Related papers: Coherence of countably many bets
New cases of the multiplicity conjecture are considered.
The topic of this paper is the subtle interplay between countability and representations. In particular, we establish that the definition of countability of a certain set $X$ crucially hinges on the associated equivalence relation $=_{X}$.…
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The…
De Finetti theorems show how sufficiently exchangeable states are well-approximated by convex combinations of i.i.d. states. Recently, it was shown that in many quantum information applications a more relaxed de Finetti reduction (i.e. only…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
We give simple necessary and sufficient conditions for the inclusion-exclusion identity to hold for an infinite countable number of sets. In terms of a random variable, whose range are nonnegative integers, this condition is equivalent to…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
We generalize Ebert's Hat Problem for three persons and three colors. All players guess simultaneously the color of their own hat observing only the hat colors of the other players. It is also allowed for each player to pass: no color is…
We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins to study…
Multicriteria decision analysis aims at supporting a person facing a decision problem involving conflicting criteria. We consider an additive utility model which provides robust conclusions based on preferences elicited from the decision…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finetti's theorem characterizes all $\{0,1\}$-valued exchangeable sequences as a "mixture" of…
This paper reports on empirical work aimed at comparing evidential reasoning techniques. While there is prima facie evidence for some conclusions, this i6 work in progress; the present focus is methodology, with the goal that subsequent…
The benefits of portfolio diversification is a central tenet implicit to modern financial theory and practice. Linked to diversification is the notion of breadth. Breadth is correctly thought of as the number of in- dependent bets available…
The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic…
We give a simple proof of the exponential de Finetti theorem due to Renner. Like Renner's proof, ours combines the post-selection de Finetti theorem, the Gentle Measurement lemma, and the Chernoff bound, but avoids virtually all…
We propose a new determinacy hypothesis for transfinite games, use the hypothesis to extend the perfect set theorem, prove relationships between various determinacy hypotheses, expose inconsistent versions of determinacy, and provide a…