Probability Neglect: Emotions, Worst Cases, and Law

Worst-case Optimal Probability Updating

This paper discusses an alternative to conditioning that may be used when the prob-ability distribution is not fully specified. It does not require any assumptions (suchas CAR: coarsening at random) on the unknown distribution. The well-known MontyHall problem is the simplest scenario where neither naive conditioning nor the CARassumption suffice to determine an updated probabil...

Worst Cases and Lattice Reduction

We propose a new algorithm to find worst cases for correct rounding of an analytic function. We first reduce this problem to the real small value problem — i.e. for polynomials with real coefficients. Then we show that this second problem can be solved efficiently, by extending Coppersmith’s work on the integer small value problem — for polynomials with integer coefficients — using lattice redu...

The Roles of Emotions in the Law

Probability, fuzziness and borderline cases

An integrated approach to truth-gaps and epistemic uncertainty is described, based on probability distributions defined over a set of three-valued truth models. This combines the explicit representation of borderline cases with both semantic and stochastic uncertainty, in order to define measures of subjective belief in vague propositions. Within this framework we investigate bridges between pr...

Zipf's law and L. Levin's probability distributions

Zipf’s law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing and satisfactory mathematical explanation. In this paper I suggest that at least in certain situations, Zipf’s law can be explained as a special case of the a priori distribution introduced and studied...