 1 91 3 "This is an information cascade problem, we should only look at the first 2 teams, the first team probbaly saw Black Seciond team saw Black or White. Since they picked A, I think they saw White We see white, so we should go with A " 4 1 92 4 1 93 2 "I honestly have no idea. There is probably a 50 percent chance of each if we look at it. The first team would choosing according to their ball, meaning they drew black and chose urn B. The second team deviated and therefore went according to their draw, meaning they drew a white ball and chose urn A. The third team was going off of a 50 50 chance so they probably went with their own draw, and chose A. We contrast them so there is an exact probability from the information we can gather. Therefore, I don't know.. " 4 1 94 2 "As we saw in the previous three rounds (my team won all three) - here, the two teams before us chose A, so it means they saw a white ball (2/3 chance of coming from A) we see a white too, which means it is definitely coming from A Choose A I am pretty sure " 4 2 95 4 1 96 4 1 97 1 I think we have a better chance choosing A if our ball drawn is white. 4 1 98 2 No real good reason. It has the highest probability I guess and the two teams before also picked A 4 1 99 2 "The first team saw black, so they chose B. But the second and third teams saw white, so they chose A. We also see white, so logically the true urn is urn A " 4 1 100 2 "we assume that team 1 got a black ball, team 2 got a white ball, and team 3 got a white ball. we also got a white ball, so the probability of the urn being A is much greater than it being B. " 4 1 101 2 First team got a black ball so they chose B second and third team got white so they chose A we get white so probability wise its going to be A 4 1 102 4 1 103 4 1 104 4 1 105 4 1 106 2 "Only one blsck ball came out and the rest are white, therefore I will go with A " 5 2 1 1 "Regardless of the other teams choices, a black ball is more likely to be from B. " 5 1 2 5 1 3 idk..this could be a trick! I dont know if to continue playing probobility or go with majority? 5 2 4 1 2 out of 3 5 2 5 1 more blacks in B so more chances to be from B 5 1 6 2 4 out of 5 chose A previously. even higher chance than before that it is urn A even if we got a black ball. 5 1 7 2 same reason as last time - its better for us to go with what the majority chose instead of what ball we chose 5 1 8 2 "Since 4 out of 5 previous teams picked A, i'd say that there is a good chance that it is a (even though our draw doesn't indicate that) " 5 2 9 1 "Two black balls in Urn B, 2/3 probability it was picked from there. " 5 1 10 2 Based on the other 5 previous teams guessing A 5 1 11 2 "I will choose urn A, since other teams had more A. " 5 2 12 1 more chances to get it black. 5 1 13 2 they all practiacally picked A 5 2 14 5 1 15 2 "It's definitely urn A, there's a majority of white's, 4 previous teams saw white " 5 2 16 5 2 17 I am not really sure. I will go with your answer if you are more confident with this. 5 1 18 2 go with the majority? 5 1 19 2 way more as than bs 5 1 20 2 A- There are 4 A's 1 B. 5 1 21 Why are people so slow with this? Slow people suck 5 1 22 5 2 23 5 1 24 2 Lots of A's. Going with my gut here. 5 1 25 2 "3 A's in a row along with there being more white balls chosen then black, suggests the Urn A " 5 1 26 2 based on the other teams... 5 2 27 5 2 28 5 1 29 2 most of the teams ahead of us chose A 5 1 30 2 4 other teams selected A 5 1 31 2 Previous team chooses A ove B and we could guess that white balls came out more before we should choose A 5 2 32 5 1 33 5 2 34 5 2 35 5 1 36 2 "Even though our ball was black, there have (presumably) been more white balls seen by other teams, making A more likely (although not by that much). " 5 1 37 2 "The first team saw white, so they chose A the second team saw black, so they chose B The last three teams all saw white, sot they chose A. It is probably A " 5 1 38 2 "a lot of white balls, must be urn A " 5 1 39 5 1 40 2 "This is what is expected if you draw 6 balls from Urn A. It is possible