Ordered data is ubiquitous. Recommendation systems attempt to leverage
information regarding one’s preferences to suggest new content (e.g. music,
movies) or products (e.g. books). Ranked-choice voting is used for local,
provincial/state, and national level elections across the globe. Even
Cornell uses ranked-choice for its elections! In sports, orderings
frequently determine tournament structures and season schedules, and in
games or general forms of competition, ordered data is a natural way to
express outcomes. While the expanding areas of application shows no signs
of slowing down, it also reflects two main difficulties: 1) disunity of the
theories that underpin available models and 2) computational issues that
arise when dealing with permutations of k objects, which scales
factorially. Both of these difficulties contribute to the ad-hoc flavor of
available methods as well as the relatively small body of work focused on
inference. Using the most complete dataset on surfing competitions, we take
a four step approach to present the material: First, we define ordered data
as a set of objects endowed with a strict order relation (ie. a
permutation) and discuss the various ways to represent ordered data
mathematically and as a data structure. Second, we construct the main
methods/models from the ground up and implement them using the surf
competition data. Third, we present a simplified and portable probability
model on permutations and demonstrate its effectiveness by identifying
empirical distribution(s). Lastly, we present some of the hurdles
encountered throughout this project that suggest areas for further
collaboration, namely, how to leverage computational algebra systems (which
I have used in this project) and how to visualize ordered data to
effectively communicate insights.