Quality & Quantity

, Volume 50, Issue 3, pp 1185–1200 | Cite as

Egalitarianism in the rank aggregation problem: a new dimension for democracy

  • Pierluigi Contucci
  • Emanuele Panizzi
  • Federico Ricci-Tersenghi
  • Alina SîrbuEmail author


Winner selection by majority, in elections between two candidates, is the only rule compatible with democratic principles. Instead, when candidates are three or more and voters rank candidates in order of preference, there are no univocal criteria for the selection of the winning (consensus) ranking and the outcome is known to depend sensibly on the adopted rule. Building upon eighteenth century Condorcet theory, whose idea was maximising total voter satisfaction, we propose here a new basic principle (dimension) to guide the selection: satisfaction should be distributed among voters as equally as possible. With this new criterion we identify an optimal set of rankings, ranging from the Condorcet solution to the the most egalitarian one with respect to the voters. Most importantly, we show that highly egalitarian rankings are much more robust, with respect to random fluctuations in the votes, than consensus rankings returned by classical voting rules (Copeland, Tideman, Schulze). The newly introduced dimension provides, when used together with that of Condorcet, a more informative classification of all the possible rankings. By increasing awareness in selecting a consensus ranking our method may lead to social choices which are more egalitarian compared to those achieved by presently available voting systems.


Preferential voting Rank aggregation Pareto frontier Variance minimization 



We thank Flavio Chierichetti for drawing our attention to the rank aggregation problem. We thank the Airesis platform for providing access to their data. This work has received financial support from the Italian Research Ministry through the FIRB projects No. RBFR086NN1 and RBFR10N90W and PRIN project No. 2010HXAW77.

Supplementary material

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Pierluigi Contucci
    • 1
  • Emanuele Panizzi
    • 2
  • Federico Ricci-Tersenghi
    • 3
  • Alina Sîrbu
    • 4
    Email author
  1. 1.Department of MathematicsAlma Mater Studiorum - University of BolognaBolognaItaly
  2. 2.Dipartimento di InformaticaSapienza Università di RomaRomaItaly
  3. 3.Dipartimento di FisicaINFN – Sezione di Roma 1 and CNR – IPCF, UOS di Roma, Sapienza Università di RomaRomaItaly
  4. 4.Department of Computer Science and EngineeringAlma Mater Studiorum - University of BolognaBolognaItaly

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