Related papers: The Principle of Redundant Reflection
We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making…
To fully characterize the information that two `source' variables carry about a third `target' variable, one must decompose the total information into redundant, unique and synergistic components, i.e. obtain a partial information…
A principle is modified that underlies the theory of organic fiducial inference as this theory was presented in an earlier paper. This modification, which is arguably a natural one to make, allows Bayesian inference to sometimes have a…
The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In order to apply the rationality result of belief dynamics theory to various…
Of the various attempts to generalize information theory to multiple variables, the most widely utilized, interaction information, suffers from the problem that it is sometimes negative. Here we reconsider from first principles the general…
This paper considers the problem of defining a measure of redundant information that quantifies how much common information two or more random variables specify about a target random variable. We discussed desired properties of such a…
To make decisions we are guided by the evidence we collect, as well as the opinions of friends and neighbors. How do we integrate our private beliefs with information we obtain from our social network? To understand the strategies humans…
We characterize information as risk reduction between knowledge states represented by partitions of the underlying probability space. Entropy corresponds to risk reduction from no (or partial) knowledge to full knowledge about a random…
The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we…
Bayesian experts who are exposed to different evidence often make contradictory probabilistic forecasts. An aggregator, ignorant of the underlying model, uses this to calculate her own forecast. We use the notions of scoring rules and…
Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…
In this paper, we define a new measure of the redundancy of information from a fault tolerance perspective. The partial information decomposition (PID) emerged last decade as a framework for decomposing the multi-source mutual information…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
An updating rule specifies how an agent reacts to information. An updating rule is Blackwell monotone if more information is always better for an agent in a decision problem and strictly Blackwell monotone if, in addition, there is always a…
Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential…
Traditional belief revision frameworks often rely on the principle of minimalism, which advocates minimal changes to existing beliefs. However, research in human cognition suggests that people are inherently driven to seek explanations for…
This paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency…
We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…
We analyze boundedly rational updating from aggregate statistics in a model with binary actions and binary states. Agents each take an irreversible action in sequence after observing the unordered set of previous actions. Each agent first…
Given only aggregate choice data and limited information about how menus are distributed across the population, we describe what can be inferred robustly about the distribution of preferences (or more general decision rules). We strengthen…