Change rules for hierarchical beliefs

Abstract

The paper builds a belief hierarchy as a framework common to all uncertainty measures expressing that an actor is ambiguous about his uncertain beliefs. The belief hierarchy is further interpreted by distinguishing physical and psychical worlds, associated to objective and subjective probabilities. Various rules of transformation of a belief hierarchy are introduced, especially changing subjective beliefs into objective ones. These principles are applied in order to relate different contexts of belief change, revising, updating and even focusing. The numerous belief change rules already proposed in the literature receive epistemic justifications by associating them to specific belief hierarchies and change contexts. As a result, it is shown that the resiliency of probability judgments may have some limits and be reconciled with the possibility of learning from factual messages

Rationality, the Bayesian standpoint, and the Monty-Hall problem

“…Following Walliser and Zwirn ( 2011 ), your beliefs before learning message ‘ g 3 ’ assuming your initial choice is D 1 (Stage 2) can be represented as a hierarchical dynamic probabilistic structure (see Figure 1 ). The layer 0 depicts the four possible strategies of the host, i.e., showing a goat behind D 2 or D 3 (‘ g 2 ’ or ‘ g 3 ’) or showing a car when the two players have originally chosen two different doors with goats behind (‘ c 2 ’ or ‘ c 3 ’).…”

Updating our beliefs about inconsistency: The Monty-Hall case

“…1996; Dubois & Prade 1997;Walliser & Zwirn forthcoming). In such focusing situation the message concerns an object drawn at random from a population of objects (fixed universe).…”