Related papers: Solving the Hard Problem of Bertrand's Paradox

In a context where a decision has to be taken collectively by several agents, the social choice problem consists in deciding whether there exists a socially acceptable rule that aggregates the individual preferences of the agents into a…

The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…

The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…

The Fermi Paradox is the apparent contradiction between the high probability extraterrestrial civilizations' existence and the lack of contact with such civilizations. In general, solutions to Fermi's paradox come down to either estimation…

This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…

According to Aumann's celebrated theorem, rational agents cannot agree to disagree. In other words, agents who once shared a common prior probability distribution and who have common knowledge about their posteriors cannot assign different…

This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take…

The friendship paradox -- the observation that, on average, one's friends have more friends than oneself -- admits two common formulations depending on whether averaging is performed over edges or over nodes. These two definitions, the…

Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast…

The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…

Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov-Bergmann-Lebowitz rule. In this short note we present a seemingly disturbing paradox that appears…

In research policy, effective measures that lead to improvements in the generation of knowledge must be based on reliable methods of research assessment, but for many countries and institutions this is not the case. Publication and citation…

The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…

The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…

The definition of probabilities in eternally inflating universes requires a measure to regulate the infinite spacetime volume, and much of the current literature uses a global time cutoff for this purpose. Such measures have been found to…

The EPR paradox is known as an interpretive problem, as well as a technical discovery in quantum mechanics. It defined the basic features of two-quantum entanglement, as needed to study the relationships between two non-commuting variables.…

One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…

This article solves the Hume's problem of induction using a probabilistic approach. From the probabilistic perspective, the core task of induction is to estimate the probability of an event and judge the accuracy of the estimation.…

We prove the expected disturbance caused to a quantum system by a sequence of randomly ordered two-outcome projective measurements is upper bounded by the square root of the probability that at least one measurement in the sequence accepts.…

We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…