A proposed voting scheme to reduce the sensitivity of the Markov method

Abstract

The Markov method is one of many successful ranking methods that uses Markov chains to obtain its ratings and rankings of alternatives. It has been shown, however, that the method is sensitive to upsets, particularly in the tail of its ranking. The method also exhibits faulty behaviour when it has a periodic Markov chain. This study proposes a modification to the voting scheme of the Markov method that will alleviate the sensitivity to upsets and remove the issue of periodicity in the Markov chain. To examine the sensitivity, we first provide an example and see how both voting schemes react to an upset. Next, we generalise both voting schemes and examine a ratio of rating increments to understand why the tailing effect occurs, and how we can subside its effect.