Impartial selection, additive guarantees, and prior information
We study the problem of impartial selection, a topic that lies in the intersection of computational social choice and mechanism design. The goal is to select the most popular individual among a set of community members. The input can be modelled as a directed graph, where each node represents an individual, and a directed edge indicates nomination or approval of a community member to another. An impartial mechanism is robust to potential selfish behaviour of the individuals and provides appropriate incentives to voters to report their true preferences by ensuring that the chance of a node to become a winner does not depend on its outgoing edges. Our goal is to design impartial mechanisms that select a node with an in-degree that is as close as possible to the highest in-degree. Recent progress has identified impartial selection rules with optimal approximation ratios. It was noted though that worst-case instances are graphs with few vertices. Motivated by this fact, we propose the study of additive approximation, the difference between the highest number of nominations and the number of nominations of the selected member, as an alternative measure of quality. We present randomized impartial selection mechanisms with additive approximation guarantees of , where is the number of nodes in the input graph. We furthermore demonstrate that prior information on voters’ preferences can be useful in the design of simple (deterministic) impartial selection mechanisms with good additive approximation guarantees. In this direction, we consider different models of prior information and analyze the performance of a natural selection mechanism that we call approval voting with default (AVD).