that B is right, but that probability is much lower than A's probability. " 5 1 41 2 "similar to the previous decision. The probability that the ball coming from B is higher because it is black. But, looking at what the other teams chose, i think that they got white balls from A. " 5 2 42 higher prob its from b 5 1 43 2 same as round 1 most likely they got white balls 5 2 44 This one is tricky b/c most of our peers said A but since we drew black it suggests we should go with B. I'm very uncertain about this hence 50% confidence 5 1 45 2 "Most teams chose A, which signifies that they most likely saw a white ball as their test draw we should go with their decisions " 5 1 46 "at worst, 2 whites were drawn and 3 blacks were at best 4 whites were drawn " 5 1 47 5 2 48 0 Higher joint probability that the ball came from urn B. 5 1 49 5 2 50 1 Greater odds of black in B 5 2 51 0 "randomly choose my selection. i will choose B, u select A and computer will take decison randomly on behalf of us " 5 1 52 "Most people must have got white balls, so it's probably A. " 5 1 53 2 guessing A bc so many other teams picked it 5 2 54 1 The likelihood of getting black ball from urn B is higher. I don't think the decision from previous teams should affect our team's decision. 5 1 55 2 "so even though our private draw was black and indicates urn b, we are in an information cascade and there were 4 other groups that saw white, therefore the chances that teh black ball was drawn from urn A is increased " 5 1 56 "Once again, based on the other teams decisions. " 5 1 57 2 "The first team must have chosen a white ball, and the second team must have chosen a black ball. since the 3rd team chose A i'm assuming they drew a white ball as did the last 2 teams. " 5 1 58 5 1 59 2 Edge to urn A 5 2 60 1 5 1 61 5 1 62 2 5 1 63 2 "BASED ON OTHER TEAM'S ANSWER, URN A GOT MORE CHANCE " 5 2 64 1 we must pick the same number better odds with 2/3 pick B 5 2 65 5 2 66 2 "With ours the division is 3 choices of a (assume they got white) and 3 choices of b (assume they got black) Since it is even I say we go with B because we know we got black and it is a 2/3 chance of being correct, " 5 2 67 5 2 68 urn b has more black balls 5 2 69 1 just assuming it could either be urn a or b and since it was black so it could be a 60ish percent chance that its urb b 5 2 70 2 i would guess urn b based on the fact we drew a black and on the fact that previously there have been 3 a and 2 b 5 2 71 5 2 72 5 2 73 2 it doesnt matter which one i can't tell because its 50/50 now 5 1 74 2 "team 1, 4 and 6 drew a black and the rest drew a white. so 50/50 " 5 2 75 5 2 76 3 same idea as before 1st person mustve drawn a black 2nd team had to draw a white we drew a black 2/3 chance of being B 5 1 77 5 2 78 2 since both colors came up equally thers no way to tell which urn it really is im just going with b for the final 5 2 79 0 just a guess 5 2 80 1 the previous choices are weird i cant get anything from them so lets just look at our own and black is b 5 1 81 5 2 82 2 "three B's three A's, its 50/50 " 5 2 83 5 2 84 2 "Black more likely to come from B, other picks about even " 5 2 85 1 Same reasoning as first choice 5 1 86 5 2 87 5 2 88 0 not sure 5 2 89 5 2 90 0 Not so sure on this one. It's a toss-up to me. 5 2 91 3 "This is an information cascade problem, we can only rely on teh first 2 teams. Team 1 picked B so they saw Black Team 2 Picked A, so they probably saw White We see black, so I think we should pick B especially since team 4 saw black as well... " 5 1 92 2 "likely 3 of the 5 teams got a white ball which is why they chose A, we should too " 5 2 93 2 "There is a 50 50 chance due to the first person obviously choosing what they got, the second person would choose what they got since they contrasted, the third person would go wtih what they got since they were choosing against a 50 50 chance the fourth person probably chose what they got since there would be no reason to choose B if they had gotten a white ball since the majority had chosen A, and then the last person probably