A Devastating Example for the Halfer Rule

TL;DR

This paper presents a counterexample demonstrating that the Halfer Rule can prescribe beliefs that violate rational principles like the Reflection Principle, raising questions about its validity in updating beliefs.

Contribution

It introduces a specific example where the Halfer Rule leads to irrational credences, challenging its general applicability in belief updating.

Findings

The example shows the Halfer Rule can prescribe irrational credences.

Credences violate the Reflection Principle in the example.

Raises doubts about the universal validity of the Halfer Rule.

Abstract

How should we update de dicto beliefs in the face of de se evidence? The Sleeping Beauty problem divides philosophers into two camps, halfers and thirders. But there is some disagreement among halfers about how their position should generalize to other examples. A full generalization is not always given; one notable exception is the Halfer Rule, under which the agent updates her uncentered beliefs based on only the uncentered part of her evidence. In this brief article, I provide a simple example for which the Halfer Rule prescribes credences that, I argue, cannot be reasonably held by anyone. In particular, these credences constitute an egregious violation of the Reflection Principle. I then discuss the consequences for halfing in general.