Related papers: Coherence of countably many bets

We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.

We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…

We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true. A further result is that the Hauptvermutung is true if we…

Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…

This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…

We consider contests with a large set (continuum) of participants and axiomatize contest success functions that arise when performance is composed of both effort and a random element, and when winners are those whose performance exceeds a…

The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two…

This paper studies Ebert's hat problem with four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning strategies…

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are…

We investigate differences between a simple Dominance Principle applied to sums of fair prices for variables and dominance applied to sums of forecasts for variables scored by proper scoring rules. In particular, we consider differences…

The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…

We give a nonstandard analytic proof of de Finetti's theorem for an exchangeable sequence of Bernoulli random variables. The theorem postulates that such a sequence is uniquely representable as a mixture of iid sequences of Bernoulli random…

We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical…

We recall a combinatorial derivation of the functions generating probability of winnings for each of many participants of the Penney's game and show a generalization of the Conway's formula to this case.

Dummett's argument for intuitionism is well known. There is a concern that the argument proves too much, specifically, that it supports the extreme and apparently incoherent position of strict finitism. The central question is how to…

For every sports tournament, it is an important requirement to provide contestants with the appropriate incentives to perform. However, incentive compatibility is usually considered an all or nothing (binary) concept in the academic…

We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra.

This paper studies Ebert's hat problem for three and four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning…