The US Constitution establishes an indirect system to elect the president and vice president. People elect a college (a group) of electors that then elects the president. This used to be a non-issue and non-event for ages up until in November of 2000 the election was so close in Florida that it required waiting for a few weeks and a Supreme Court decision to decide the winner. Another eventful election happened in 2016 (sans the Supreme Court intervention).
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analytics
Hall’s Marriage Theorem Meets the DraftKings Entry Form
This is the last post in my accidental Fourier-Motzkin trilogy (part one: the method; part two: the baseball lineups), and it’s about the bill coming due. Because when you use elimination to throw variables out of a model, the mathematics is very clear about what you keep — and very quiet about what you lose. I found out exactly what I’d lost the first time DraftKings rejected a lineup my spreadsheet swore was legal. The story runs straight through a beautiful piece of combinatorics called Hall’s marriage theorem, so we’ll pick that up along the way.
Continue reading “Hall’s Marriage Theorem Meets the DraftKings Entry Form”A neural network approach to college football rankings
The usual image of an artificial neural network:
What follows is a paper that I wrote in the Spring of 2001 for an “Introduction to Neural Networks” class that I took as part of my Master’s degree. It is mostly a review of someone else’s paper on the subject, except that I wrote the network in Excel and ran it on that year’s football season games. Fun, fun.
Continue reading “A neural network approach to college football rankings”A Fourier-Motzkin Elimination Example: DraftKings Lineups
In my last post about Fourier-Motzkin elimination I promised a real example involving baseball, and I keep my promises. This is the story of how a dusty 19th-century math trick ended up picking my daily fantasy lineups — and how I stumbled into a genuine Fourier-Motzkin elimination example without fully realizing that’s what I was doing until much later.
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Fourier-Motzkin Elimination: An Old Trick I Still Use
Fourier-Motzkin elimination is one of those methods that gets a page and a half in the linear programming textbooks, right before the simplex method shows up and steals the whole show. I was first introduced to it while working as an OR analyst at Cargill, and my honest first reaction was: nice, but why would I ever use this? It took me years (and one very stubborn model) to change my mind. This post is the explanation I wish someone had given me back then: what the method actually does, how the mechanics work, and a small worked example showing a model before and after the elimination.
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