Insuring against loss of evidence in game-theoretic probability

TL;DR

This paper addresses the problem of accurately measuring evidence against a forecaster in game-theoretic probability, proposing a method to prevent exaggeration of evidence by Sceptic's capital.

Contribution

It characterizes all increasing functions that correct for evidence exaggeration, enabling more reliable evidence measurement in game-theoretic probability.

Findings

Identifies functions that remove evidence exaggeration

Provides a framework for insuring against evidence loss

Enhances reliability of evidence measurement in forecasting

Abstract

We consider the game-theoretic scenario of testing the performance of Forecaster by Sceptic who gambles against the forecasts. Sceptic's current capital is interpreted as the amount of evidence he has found against Forecaster. Reporting the maximum of Sceptic's capital so far exaggerates the evidence. We characterize the set of all increasing functions that remove the exaggeration. This result can be used for insuring against loss of evidence.