Related papers: Generalising Aumann's Agreement Theorem
We study opinion dynamics in a population of interacting adaptive agents voting on a set of complex multidimensional issues. We consider agents which can classify issues into for or against. The agents arrive at the opinions about each…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
In approaches to quantum theory in which the quantum state is regarded as a representation of knowledge, information, or belief, two agents can assign different states to the same quantum system. This raises two questions: when are such…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory which removes this indeterminism, as suspected…
Agent based systems are more common than we may think. A Promise Theory perspective on cooperation, in systems of human-machine agents, offers a unified perspective on organization and functional design with semi-automated efforts, in terms…
Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through…
Which theories lead to a contradiction between simple reasoning principles and modelling observers' memories as physical systems? Frauchiger and Renner have shown that this is the case for quantum theory, with a thought experiment that…
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…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
We study a model of consensus decision making, in which a finite group of Bayesian agents has to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
The notorious Wigner's friend thought experiment (and modifications thereof) has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
We propose a multi-agent epistemic logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents, and in the order in which they were sent. Additional to epistemic modalities the…