Information Cascades and Aumann’s Agreement Theorem
This blog post relates to the article titled “Arresting irrational information cascades” by Robert Wiblin. The article can be accessed and downloaded at the following link: http://www.overcomingbias.com/2012/10/arresting-irrational-information-cascades.html
This article discusses a few of the theorems associated with information cascades. Specifically, the article states Aumann’s Agreement Theorem, which is a theorem that states that two people who are acting rationally (in which the rational decision is and with common knowledge of each other’s beliefs cannot agree to disagree. The article notes that this theorem basically states is that two individuals positions should converge to the same position, even if they don’t know how the other person reached their conclusion. The article then notes how information cascades arise from applying AAT to real life. The author notes that nobody lives AAT in real life because people believe that other individuals disagreeing with them are probably wrong — in order to not feel submissive or less informed.The article continues to discuss potential ways to prevent information cascades from occurring. The author notes that the main problems with the creation of information cascades is that one group strictly copies the position of the other group. The author suggests instead that information cascades can be halted by the mutual updating of each other’s positions.
The article relates to information cascades discussed in lecture. In particle, the article notes that information cascades evolve from applying Aumann’s Agreement Theorem to real life situations. Then, as in lecture, the article discusses the four key conditions that must be met in an information cascade model:
1. Agents make decisions sequentially
2. Agents make decisions rationally based on the information they have
3. Agents do not have access to the private information of others. and
4. A limited action space exists.
The author provides a formal definition of an information cascade, and notes that “A cascade develops when people ‘abandon their own information in favor of inferences based on earlier people’s actions'”. The idea of information cascades can be related to the iclicker example conducted in the class lecture, in which the question “How many b’s appeared on the picture above”. Different sections of the class(who can be thought of as the agents in the definition of an information cascade) were asked to answer the questions sequentially. The results converged on the correct answer, and the number of people who chose this correct answer increased after each poll.