chosen what they got because they were choosing after we should just chose B i guess to go with our draw " 5 1 94 2 "3 teams chose A, which means white came 3 out of 5 times so far we see a black but i still think it is from A what do you think? I am still going with A " 5 1 95 5 2 96 5 2 97 More teams are choosing urn A. I think we have a better chance if we go with urn B since we have a black ball. 5 1 98 2 More teams selected it. 5 2 99 2 "The first team saw B, so they chose Black. However, teh second and third teams saw white, so they chose A. But then the fourth team saw black, so they chose B, and the last team saw white, so they chose A So, including the fact that we see Black, there have been three draws that are black and three draws that are white In this case the best strategy is to pick what we see, which is Black " 5 1 100 "so team 1 got a black ball, team 2 got a white ball, team 3 got a white ball, for team 4 to have chosen B over A, they probably got a black ball, and we cannot be sure of what team 5 got. soo.... this is a toss up. " 5 2 101 2 "So at this point the probabilty reflects that it could be either urn It's 50% that it could be either or For your final decision, make sure you pick A, that way theres a 50% chance we could get it right, if we both pick B and its urn A theres no way we could get it right thus we need to make sure we have differing answers REPEAT: PICK A FOR YOUR FINAL ANSWER its better to have a 50-50 shot than to have a 100-0 shot " 5 2 102 5 1 103 5 2 104 5 2 105 5 2 106 Here it could really go either way.....I'm not sure 6 2 1 1 "Doesn't matter what the others picked, a black ball is more likely from Urn B " 6 1 2 6 1 3 majority or probability game? choicesssss lol 6 1 4 2 3 out of 4 chose A 6 2 5 1 More blacks in B so better to choose B 6 1 6 2 3 out of 4 chose A. so A for us too? 6 1 7 2 same reason 6 1 8 2 "Since 3 out of 4 previous teams picked A, i'd say that there is a good chance that A is the correct urn " 6 2 9 1 Same argument as before. 6 1 10 2 Again based on what previous teams have drawn 6 1 11 2 I will choose A. Seems like a higher probability. 6 2 12 not sure 6 1 13 2 "the three teams before us probably all drew whites, so its most likely A. " 6 2 14 6 1 15 2 "It's almost 50 50, but I'd still go with urn A team 1 definitely saw black, but 2, 3, and 4 definitely saw white its 2 black against 3 white, more likely to be urn A " 6 2 16 "what I was saying before is if out of 3 choices of black, you choose 2 from B and 1 from A, then math from earlier shows the probability. If you choose 1 from B and 2 from A for 3 blacks, the probability would even be lower " 6 2 17 6 2 18 3 let's take a risk. The third A may only have chosen A based on the first 2 As. 6 1 19 2 more as than bs 6 1 20 2 "A- 3 A's, 1 B " 6 1 21 Done! 6 1 22 6 2 23 6 1 24 2 Lots of A's. Just going with the flow. 6 1 25 2 "3 white balls in a row, I would think Urn A even though we pulled a black ball " 6 1 26 2 based on the other team's draws 6 2 27 0 I have no clue. 6 2 28 6 1 29 0 "not sure, could go either way. " 6 1 30 2 3 other teams selected A\ 6 1 31 6 2 32 6 1 33 6 2 34 6 2 35 6 1 36 2 "Even though we saw a black, three previous teams apparently saw a white, while only one apparently saw a black, making A slightly more likely. " 6 1 37 "it's probably urn A since the last three chose A, meaning they most likely saw white " 6 1 38 2 majority white balls. A 6 2 39 0 I think they're equally likely. 6 1 40 2 "Even though we got a black ball, I would go with A since 3/5 balls are white. That is more likely to come from Urn A. " 6 2 41 0 I think that it is equally likely that this ball came from either urns. 6 2 42 6 2 43 first group selected B but others selected A seems others got white balls but should go for the first group's decision they might be playing 6 2 44 1 "This one is tricky, most of our peers said A but since we drew black I'm tempted to say B. Thats why my confidence is low. " 6 1 45 3 "If the first team saw a black ball, they wouldve chosen B. The second team probably saw a white ball and chose A the third team probably saw a white ball and chose A as well the fourth team may have seen either but went witht he majority " 6 1 46 6 2 47 6 2 48 Higher joint probability that the ball came from urn B. 6 2 49 6 2 50 Greater odds of Black in B 6 2 51 0 "randomly choose my selection. i will choose B, u select A and computer will take decison randomly on behalf of us " 6 1 52 2 probably A 6 2 53 1 more black balls in B 6 2 54 2 The likelihood of getting black ball from urn B is higher. Our team's decision should not be affected by other previous teams'. 