TITLE: The 3-candidate left-middle-right scenario AUTHOR: Warren D. Smith DATE: July 2006 ABSTRACT: The most common nontrivial scenario in single-winner political races is the 1-dimensional political scenario consisting of a ``left,'' ``middle'' and ``right'' candidate in a 3-way contest. We attempt an exhaustive computer-aided analysis of how well commonly proposed voting systems handle this scenario. The clear conclusion is that (within this model) \emph{range voting} is the best voting system among all common proposals. KEYWORDS: Democracy, single winner voting systems, Bayesian regret, computer simulation.