Flexible Level-1 Consensus Ensuring Stable Social Choice: Analysis and Algorithms

Level-1 Consensus is a property of a preference-profile. Intuitively, it means that there exists a preference relation which induces an ordering of all other preferences such that frequent preferences are those that are more similar to it. This is a desirable property, since it enhances the stability of social choice by guaranteeing that there exists a Condorcet winner and it is elected by all scoring rules. In this paper, we present an algorithm for checking whether a given preference profile exhibits level-1 consensus. We apply this algorithm to a large number of preference profiles, both real and randomly-generated, and find that level-1 consensus is very improbable. We support these empirical findings theoretically, by showing that, under the impartial culture assumption, the probability of level-1 consensus approaches zero when the number of individuals approaches infinity. Motivated by these observations, we show that the level-1 consensus property can be weakened while retaining its stability implications. We call this weaker property Flexible Consensus. We show, both empirically and theoretically, that it is considerably more probable than the original level-1 consensus. In particular, under the impartial culture assumption, the probability for Flexible Consensus converges to a positive number when the number of individuals approaches infinity

Numerical studies of the interaction of an atomic sample with the electromagnetic field in two dimensions

We consider the interaction of electromagnetic radiation of arbitrary polarization with multi-level atoms in a self-consistent manner, taking into account both spatial and temporal dependencies of local fields. This is done by numerically solving the corresponding system of coupled Maxwell-Liouville equations for various geometries. In particular, we scrutinize linear optical properties of nanoscale atomic clusters, demonstrating the significant role played by collective effects and dephasing. It is shown that subwavelength atomic clusters exhibit two resonant modes, one of which is localized slightly below the atomic transition frequency of an individual atom, while the other is positioned considerably above it. As an initial exploration of future applications of this approach, the optical response of core-shell nanostructures, with a core consisting of silver and shell composed of resonant atoms, is examined.Comment: re-submitted to PR

Revenue Loss in Shrinking Markets

We analyze the revenue loss due to market shrinkage. Specifically, consider a simple market with one item for sale and $n$ bidders whose values are drawn from some joint distribution. Suppose that the market shrinks as a single bidder retires from the market. Suppose furthermore that the value of this retiring bidder is fixed and always strictly smaller than the values of the other players. We show that even this slight decrease in competition might cause a significant fall of a multiplicative factor of $\frac{1}{e+1}\approx0.268$ in the revenue that can be obtained by a dominant strategy ex-post individually rational mechanism. In particular, our results imply a solution to an open question that was posed by Dobzinski, Fu, and Kleinberg [STOC'11]

Kinetic Schemes in Open Interacting Systems

We discuss utilization of kinetic schemes for description of open interacting systems, focusing on vibrational energy relaxation for an oscillator coupled to a nonequilibirum electronic bath. Standard kinetic equations with constant rate coefficients are obtained under the assumption of timescale separation between system and bath, with the bath dynamics much faster than that of the system of interest. This assumption may break down in certain limits and we show that ignoring this may lead to qualitatively wrong predictions. Connection with more general, nonequilibrium Green's function (NEGF) analysis, is demonstrated. Our considerations are illustrated within generic molecular junction models with electron-vibration coupling.Comment: 22 pages, 4 figure