We study random choice rules to capture violations of the weak axiom of revealed preference. We show that the Luce rule is the unique random choice rule that admits a well-defined ranking of option sets. We consider two extensions of the Luce rule. The first, addresses the duplicates problem

I characterize mean (or market) demands derived from a general random choice model that does not require the use of preferences or maximizing behavior. I show that mean demands satisfy the compensated Law of Demand and all the properties of standard demand theory including symmetry and negative

, or the simplest, or both. A randomized algorithm is an algorithm that uses random numbers to influence the choices it makes in the course of its computation. Thus its behavior (typically quantified as running time or quality of output) varies from

We consider an agent who chooses from a set of options after receiving some private information. This information however is unobserved by an analyst, so from the latter’s perspective, choice is probabilistic or random. We provide a theory in which information can be fully identified from random

This paper uses a unique data set to measure peer effects among college roommates. Freshman year roommates and dormmates are randomly assigned at Dartmouth College. I find that peers have an impact on grade point average and on decisions to join social groups such as fraternities. Residential peer

We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique has had several striking applications to Extremal Graph Theory, Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this survey we discuss some of them.

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diffusion process, but leakage and mutual inhibition work together to address several challenges to existing diffusion, random-walk, and accumulator models. The model provides a good account of data from choice tasks using both time-controlled (e.g., deadline or response signal) and standard reaction time

A random choice method for solving nonlinear hyperbolic systems of conservation laws is presented. The method is rooted in Glirnm’s constructive proof that such systems have solutions. The solution is advanced in time by a sequence of operations which includes the solution of Riemann problems and a

needs to be restricted so not to reveal the outcome of the protocol’s random choices, or otherwise the model of adversary would be too strong even for “obviously correct ” protocols. We propose a process-algebraic framework in which the control on the scheduler can be specified in syntactic terms