Related papers: Anna Karenina and The Two Envelopes Problem

As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing…

Happiness, in the U.S. Declaration of Independence, was understood quite differently from today's popular notions of personal pleasure. Happiness implies a flourishing life - one of virtue, purpose, and contribution to the common good. This…

The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave…

We consider a novel setting where a set of items are matched to the same set of agents repeatedly over multiple rounds. Each agent gets exactly one item per round, which brings interesting challenges to finding efficient and/or fair {\em…

The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of…

We count the number and patterns of pairs and tuples of independent events in a simple random experiment: first a fair coin is flipped and then a fair die is tossed. The first number, equal to 888,888, suggest that there are some open…

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…

In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…

In this paper, we consider the problem of making skeptical inferences for the multi-label ranking problem. We assume that our uncertainty is described by a convex set of probabilities (i.e. a credal set), defined over the set of labels.…

The intriguing and still open question concerning the composition law of $\kappa$-entropy $S_{\kappa}(f)=\frac{1}{2\kappa}\sum_i (f_i^{1-\kappa}-f_i^{1+\kappa})$ with $0<\kappa<1$ and $\sum_i f_i =1$ is here reconsidered and solved. It is…

A framework for asynchronous, signature free, fully local and probabilistically converging total order algorithms is developed, that may survive in high entropy, unstructured Peer-to-Peer networks with near optimal communication efficiency.…

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring…

The doctrinal paradox is analysed from a probabilistic point of view assuming a simple parametric model for the committee's behaviour. The well known issue-by-issue and case-by-case majority rules are compared in this model, by means of the…

The Frankl conjecture, also known as the union-closed sets conjecture, states that in any finite non-empty union-closed family, there exists an element in at least half of the sets. From an optimization point of view, one could instead…

To provide an explanation of the evolution of scientific knowledge, I start from the assumption that knowledge is based on concepts, and propose that each concept about reality is affected by vagueness. This entails a paradox, which I term…

Logics for reasoning about knowledge and actions have seen many applications in various domains of multi-agent systems, including epistemic planning. Change of knowledge based on observations about the surroundings forms a key aspect in…

In statistical thermodynamics the 2nd law is properly spelled out in terms of conditioned probabilities. As such it makes the statement, that `entropy increases with time' without preferring a time direction. In this paper I try to explain…

Two types of approximation to the paradoxical Russell Set are presented, one approximating it from below, one from above. It is shown that any lower approximation gives rise to a better approximation containing it, and that any upper…

I prove an envelope theorem with a converse: the envelope formula is equivalent to a first-order condition. Like Milgrom and Segal's (2002) envelope theorem, my result requires no structure on the choice set. I use the converse envelope…

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…