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Polarization in Politics and Bayesian Memory Modeling

Bayesian analysis is a constant conscious and unconscious procedure in our lives, and the interpretation of mixed signals is a challenge. In class we were faced with the problem of how to interpret the moves of a participant whose information we could not see. At a single step this was complex; in aggregate it becomes impossible to accurately assess the probabilities created from multiple mixed messages. A common approach to this challenge is to store only the interpretation of each step. In Updating Beliefs with Ambiguous Evidence: Implications for Polarization (Draft form) Roland G. Fryer, Jr., Philipp Harms and Matthew O. Jackson look at the possible results of Bayes’ analysis with limited storage (such as human memory), and apply them to understanding the polarization of beliefs among agents (people) exposed to the same signals.

According to the model proposed by Fryer et al, an agent with a previously formed inclination as to the state of a situation, when faced with mixed signals, will remember these mixed signals as being true signals for the outcome they were inclined towards. In the provided example an agent, with a prior inclination to state A, sees a series of signals: a; b; ab; ab; a; ab; b; b (3). Because the agent has limited memory, the agent interprets the signals as a; b; a; a; a; a; b; b, seeing more evidence of a then b, when there was actually more evidence of b. The paper follows this model, determining that if the believed probability of a false outcome is high enough, and unclear signals frequent enough in relation to true signals, then it is inevitable that the conclusion reached by the agent will be wrong (10). Furthermore, if beliefs are based on early impressions then early signals alone can create a cascade of evidence (within an agent’s interpretation), similar to what we studied in chapter 16.

The conclusion of this paper discusses the polarization of people with regards to political and social policies. It seeks to answer the question as to why people facing similar evidence (such as the correlation between human activity and global warming) display highly polarized beliefs. The conclusion the paper draws is that, with this model, it is possible for two agents to view identical information and come to different conclusions, while both rationally applying Bayesian analysis. The model is also applied to discrimination, identifying a process whereby discrimination, once formed, can be perpetuated indefinitely (15).

This relates to chapter 16 in that it uses the same type of repetitive Bayesian analysis. The difference is that the subsequent Bayesian steps happen within a single agent, not in a group of agents observing each other’s practices. The limited storage (memory) available to one agent creates a situation whereby the agent only observes her own actions, but does not recall and accurately access the evidence that propelled those reactions; engendering the possibility of a false cascade within a rational agent.

This paper was chilling to read, however in its application to polarization in politics it requires agents to make binary choices when faced with limited storage. Whether or not people do this, even under extreme stress, is an interesting question.

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