0.1. Preface. In 1963 Ya. G. Sinai [Sin(1963)] formulated a modern version of Boltzmann’s ergodic hypothesis, what we now call the “Boltzmann-Sinai Ergodic Hypothesis”: The billiard system of N (N ≥ 2) hard balls of unit mass moving on the flat torus T = R/Z (ν ≥ 2) is ergodic after we make the standard reductions by fixing the values of trivial invariant quantities. It took fifty years and the...

Many institutional investors periodically adopt an asset allocation policy that specifies target percentages of value for each of several asset classes. Typically a policy is set by a fund’s board after evaluating the implications of a set of alternative policies. The staff is then instructed to implement the policy, usually by maintaining the actual allocation to each asset class within a spec...

A voting protocol is said to be strongly participatory if for any player i and any strategy profile either the outcome is i‘s preferred one or i has a strategy which would ensure her a better outcome, and VNMstrategy proof if at any preference profile the set of sincere strategies of each player is a VNM-stable set. It is shown that the proportional lottery (PL) modular voting protocol is both ...