Full Rank Voting: The Closest to Voting with Intensity of Preferences

Abstract

Voting is a fundamental aspect of democracy, but traditional voting schemes often fail to capture the intensity of preferences individuals possess. This loss of intensity can lead to an oversimplification of complex issues and a lack of accurate representation of diverse opinions. To address this limitation, we propose a voting method called “Full Rank Voting” that incorporates the intensity of preferences into the voting process. By using pairwise comparisons and Saaty’s fundamental scale, we transform individual preferences into numerical values and construct a matrix that represents the intensity of preferences for different candidates or options. In the case of two candidates, each voter expresses their preference intensity by assigning a numerical value from the fundamental scale. These values are then used to calculate the priorities or percentages of votes for each candidate. By incorporating intensity of preferences, the voting process becomes more nuanced, and ordinal preferences become a specific case of cardinal preferences. When multiple candidates are involved, we encounter the challenge of combining intensity of preferences with rank voting. We conduct simulation experiments to demonstrate that rank voting and voting with intensity of preferences yield similar results, even for relatively small sample sizes. Overall, Full Rank Voting offers a solution for capturing the intensity of preferences in voting, leading to a more accurate representation of individual choices, increased democratic legitimacy, and the ability to identify common ground and prioritize preferences based on their strength.