Who's #1?

Abstraction: Critical book review of rating and ranking methods in sports

Key points:

• "Who's #1? The Science of Rating and Ranking" by Langville & Meyer covers 8+ ranking methods based on pairwise comparisons
• Critic (statistician Christian Robert) faults the book for lacking probabilistic grounding — methods are conventions, not statistical models
• Elo rating system (used in chess) described as elegantly simple but ultimately arbitrary convention, not truth
• Markov chain ranking constructs a transition matrix to derive stationary distribution as ranking — criticized for non-dynamical misuse
• Methods covered include Sinkhorn-Knopp, Kendall's tau, Spearman's footrule, Arrow/Condorcet, and relaxation/evolutionary optimization
• Key insight: different ranking methods produce vastly different orderings with no objective criterion to prefer one

Connections: Christian Robert · Ranking · Statistics

Source: http://xianblog.wordpress.com/2012/05/02/whos-1/