Arresting irrational information cascades
https://www.overcomingbias.com/2012/10/arresting-irrational-information-cascades.html
In Robert Wilbin’s Arresting irrational information cascades, he begins by introducing Aumann’s Agreement Theorem which states:
…two people acting rationally (in a certain precise sense) and with common knowledge of each other’s beliefs cannot agree to disagree. More specifically, if two people are genuine Bayesian rationalists with common priors, and if they each have common knowledge of their individual posteriors, then their posteriors must be equal.
In other words, if two entirely rational agents have similar priors, or beliefs regarding the probability of a fact being true, and share knowledge about what the other has observed to produce their posterior probabilities, the probability of a fact given relevant observations, they must ultimately hold the same posteriors. This means that given sufficient rational deliberation between the agents, they will always converge to the same conclusion given that they have common priors. However, this is clearly not how deliberations between humans always play out. This is because taking this theorem into the real world would result in an imperfect implementation that would leave society vulnerable to informational cascades.
An informational cascade occurs when a person observes the prior decisions of others and follows the choice that others have made independent of their own personal information. This occurs because people infer information and adjust their views about the correct decision based off of the prior decisions that they witnessed others make. For example, if one person witnesses many others buy a certain stock, and he assumes them to be rational agents acting on their own private information, he might be inclined to buy the stock even if his own signals suggest that he should not buy the stock. This effect can compound each time someone follows the crowd and eventually no amount of private information would be able to sway someone to not follow the crowd. It is then apparent how the public’s confidence in a decision could vary significantly from the confidence they should hold based on the community’s collective information.
Aumann’s Agreement Theorem suggests that in a world where we could share private information and deliberate indefinitely, information cascades like the one above would not occur. This is because unlike in an informational cascade, sharing of private information occurs, and thus everyone would know everyone else’s priors and posteriors. Under these circumstances, assuming only rational agents and common priors, all person’s conclusions would converge to a decision invulnerable to informational cascades. There are many reasons, some obvious and some less obvious, why the world we live in is not a world in which Aumann’s Agreement Theorem can be applied faithfully. While many of these reasons can not be fully resolved, Wilbin offers a few plausible adjustments in decision processes to reduce the risk of informational cascades. I encourage anyone interested in understanding them more fully to read the post linked at the top of this post.