Minimax is the best electoral system after all

TL;DR

This paper demonstrates that the minimax electoral system is highly effective, surpassing most other systems in selecting the best candidate, and introduces an improved version called minimax-T with enhanced features.

Contribution

The paper provides a comprehensive analysis of electoral systems, validating minimax's robustness and proposing minimax-T with improved transparency, privacy, and resistance to strategic voting.

Findings

Minimax system consistently outperforms 18 other electoral systems in simulations.

Minimax-T improves on minimax with a new tie-breaker, enhancing fairness and simplicity.

Simulations show minimax and minimax-T closely match the optimal CMO system in candidate selection.

Abstract

When each voter rates or ranks several candidates for a single office, a strong Condorcet winner (SCW) is one who beats all others in two-way races. Among 21 electoral systems examined, 18 will sometimes make candidate X the winner even if thousands of voters would need to change their votes to make X a SCW while another candidate Y could become a SCW with only one such change. Analysis supports the intuitive conclusion that these 18 systems are unacceptable. The well-known minimax system survives this test. It fails 10 others, but there are good reasons to ignore all 10. Minimax-T adds a new tie-breaker. It surpasses competing systems on a combination of simplicity, transparency, voter privacy, input flexibility, resistance to strategic voting, and rarity of ties. It allows write-ins, machine counting except for write-ins, voters who don't rate or rank every candidate, and tied ratings or ranks. Eleven computer simulation studies used 6 different definitions (one at a time) of the best candidate, and found that minimax-T always soundly beat all other tested systems at picking that candidate. A new maximum-likelihood electoral system named CMO is the theoretically optimum system under reasonable conditions, but is too complex for use in real-world elections. In computer simulations, minimax and minimax-T nearly always pick the same winners as CMO.