6 1 55 2 "we are in an information cascade. there was only one other black ball draw, so the chances that it was teh one black ball in urn A is increased " 6 1 56 2 Based on the other teams decisions. 6 1 57 2 going based on the other teams 6 1 58 6 1 59 2 so all our choices went against the other choices edge goes to urn A 6 2 60 I am choosing Urn B because there is a higher probability of it being drawn from there. 6 1 61 6 1 62 2 It may or may not be A. Most likely A. or it seems so to me 6 2 63 1 "SINCE IT'S BLACK, I THINK I HAVE MORE CHANCE FOR URN B " 6 2 64 1 2/3 is always better must pick the same number as a team B is the better choice 6 2 65 6 2 66 2 We know teams 1 and 2 and us got black. I am 100% sure it is urn b. 6 2 67 6 2 68 6 2 69 1 "it could be urb b because a black ball was drawn therefore, higher chance of it being urb b. " 6 1 70 I say urn a because the first 2 must have been black and believe this black one came from urn a 6 2 71 2 "More teams seem to think this ball is from B, probably because more black balls were drawn than white, right? So this is probably urn B. I finally understand this game! Always go for the urn that the majority of the team believed it to be! Trust me, both of us will get a payoff. " 6 2 72 6 2 73 2 the proportions of the draws fit urn B better because there are more black balls drawn 6 2 74 3 team 1 and 4 definitely drew a black. team 3 drew a white. team 2 could go either way. so higher chance for Urn B. 6 2 75 6 2 76 hey lets win some money thanks experimenter#2348592-04197593\ 6 2 77 2 more teams before picked B 6 2 78 2 since there are more b's im assuming they saw black too 6 2 79 0 just a guess 6 2 80 2 black is b 2 out of 3 teams chose b so b is good if u seek amy 6 2 81 2 theres a higher probability of the black ball being chosen in B two other teams also picked B 6 2 82 6 2 83 6 2 84 "Black more likely to come from B, other evidence mixed but leaning a little toward B " 6 2 85 1 same reasoning as before 6 2 86 6 2 87 6 2 88 best choice because of probabilities 6 1 89 6 2 90 2 Most teams chose B and it's black. 6 2 91 3 "This is an information cascade problem, so we can only rely on the first 2 or so picks Since the first person picked B, they sawe Black since the second picked B, they most liiely saw black we see black, so lets pick B " 6 2 92 6 2 93 2 "We should choose black because the first group would choose according to their ball, the second person would be choosing according to their own because if they actually drew a white ball there would be no reason to be choosing the opposite urn based off of one other answers nad the last team contrasted meaning they went off their own. We match the first two so I believe it is urn B. " 6 2 94 2 2 teams chose B so far which means they saw BLACK we see a BLACK too I am pretty sure this is coming from B Choose B 6 1 95 6 2 96 6 1 97 6 2 98 6 2 99 2 "the first two teams saw black, so they chose black. but the second team saw white so they chose A We see black, so it is probably the black urn (3 black to 1 white ball being drawn) logically, it is urn B " 6 2 100 2 "team 1 got black team 2 got black team 3 happened to get white we got black, so it's with a much greater probability that the urn is B " 6 2 101 2 This one has to be black first two got black and team 3 got white we got black to so the probability works to our favor if we choose black 6 2 102 6 2 103 6 2 104 6 2 105 6 2 106 It is more likely that it came from B. More black balls came out