Dominating countably many forecasts

TL;DR

This paper explores the differences between dominance principles applied to fair prices and forecasts, especially when considering infinitely many variables and finitely additive expectations, revealing nuanced distinctions in their application.

Contribution

It introduces an analysis of dominance principles in the context of infinitely many forecasts and fair prices, highlighting differences under finitely additive expectations.

Findings

Differences between dominance applied to prices and forecasts are significant in infinite settings.

Finitely additive expectations lead to distinct dominance considerations.

The study clarifies the theoretical implications of applying dominance principles to infinite collections.

Abstract

We investigate differences between a simple Dominance Principle applied to sums of fair prices for variables and dominance applied to sums of forecasts for variables scored by proper scoring rules. In particular, we consider differences when fair prices and forecasts correspond to finitely additive expectations and dominance is applied with infinitely many prices and/or forecasts.