Aggregation of ranked votes considering different relative gaps between rank positions

Abstract

This paper considers ranked voting systems to determine the rank order of candidates who compete for a limited number of positions. We show that the preferential voting problems based on the data envelopment analysis (DEA) (Wang et al, 2007) can be solved using the extreme points of constraints on rank position importance incorporated in the formulation. This is basically due to the fact that the so-called inverse positive property of the constraints makes it possible to easily find their extreme points. Further, we emphasize that this finding is not restricted to Wang et al’s two linear models, but is also applicable to other DEA-based preferential voting problems, which include the constraints accounting for different relative gaps between rank positions.

Keywords:

• preference vote
• data envelopment analysis (DEA)
• rank position
• extreme points

Acknowledgments

The author would like to thank Eun Young Kim and Eugene Ahn for their assistance.

Notes

1 Even though was not designated in the original LP-2 model, it is legitimate to consider it such a way because of .