Geometric Comparisons of Electoral Rules Under Feedback

Researcher Sumit Mukherjee has published a novel computational study titled 'Geometric Comparisons of Electoral Rules Under Feedback' that applies geometric AI modeling to political science. The paper introduces two key metrics for analyzing voting systems under dynamic conditions: the 'winner radius' (R_t), which measures the distance from an election winner to the farthest voter, and the 'supporter centroid radius' (S_t), which measures the gap between candidates and their core supporters. The core theoretical finding is that these two objectives are in direct tension; optimizing for one worsens the other.

The research involved an extensive simulation of over 1,000 election runs across seven standard electoral rules and one convex-combination benchmark. The empirical results confirm the tradeoff: winner-take-all rules (like plurality) achieve a small S_t, keeping candidates close to their bases, but at the cost of a large R_t and weaker voter depolarization. Conversely, proportional or convex-combination rules reduce voter disagreement (smaller R_t) but lead to greater candidate dispersion (larger S_t). The study further demonstrates that even positioning a winner near the voter median does not resolve this inherent conflict, as different geometric centers represent competing objectives.