Abstract
We study the degree of individual and coalitional manipulability of q-Paretian social choice rules under Impartial Culture. Manipulability is defined as a situation, when an agent or a coalition, which consists of some agents, misrepresents her/their preferences to obtain a better outcome of the social choice rule. We study a class of q-Paretian social choice rules, which consists of four rules: Strong q-Paretian simple majority rule, Strong q-Paretian plurality rule, Strongest q-Paretian simple majority rule, and Condorcet practical rule. For the cases of 3, 4, and 5 alternatives and for the cases from 3 to 100 agents, we use computer modelling to calculate a number of manipulability indices. We provide the analysis of the results for different cases.
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References
Aleskerov, F. (1985). Procedures of multicriterial choice. In Preprints of the IFAC/IFORS Conference on Control Science and Technology for Development (pp. 858–869).
Aleskerov, F. (1992). Relational-functional voting operators. California Institute of Technology, Social Science Working Paper 818.
Aleskerov, F. (1999). Arrovian aggregation models. Kluwer Academic Publishers.
Aleskerov, F., Karabekyan, D., Ivanov, A., & Yakuba, V. (2021). Further results on the manipulability of social choice rules—A comparison of standard and Favardin–Lepelley types of individual manipulation. In M. Diss & V. R. Merlin (Eds.), Evaluating voting systems with probability models, essays by and in Honor of William V. Gehrlein and Dominique Lepelley, Studies in Choice and Welfare (pp. 231–249). Springer.
Aleskerov, F., Karabekyan, D., Sanver, R., & Yakuba, V. (2009). Evaluating the degree of manipulability of certain aggregation procedures under multiple choices. Journal of the New Economic Association, 1, 37–61.
Aleskerov, F., & Kurbanov, E. (1999). Degree of manipulability of social choice procedures. In A. Alkan, C. D. Aliprantis, & N. C. annelis (Eds.), Current trends in economics, Studies in Economic Theory (Vol. 8, pp. 13–27). Springer, Berlin
Barberà, S., Bossert, W., & Pattanaik, P. K. (2004). Ranking sets of objects. In S. Barberà, P. J. Hammond, & C. Seidl (Eds.), Handbook of utility theory (pp. 893–977). Springer.
Chamberlin, J. R. (1985). An investigation into the relative manipulability of four voting systems. Behavioral Science, 30, 195–203.
de Condorcet, M. (1785). Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. Imprimerie Royale.
Duggan, J., & Schwartz, T. (2000). Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized. Social Choice and Welfare, 17, 85–93.
Gibbard, A. (1973). Manipulation of voting schemes: A general result. Econometrica, 41, 587–601.
Karabekyan, D. (2011). On the manipulability of \(q\)-Paretian social choice rules. In Proceeding of the Seminar “Mathematical Modeling of Political Systems and Processes” (pp. 142–156) (in Russian).
Karabekyan, D. (2012). The problem of manipulability in the social choice theory. Ph.D. thesis, HSE University (in Russian).
Kelly, J. S. (1993). Almost all social choice rules are highly manipulable, but a few aren’t. Social Choice and Welfare, 10, 161–175.
Kurz, S., Mayer, A., & Napel, S. (2020). Weighted committee games. European Journal of Operational Research, 282, 972–979.
Kurz, S., Mayer, A., & Napel, S. (2021). Influence in weighted committees. European Economic Review, 132, 103634.
Levati, M. V., Napel, S., & Soraperra, I. (2017). Collective choices under ambiguity. Group Decision and Negotiation, 26, 133–149.
Maskin, E. (1979). Implementation and strong Nash equilibrium. In J.-J. Laffont (Ed.), Aggregation and revelation of preferences (pp. 433–440). North-Holland.
Nitzan, S. (1985). The vulnerability of point-voting schemes to preference variation and strategic manipulation. Public Choice, 47, 349–370.
Satterthwaite, M. A. (1975). Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10, 187–217.
Veselova, Y. A. (2020). Does incomplete information reduce manipulability? Group Decision and Negotiation, 29, 523–548.
Xia, L., Conitzer, V., & Procaccia, A. D. (2010). A scheduling approach to coalitional manipulation. In Proceedings of the 11th ACM Conference on Electronic Commerce (pp. 275–284).
Young, H. P. (1988). Condorcet’s theory of voting. American Political Science Review, 82, 1231–1244.
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This work is an output of a research project implemented as part of the Basic Research Program at the HSE University.
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Aleskerov, F., Ivanov, A., Karabekyan, D., Yakuba, V. (2023). On the Individual and Coalitional Manipulability of q-Paretian Social Choice Rules. In: Kurz, S., Maaser, N., Mayer, A. (eds) Advances in Collective Decision Making. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-031-21696-1_7
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