A Geometric Proof of Calibration

We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and convex target set. Our proof captures the essence of existing proofs based on approachability (e.g., the proof by Foster [1999] in case of binary outcomes) and highlights the intrinsic connection between approachability and calibration. JEL codes: C72, C73

• Type: Journal
• Year: 2010
• Where: MOR
• Authors: Shie Mannor, Gilles Stoltz
• Keywords: Arbitrary Finite Number, Binary Outcomes, Convex Target, MOR 2010, Security Privacy