Related papers: Solving the Hard Problem of Bertrand's Paradox
We are lifting classical problems from single instances to regular sets of instances. The task of finding a positive instance of the combinatorial problem $P$ in a potentially infinite given regular set is equivalent to the so called…
The Jeffreys-Lindley paradox stands as the most profound divergence between frequentist and Bayesian approaches to hypothesis testing. Yet despite more than six decades of discussion, this paradox remains frequently misunderstood--even in…
If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, what arises is the problem to explain where the rates of the outcomes of statistical experiments come from, as already noticed by…
Here we continue with the ideas expressed in "On the strangeness of quantum mechanics" aiming to demonstrate more concretely how this philosophical outlook might be used as a key for resolving the measurement problem. We will address in…
Bertrand et al. introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all…
Hardy's paradox provides an all-versus-nothing fashion to directly certify that quantum mechanics cannot be completely described by local realistic theory. However, when considering potential imperfections in experiments, like imperfect…
It is hypothesized that the Langevin time of stochastic quantum quantization is a physical time over which quantum fields at all values of space and coordinate time fluctuate. The average over paths becomes a time average as opposed to an…
Hartle and Srednicki have suggested that standard quantum theory does not favor our typicality. Here an alternative version is proposed in which typicality is likely, Eventual Quantum Mechanics. This version allows one to calculate…
We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
Many writers have observed that default logics appear to contain the "lottery paradox" of probability theory. This arises when a default "proof by contradiction" lets us conclude that a typical X is not a Y where Y is an unusual subclass of…
We present a formal measure of argument strength, which combines the ideas that conclusions of strong arguments are (i) highly probable and (ii) their uncertainty is relatively precise. Likewise, arguments are weak when their conclusion…
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…
We consider a simple model of imprecise comparisons: there exists some $\delta>0$ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $\delta$, then the…
In frequently repeated matching scenarios, individuals may require diversification in their choices. Therefore, when faced with a set of potential outcomes, each individual may have an ideal lottery over outcomes that represents their…
Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
We study the discrete Bertrand pricing game with a non-increasing demand function. The game has $n \ge 2$ players who simultaneously choose prices from the set $\{1/k, 2/k, \ldots, 1\}$, where $k\in\mathbb{N}$. The player who sets the…