Sequential Choice and Self-Reinforcing Rankings

Explore the mathematical consequences of sequential choice and self-reinforcing rankings in this lecture from the Santa Fe Institute. Delve into how the probability of choosing an option often depends on its ranking, which is determined by relative popularity. Examine the long-term convergence of such systems to stable rankings, the unpredictability of outcomes, and potential suboptimal results. Learn about analytical solutions for two-option cases and convergence conditions for multiple options. Discover how these findings apply to various economic models and reinterpret classic sequential choice theories like the herding model. Gain insights into the design of rankings, self-reinforcing mechanisms, and optimal algorithms through examples such as the Music Lab experiment.