A simple integral representation of single-event scoring rules

TL;DR

This paper presents a straightforward integral representation for proper single-event scoring rules that does not rely on derivatives or continuity assumptions, simplifying their analysis and application.

Contribution

It introduces a novel integral representation for scoring rules that avoids derivatives and continuity constraints, enhancing their theoretical understanding and practical use.

Findings

Provides a new integral form for scoring rules

Simplifies analysis of scoring rules

Applicable without derivatives or continuity assumptions

Abstract

A simple integral representation involving no derivatives or continuity assumptions is given for proper single-event scoring rules.