Related papers: SOS for bounded rationality
What would you do if you were invited to play a game where you were given \$25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61…
The results in this paper add useful tools to the theory of sets of desirable gambles, a growing toolbox for reasoning with partial probability assessments. We investigate how to combine a number of marginal coherent sets of desirable…
The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
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…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
In a casino where arbitrarily small bets are admissible, any betting strategy M can be modified into a savings strategy that, not only is successful on each casino sequence where M is (thus accumulating unbounded wealth inside the casino)…
In this expository note, we give a simple proof that a gambler repeating a game with positive expected value never goes broke with a positive probability. This does not immediately follow from the strong law of large numbers or other basic…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
This paper considers the problem of learning safe policies in the context of reinforcement learning (RL). In particular, we consider the notion of probabilistic safety. This is, we aim to design policies that maintain the state of the…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…
We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a…
We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
Rationality is often related to optimal decision making. Humans are known to be bounded rational agents. However, recent advances in computing, and other scientific and technical fields along with large amount of data have led to a feeling…
In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles…