Kybernetika 48 no. 3, 536-549, 2012

Different approaches to weighted voting systems based on preferential positions

Robert Bystrický


Voting systems produce an aggregated result of the individual preferences of the voters. In many cases the aggregated collective preference - the result of the voting procedure - mirrors much more than anything else the characteristics of the voting systems. Preferential voting systems work most of the time with equidistant differences between the adjacent preferences of an individual voter. They produce, as voting systems usually do, some paradoxical results under special circumstances. However, the distances between the preferences can be understood as the function of the position in the sequence of preferences and can be aggregated in different ways fulfilling the basic attributes of the voting system. This approach at least allows us to avoid the worst paradoxical situations or to design a voting system containing some special needs.


voting system, preference, position


90A28, 90A05, 90A08, 62F07


  1. J. C. Borda: Memoire sur les elections au scrutin. Histoire de l'Academie Royale des Sciences 1784.   CrossRef
  2. S. J. Brams: Mathematics and Democracy: Designing Better Voting and Fair- Division Procedures. Princeton University Press 2008.   CrossRef
  3. R. Bystrický: Voting system with various distances between preferences. In: Proc. AGOP 2011, Benevento 2011.   CrossRef
  4. I. Contreras: A distance-based consensus model with flexible choice of rank-position weights. Group Decision and Negotiation 19, (2010), 441-456.   CrossRef
  5. W. D. Cook and L. M. Seiford: Priority ranking and consensus formation. Management Sci. 24, (1978), 16, 1721-1732.   CrossRef
  6. W. D. Cook and L. M. Seiford: On the Borda-Kendall consensus method for priority ranking problems. Management Sci. 28, (1982), 6, 621-637.   CrossRef
  7. D. Eckert, C. Klamler, J. Mitlöhner and C. Schlötterer: A distance-based comparison of basic voting rules. Central Europ. J. Oper. Res. 14, (2006), 377-386.   CrossRef
  8. P. C. Fishburn: Condorcet social choice functions. SIAM J. Appl. Math. 33, (1977), 3, 469-489.   CrossRef
  9. J. Kemeny: Mathematics without numbers. Daedalus 88, (1959), 571-591.   CrossRef
  10. M. Kendall: Rank Correlation Methods. Hafner, New York 1962.   CrossRef
  11. H. Nurmi: Voting Paradoxes and How to Deal With Them. Springer 1999.   CrossRef
  12. D. Saari: Basic Geometry of Voting. Springer 1995.   CrossRef
  13. D. Saari and V. Merlin: A geometric examination of Kemeny's rule. Soc. Choice Welfare 17 (2000), 403-438.   CrossRef
  14. L. Vavríková: Transitive Preference Structures and Multicriteria Decision Making. Ph.D. Thesis. STU Bratislava 2011.   CrossRef
  15. H. P. Young: Social choice scoring functions. SIAM J. Appl. Math. 28 (1975), 824-838.   CrossRef