Improving Randomized Metric Distortion to 2.3282

The paper proves that there exists a randomized voting rule using only ordinal rankings with metric distortion at most $11641/5000=2.3282$. This improves the previous best upper bound of $2.5$ and closes about $44\%$ of the gap to the known asymptotic lower bound of approximately $2.1126$. It does not determine the optimal randomized metric distortion: for $m\ge4$, the exact optimum and its asymptotic limit remain open.

The paper proves that there exists a randomized voting rule using only ordinal rankings with metric distortion at most $11641/5000=2.3282$. This improves the previous best upper bound of $2.5$ and closes about $44\%$ of the gap to the known asymptotic lower bound of approximately $2.1126$. It does not determine the optimal randomized metric distortion: for $m\ge4$, the exact optimum and its asymptotic limit remain open.