Maps of Tournaments: Distances, Experiments, and Data
Filip Nikolow, Piotr Faliszewski, Stanis{\l}aw Szufa

TL;DR
This paper introduces a method to visualize and analyze tournaments using a 2D map framework, comparing distance measures, generating random tournaments, and applying visualization to experimental and knockout tournament data.
Contribution
It adapts the map framework from election theory to tournaments, identifying useful distance measures and demonstrating their application in visualizing tournament data.
Findings
Identified effective distance measures for tournaments
Compared random tournament generation methods with real data
Showed how maps aid in visualizing experimental results
Abstract
We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no ties allowed). A map is a set of tournaments represented as points on a 2D plane, so that their Euclidean distances resemble the distances computed according to a given measure. We identify useful distance measures, discuss ways of generating random tournaments (and compare them to several real-life ones), and show how the maps are helpful in visualizing experimental results (also for knockout tournaments).
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Taxonomy
TopicsGame Theory and Voting Systems · Opinion Dynamics and Social Influence · Sports Analytics and Performance
