An information cascade is precisely what we assumed would not happen when we discussed the wisdom of crowds previously. This occurs when people observe the actions of others, and follow the crowd irrespective of their own instincts. And fortunately or unfortunately, this is going to occur quite often in various situations. So let's take a look at a few practical examples. First one's a homework assignment. Suppose you and your friends are working on a homework assignment together, and suppose the question asks whether or not independence is required for the wisdom of crowds to hold. So, you have a gut feeling that the answer is yes, that independence is required, but everyone else in the group is insisting that it's no, that it's not required, and they wont budge. So not wanting to be the odd man out, you also put no, and hence you follow the group answer and ignore your own, private instinct. Unfortunately, it turns out that your original instinct was correct. Now, in this case, this is a incorrect information cascade versus a correct one, which would occur if they all have the correct answer and you either have the correct or the incorrect answer but you decided to follow them, in that case it would have helped you. But, in this case it's an example of an incorrect or a bad cascade. The second example, say suppose you're walking down the street and on a street corner you see one person that stopped to look up at the sky. So you are on a street corner, and you see one person standing there, and that person's looking up at the sky. If it's just one person, you may assume that the person, you know, had a nosebleed, or suddenly became philosophical, and you would keep walking and go about your business. Now suppose you go to a street corner and you observe and you see that ten people are all looking up at the sky, or ten or more people. How many people are here? So, now you may assume that, you may start to think, well, maybe there is actually something wrong up there and you would stop and you would maybe look up at the sky too. And it wouldn't be until someone shouted, hey, this one person in the middle here has a nosebleed, which is why they stopped to tilt their head, that you would think that everyone else, just like you, was misled and then the whole crowd would then therefore disperse. That's an example of breaking a cascade. But again, the idea is that, everybody is going to follow the action of a crowd. And, additionally, here, we see that as more and more people are following the same public action, it becomes much less likely that you, as a person, are going to follow your own private instinct. Third example is YouTube. So if many others before you watched the video, which means that it has a higher view count on its page, it's more likely you're going to watch it too. You might decide to stop watching it if you don't like it, but it's still going to count towards the total viewing number that's shown next to the video. And partially determine its place on the recommendation page. Hence, other people viewing the video are causing you to watch it, which in turn influences more people like you, even if you don't like it, which then influences more people because the view count is higher. Then it influences more people and so forth and the accumulation keeps building up. So we could probably write a whole book on the places where you would see such information cascades, from stock market bubbles, where people are following the fact that the stock is rising, fashion fads, the emergence of pop stars, the collapse of totalitarian regimes throughout history, and at least to some extent, all these examples are going to involve people following the crowd. So that's the key. Following the crowd rather than listening to their own gut feeling. Let's try to generalize some of these ideas. In a situation of sequential decision making, or people are making decisions one at a time, we can point out several key observations. So each person gets a private signal. In an example of tilting your head back. This is your nose starts bleeding. That would be your private signal, being your nose starting to bleed. And then releases a public action. And the public action would be, well, now that my nose is bleeding, let me stop walking and tilt my head to the sky. Subsequent users can observe the public action but not the private signal. So this is observable, you know, tilting your head up in the sky, that's observable to everyone else whereas this is not observable. [SOUND] The second observation is information cascade. So if we come to a point where there's enough public actions of the same type, you know, like 10, 20 people looking at the sky. Then all later users are going to ignore their own private instinct, and simply follow what the others are doing. So this is where you start to follow the crowd. [BLANK_AUDIO] So a cascade then starts, and the independence assumption behind the wisdom of crowds is going to break down. Now what constitutes enough public actions, is going to depend upon the specific situation and how believable it is. For instance, it's presumably much harder to get everyone to watch your YouTube video than it would be to get someone to look up at the sky. Next observation is positive feedback. So, people are more likely to follow a public action if there are more people following the public action already. That's shown over here, in the case of our looking up example. The size of the crowd is going to increase the chance that this person will stop, which is then going to increase the size of the crowd if he does stop, which then makes it even more likely that the next person will stop, which then makes this crowd larger and so forth. This is an example of positive feedback. So, the, the idea in the information cascade is that we're going to move in the same direction as what the influence or the public action is. And if you recall our discussion on negative feedback and other, and other lectures. Like when we talked about distributive power control for cell phones we saw that there was some error signal and though, the way that, that worked was that your cell phone would talk to a cell tower, and based upon the observed by the measure SIR versus what your desired signal interference ratio was. If, if it was higher, then it should be, you would lower your transit power. And then if it was lower than it should be, you would raise your transit power to try to increase the SIR. So you are responding to some error signal in the negative feedback case. There is some error happening. In this case, we're doing the opposite. So, if there was positive feedback in the case of distributive power control it would be a very bad thing. Because what that would mean was that, if you had a higher measure SIR than what the desired was, you would increase your transit power again and become more greedy and keep trying to increase and increase it. And therefore, you would never converge to anything like we discussed. So that's the difference between positive and negative feedback and positive feedback, we're moving in the same direction as some influence and a negative feedback we're moving in the opposite direction of some error signal. The cascades are also fragile even if a few private signals were release to the public, the cascade can quickly even reverse direction. Precisely because people don't really have a lot of faith in what they're doing even when many of them are doing the same thing. So, people know that the cascade has started because they're making a decision to follow what other people are doing. But people are also malleable in this sense too. And an example of this is that if the people who had nosebleeds here, so if this one person who had a nosebleed, maybe in the center, shouted out that he had a nosebleed, then everyone else would quickly disperse and realize that they were just following the crowd. Last thing is that cascades, as we said, can be wrong. So, a cascade is sometimes a good thing. If it's, you know, helping everyone, but sometimes it's also a bad thing because, the, the public action may not represent, the truth which is why we can't rely on the wisdom of crowds in these situations. 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