Quantifying the dynamics of ranked systems

This dissertation uses volatility and spacing to allow one to quantify the dynamics of a wide class of ranked systems. The systems we consider are any set of items, each with an associated score that may change over time. We define volatility as the standard deviation of the score of an item. We define spacing as the distance in score from one item to its neighbor. From these two concepts we construct a model using stochastic differential equations. We measure the model parameters in a variety of ranked systems and use the model to reproduce the salient features observed in the data. We continue by constructing a spacing-volatility diagram that summarizes three unique stability phases and overlay each dataset on this diagram. We end by discussing limitations and extensions to such a model.