Technical Appendix

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Model Details

The societal code model is adapted from the original model proposed by March. In every time interval, four processes occur in order:

1. The societal code learns from superior agents: The superior agents are those that have a higher accuracy than the code. Accuracy is given as the dot product of the belief vector with the environment vector divided by the number of dimensions of reality. For every component of knowledge, the sum of the superior agents' beliefs in that component is computed. If the sum is positive, the code may assume the value +1. If the sum is negative, the code may assume the value -1. If the sum is zero, the code is unaffected. The probability that the code's belief changes in any period is given by: 1 - (1 - (Code Learning Rate) ) k, where k is the absolute value of the sum of agents' beliefs, as above. Each component changes independently of all other components.

2. The agents learn from the code: The (independent) probability that a particular component of knowledge of a particular agent assumes the belief of the code is the Socialization Rate, or Agent Learning Rate.

3. The environment changes: Each component of the environment vector will reverse in sign, from +1 to -1, or vice-versa, with a certain probability, the Mutation Rate.

4. Agents are replaced by newcomers: An agent is replaced in every time period with probability Turnover Rate. When an agent is replaced, the new agent begins with random beliefs; each component is -1, 0, or +1 with equal probability.

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