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

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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.

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  • Airesis platform: (2013). Accessed 15 Nov 2014

  • Arrow, K.J.: A difficulty in the concept of social welfare. J. Polit. Econ. 58, 328–346 (1950). doi:10.1086/25696

    Article  Google Scholar 

  • Betzler, N., Fellows, M.R., Guo, J., Niedermeier, R., Rosamond, F.A.: Fixed-parameter algorithms for kemeny rankings. Theor Comput Sci 410(45), 4554–4570 (2009). doi:10.1016/j.tcs.2009.08.033

    Article  Google Scholar 

  • Borgers, C.: Mathematics of Social Choice: Voting, Compensation, and Division. SIAM, Philadelphia (2010)

    Book  Google Scholar 

  • Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81(2), 591 (2009)

    Article  Google Scholar 

  • Contucci, P., Panizzi, E., Ricci-Tersenghi, F., Sîrbu, A.: Rateit web tool. (2014). Accessed 15 Nov 2014

  • Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning about a Highly Connected World. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  • Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: Proceedings of the 10th international conference on World Wide Web, pp. 613–622. ACM (2001). doi:10.1145/371920.372165

  • Fagin, R., Kumar, R., Mahdian, M., Sivakumar, D., Vee, E.: Comparing and aggregating rankings with ties. In: Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, pp. 47–58. ACM (2004). doi: 10.1145/1055558.1055568

  • Feldman, A.M., Serrano, R.: Welfare Economics and Social Choice Theory. Springer, Berlin (2006)

    Google Scholar 

  • Godfrey, P., Shipley, R., Gryz, J.: Algorithms and analyses for maximal vector computation. VLDB J. 16(1), 5–28 (2007)

    Article  Google Scholar 

  • Goldberg, K., Roeder, T., Gupta, D., Perkins, C.: Eigentaste: A constant time collaborative filtering algorithm. Inf. Retr. 4(2), 133–151. (2001). Accessed 7 April 2015

  • GroupLens Research: Movielens dataset. (2014). Accessed 15 Nov 2014

  • Heiser, W.J., D’Ambrosio, A.: Clustering and prediction of rankings within a kemeny distance framework. In: Lausen, B., Van den Poel, D., Ultsch, A. (eds.) Algorithms from and for Nature and Life, pp. 19–31. Springer, Berlin (2013)

    Chapter  Google Scholar 

  • Kemeny, J.G.: Mathematics without numbers. Daedalus 88(4), 577–591 (1959)

    Google Scholar 

  • Kemeny, J.G., Snell, J.L.: Mathematical Models in the Social Sciences, vol. 9. Blaisdell, New York (1962)

    Google Scholar 

  • Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet: Essai sur l’application de l’analyse à la probabilité des décisions rendus à la pluralité des voix. L’Imprimerie Royale, Paris (1785)

  • Markowitz, H.: Portfolio selection*. J. Financ. 7(1), 77–91 (1952)

    Google Scholar 

  • Monjardet, B.: “mathématique sociale” and mathematics. a case study: Condorcet’s effect and medians. Electron. J. Hist. Probab. Stat 4(1), 1–26 (2008)

    Google Scholar 

  • Moore, M., Katzgraber, H.G.: Dealing with correlated choices: How a spin-glass model can help political parties select their policies. Phys. Rev. E 90, 042117 (2014)

    Article  Google Scholar 

  • OEIS foundation: The on-line encyclopedia of integer sequences. (2014). Accessed 15 Nov 2014

  • Raffaelli, G., Marsili, M.: Statistical mechanics model for the emergence of consensus. Phys. Rev. E 72(1), 016114 (2005)

    Article  Google Scholar 

  • Renda, M.E., Straccia, U.: Web metasearch: rank vs. score based rank aggregation methods. In: Proceedings of the 2003 ACM symposium on Applied computing, pp. 841–846. ACM (2003). doi: 10.1145/952532.952698

  • Saari, D.G., Merlin, V.R.: A geometric examination of Kemeny’s rule. Soc. Choice Welf. 17(3), 403–438 (2000)

    Article  Google Scholar 

  • Truchon, M.: Aggregation of rankings: a brief review of distance-based rules and loss functions for the expected loss approach. Cahier de recherche/Working Paper 5, 34 (2005). doi: 10.2139/ssrn.984305

  • Young, H.P.: Condorcet’s theory of voting. Am. Polit. Sci. Rev. 82(04), 1231–1244 (1988)

    Article  Google Scholar 

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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.

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Correspondence to Alina Sîrbu.

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Contucci, P., Panizzi, E., Ricci-Tersenghi, F. et al. Egalitarianism in the rank aggregation problem: a new dimension for democracy. Qual Quant 50, 1185–1200 (2016).

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