Related papers: Impugning Randomness, Convincingly
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named…
In recent years, there has been an increased need for the use of active systems - systems required to act automatically based on events, or changes in the environment. Such systems span many areas, from active databases to applications that…
We review what we call "event-enhanced formalism" of quantum theory. In this approach we explicitly assume classical nature of events. Given a quantum system, that is coupled to a classical one by a suitable coupling, classical events are…
A growing class of applications depends on fair ordering, where events that occur earlier should be processed before later ones. Providing such guarantees is difficult in practice because clock synchronization is inherently imperfect:…
Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by…
Life forms exhibit such a degree of exquisite organization that it seems impossible that they could have developed out of a process of trial and error, as intimated by the theory of Darwinian evolution. In this general public paper I…
We introduce a new mathematical framework for the probabilistic description of an experiment upon a system of any type in terms of initial information representing this system. Based on the notions of an information state, an information…
Organisms and algorithms learn probability distributions from previous observations, either over evolutionary time or on the fly. In the absence of regularities, estimating the underlying distribution from data would require observing each…
We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a…
It is shown that an equiprobability hypothesis leads to a scenario in which it is possible to predict the outcome of a single toss of a fair coin with a success probability greater than 50%. We discuss whether this hypothesis might be…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
The recognition of the agency of the knower has enormously enriched our understanding of knowledge production. There is a growing realization that what we know about how we know affects our interpretation of reality. This realization…
The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…
The field of algorithmic fairness has rapidly emerged over the past 15 years as algorithms have become ubiquitous in everyday lives. Algorithmic fairness traditionally considers statistical notions of fairness algorithms might satisfy in…
Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
The concept of Probability of Causation (PC) is critically important in legal contexts and can help in many other domains. While it has been around since 1986, current operationalizations can obtain only the minimum and maximum values of…
In this article we take a probabilistic look at H\"older's inequality, considering the ratio of terms in the classical H\"older inequality for random vectors in $\mathbb{R}^n$. We prove a central limit theorem for this ratio, which then…