The likelihood of choosing the Borda-winner with partial preference rankings of the electorate

Abstract

Given that n voters report only the first r (1 ? r < m) ranks of their linear preference rankings over m alternatives, the likelihood of implementing Borda outcome is investigated. The information contained in the first r ranks is aggregated through a Borda-like method, namely the r-Borda rule. Monte-Carlo simulations are run to detect changes in the likelihood of r-Borda winner(s) to coincide with the original Borda winner(s) as a function of m, n and r. The voters' preferences are generated through the Impartial Anonymous and Neutral Culture Model, where both the names of the alternatives and voters are immaterial. It is observed that, for a given r, the likelihood of choosing the Borda winner decreases down to zero independent of n as m increases within the computed range of parameter values, 1 ? m, n ? 30. For n = 30, this likelihood is given as an approximating function of r and m through least square fit method. © 2011 JMASM, Inc.