Core Concepts
Metric distortion of C1ML rules is 4, optimal within majoritarian RSCFs.
Abstract
The content discusses the metric distortion of randomized social choice functions (RSCFs) in the context of minimizing social cost approximations. It explores the metric distortion of well-established RSCFs, focusing on C1 maximal lottery rules. The study includes computer experiments to analyze the average-case performance of various RSCFs under different preference distributions. Key insights include the impact of the number of voters and alternatives on the metric distortion of RSCFs.
Directory:
Introduction
Multi-agent systems face challenges in collective decision-making.
Social choice theory focuses on SCFs and RSCFs.
Metric Distortion
Metrics quantify the worst-case ratio of social cost approximations.
RSCFs aim to minimize metric distortion.
Analysis of C1 Maximal Lottery Rules
C1ML rules have a metric distortion of 4, optimal within majoritarian RSCFs.
Simulations
Computer experiments reveal insights into the average-case metric distortion of RSCFs.
Results show the impact of preference distributions and the number of voters and alternatives on metric distortion.
Stats
C1ML rules have a metric distortion of 4.
The uniform random dictatorship has a metric distortion close to 2 in the IC model.
Quotes
"No SCF has a metric distortion of less than 3." - Anshelevich et al.