Related papers: Common $p$-Belief with Plausibility Measures: Exte…
According to Aumann's celebrated theorem, rational agents cannot agree to disagree. In other words, agents who once shared a common prior probability distribution and who have common knowledge about their posteriors cannot assign different…
A celebrated 1976 theorem of Aumann asserts that honest, rational Bayesian agents with common priors will never "agree to disagree": if their opinions about any topic are common knowledge, then those opinions must be equal. Economists have…
Through set-theoretic formalization of the notion of common knowledge, Aumann proved that if two agents have the common priors, and their posteriors for a given event are common knowledge, then their posteriors must be equal. In this paper…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
Agreement theorems are no-go results about rational disagreement: if two agents start from a common prior and their posterior beliefs are common knowledge, they cannot assign different probabilities to the same event. Standard treatments of…
We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state, and who observe some information structure. For two agents we introduce a quantitative version of…
We study a model of information aggregation and social learning recently proposed by Jadbabaie, Sandroni, and Tahbaz-Salehi, in which individual agents try to learn a correct state of the world by iteratively updating their beliefs using…
We study a setting where Bayesian agents with a common prior have private information related to an event's outcome and sequentially make public announcements relating to their information. Our main result shows that when agents' private…
We formulate and prove an Agreement Theorem for quantum mechanics (QM), describing when two agents, represented by separate laboratories, can or cannot maintain differing probability estimates of a shared quantum property of interest.…
We present an efficient reduction that converts any machine learning algorithm into an interactive protocol, enabling collaboration with another party (e.g., a human) to achieve consensus on predictions and improve accuracy. This approach…
This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes' rule given some…
A natural way to represent beliefs and the process of updating beliefs is presented by Bayesian probability theory, where belief of an agent a in P can be interpreted as a considering that P is more probable than not P. This paper attempts…
Consensus formation is investigated for multi-agent systems in which agents' beliefs are both vague and uncertain. Vagueness is represented by a third truth state meaning \emph{borderline}. This is combined with a probabilistic model of…
We introduce a framework of layered subsets, and give a sufficient condition for when a set system supports an agreement test. Agreement testing is a certain type of property testing that generalizes PCP tests such as the plane vs. plane…
Standard models of multi-agent modal logic do not capture the fact that information is often ambiguous, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different…
We give efficient "collaboration protocols" through which two parties, who observe different features about the same instances, can interact to arrive at predictions that are more accurate than either could have obtained on their own. The…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…
In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes' posterior probability of a measurable set $A$, when the prior lies in a class of probability measures $\mathcal{P}$ and the likelihood is precise.…
We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs…