The case for minimax-TD

Abstract

In spatial-model computer simulations with artificial voters and candidates, the well-known minimax single-winner voting system far outperformed 10 other systems at picking the best winners. It essentially tied with two others (Schulze and ranked pairs), both of which are far more complex than minimax. Minimax’s other advantages include Condorcet consistency, simplicity, monotonicity, and ease of voting because it allows tied and missing ranks. It also makes insincere strategic voting schemes difficult and dangerous for the schemers. The new minimax-TD system modifies minimax in three ways, all of which make it pick better winners, according to simulation studies: (a) TD includes Smith/minimax, (b) TD uses one particular definition of a candidate’s “largest loss” in two-way elections, and (c) TD includes a multi-stage tie-breaker which breaks nearly all ties. TD avoids four of the worst anomalies afflicting classic minimax. Four other minimax anomalies can be ignored, leaving TD arguably free of anomalies.