Murdoch University - Departments of Mathematics & Statistics
Some non-parametric statistical methods based on ranks, such as the Friedman statistic, are closely related to methods of election that are known to have severe defects in some situations. This relationship is explored and the resulting defects of the statistical methods illustrated. The Condorcet criterion states that if a candidate is preferred to all of her opponents by a majority of voters, then she should be elected. This is an appealing criterion for a method of election to possess. A statistical method to analyze rank data that adheres to the Condorcet criterion is explored as an alternative. We show how the new method can have higher power and lead to less misleading conclusions than an analysis based on the Friedman statistic. A test statistic to indicate when an analysis based on the Friedman statistic may be misleading is also provided.