A Geometric Proof of Calibration

Abstract

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 a 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 [Foster, D. 1999. A proof of calibration via Blackwell's approachability theorem. Games Econom. Behav. 29 73–78] in the case of binary outcomes) and highlights the intrinsic connection between approachability and calibration.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 27 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.