Related papers: Decision Making for Symbolic Probability
We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is…
This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
Social choice theory is the study of preference aggregation across a population, used both in mechanism design for human agents and in the democratic alignment of language models. In this study, we propose the representative social choice…
We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of…
If we accept Savage's set of axioms, then all uncertainties must be treated like ordinary probability. Savage espoused subjective probability, allowing, for example, the probability of Donald Trump's re-election. But Savage's probability…
While preference modelling is becoming one of the pillars of machine learning, the problem of preference explanation remains challenging and underexplored. In this paper, we propose \textsc{Pref-SHAP}, a Shapley value-based model…
Criticisms of so called `subjective probability' come on the one hand from those who maintain that probability in physics has only a frequentistic interpretation, and, on the other, from those who tend to `objectivise' Bayesian theory,…
A central concept in active inference is that the internal states of a physical system parametrise probability measures over states of the external world. These can be seen as an agent's beliefs, expressed as a Bayesian prior or posterior.…
A basic experiment in probability theory is drawing without replacement from an urn filled with multiple balls of different colours. Clearly, it is physically impossible to overdraw, that is, to draw more balls from the urn than it…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
This paper axiomatizes, in a two-stage setup, a new theory for decision under risk and ambiguity. The axiomatized preference relation $\succeq$ on the space $\tilde{V}$ of random variables induces an ambiguity index $c$ on the space…
This survey reviews recent developments in revealed preference theory. It discusses the testable implications of theories of choice that are germane to specific economic environments. The focus is on expected utility in risky environments;…
If uncertainty is modelled by a probability measure, decisions are typically made by choosing the option with the highest expected utility. If an imprecise probability model is used instead, this decision rule can be generalised in several…
In [12], Nilsson proposed the probabilistic logic in which the truth values of logical propositions are probability values between 0 and 1. It is applicable to any logical system for which the consistency of a finite set of propositions can…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
This paper offers a commentary on the use of notions of statistical significance in choice modelling. We review the reasons for uncertainty in parameter estimates, provide a precise discussion on the computation of measures of uncertainty…
A number of writers(Joseph Halpern and Fahiem Bacchus among them) have offered semantics for formal languages in which inferences concerning probabilities can be made. Our concern is different. This paper provides a formalization of…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
Mutually exclusive decisions have been studied for decades. Many well-known decision theories have been defined to help people either to make rational decisions or to interpret people's behaviors, such as expected utility theory, regret…