The mathematical theory of ranked-choice voting is reviewed, with particular focus on Condorcet, Plurality, and Borda Count methods. Maximizing the Borda Count score is shown to be equivalent to minimizing the weighted arithmetic mean across ranks. This leads to alternate Borda methods associated with different weighted means: geometric; harmonic; and root-mean-square. The notion of an ergodic voter population is introduced, together with a statistical confidence interval approach to estimating requisite population size, which is essential to avoid small-population noise. Population size and voting method consistency are further examined via simulation where it is shown that principal voting methods, other than Plurality, converge for a sufficiently large, ergodic voter population. This again highlights pitfalls associated with small voter populations, in terms of both voting method consistency and elicitation of overall voter/social preference.
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