Frequency of paradox in a common n-winner voting scheme

This paper investigates the extent to which a commonly used electoral scheme — voting for n candidates when there are n vacancies to fill — is likely to lead, in practice, to paradoxical results. Two types of paradox are investigated. One occurs when an increase in the number of vacancies causes a candidate to drop from the list of winners. The second occurs when the Condorcet candidate fails to win. Using a Monte Carlo study, we show that the likelihood of paradox can be substantial and depends critically on the degree of homogeneity of voters' preferences and on the number of voters.