Essay On Inferential Naivety

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earning with Inferential Naivety[edit]
Research in rational inference in social-learning began with the work of Abhijit V. Banerjee[5], Sushil Bikhchandani, David Hirshleifer, and Ivo Welch[6]. In the basic setting of the model, rational agents end up herding. This characteristic is a feature of even more general settings and can be rationaled by the following argument: Given a finite action space and a finite and imperfect signal space, rational agents eventually "heard" as a consequence of "Information cascade", while ignoring their own signal, each person imitates others' behavior[7]:221. Though much of the basic logic regarding the proportion of private information and the proportion of information revealed by others' actions is well predicted by the model, it does have some core implications that seem unrealistic. Among its unrealistic statements is the claim that the agents have a level of sophistication that allows them to predict very unlikely behavior.
In simple cases of inferential naivety players are capable of realizing that the actions taken by previous movers reflect their own signals, however they fail to comprehend that these previous movers themselves infer with the same logic from even earlier actions. In a paper by Erik Eyster and Matthew Rabin, this process is described as follows:
Not realizing that the second mover’s action reflects beliefs that combine the first and second movers’ signals, the third mover’s inference from both predecessors leads her, in fact, to count the first mover’s signal twice. The (naive) fourth mover, in turn, unintentionally counts the first mover’s signal four times: once from the first action, once from the second action, and twice from the third action[7].:223
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...ders can converge to a erroneous statement with a positive probability. Nonetheless, there is one exception worth noting originating from the work of Eyster and Rabin[10], who adjust the model to permit each agent to exclusively observe only the immediate predecessor. In this variation of the model, the actions, and as a result, the outcomes, of naive herders exactly match those of rational agents. The reason why this exception is capable of realizing satisfactory results is that by limiting the observation horizon, naive herders are unable to double count previous actions, consequently, all signals are counted only once. Still, relaxing this assumption even by a margin of one, where naive herders can observe the last two moves, suffices to yet again create the conditions that ensure with a positive probability that these agents end up converging to a wrong belief.

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