A Bayesian View on the Dr. Evil Scenario

TL;DR

This paper critically examines Elga's Bayesian argument for the principle of indifference in self-locating beliefs, highlighting a circular reasoning flaw and discussing the justification of equal credences.

Contribution

It provides a Bayesian critique of Elga's derivation of the principle of indifference, revealing a circularity in his thought experiments.

Findings

Identifies circular reasoning in Elga's argument

Argues that equal credences should not be derived from the thought experiments

Supports the idea that equal credences are reasonable without derivation

Abstract

In "Defeating Dr. Evil with Self-Locating Belief", Adam Elga proposes and defends a principle of indifference for self-locating beliefs: if an individual is confident that his world contains more than one individual who is in a state subjectively indistinguishable from his own, then he should assign equal credences to the hypotheses that he is any one of these individuals. Through a sequence of thought experiments, Elga in effect claims that he can derive the credence function that should apply in such situations, thus justifying his principle of indifference. Here we argue, using a Bayesian approach, that Elga's reasoning is circular: in analyzing the third of his thought experiments, he uses an assertion that is justifiable only if one assumes, from the start, the principle of indifference that he is attempting to justify. We agree with Elga that the assumption of equal credences is a very reasonable principle, in the absence of any reason to assign unequal credences, but we do not agree that the equality of credences can be so derived.