How I built the SoME3 voting system with graph theory
I will explain to you how to create a voting system for a massive competition using graph theory. This is how I developed the algorithm for the Summer of Maths Exposition competition.
I will explain all the principles starting from scratch. We will cover the following concepts: what is a graph, the diameter of a graph, the adjacency matrix of a graph, the concept of an expander graph, the expansion rate of a graph, and its impact on the graph's diameter.
00:00 Introduction
00:54 Naive approach and three criteria
05:13 Mathematical approach
07:18 Three examples of the expansion rate concept
10:00 How to construct a good expander graph?
12:19 Conclusion and final example
Thanks to James Schloss and Grant Sanderson for all the organization.
Links:
Video excerpts
SoME 2: • What makes a great math explanation? | SoM...
Fouloscopie: • 4 expériences sociales pour comprendre les...
Articles
Social Choice: https://en.wikipedia.org/wiki/Social_...
The Anatomy of the Facebook Social Graph: https://arxiv.org/abs/1111.4503
Analyzing Twitter User Network: https://towardsdatascience.com/analyz...
Expander graph: https://en.wikipedia.org/wiki/Expande...
Alon-Boppana bound: https://en.wikipedia.org/wiki/Alon%E2...
Joel Friedman's proofs of Alon's conjecture: https://arxiv.org/abs/cs/0405020
Websites
Six Degrees of Music Separation: https://www.whosampled.com/six-degrees/
SoME 3: https://some.3b1b.co/
Source code of the platform
https://github.com/fcrozatier/champagne
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