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Manipulability of Aggregation Procedures for the Case of Large Numbers of Voters
P. 157–168.
Manipulation is a situation when an agent misrepresents his/her preferences to obtain a better result of an aggregation procedure. It was proven in literature, that there is no non-dictatorial aggregation procedure which is non-manipulable. A number of papers studying the degree of manipulability of aggregation procedures have been published since then. Such papers either look for theoretical formulae for particular cases or use computer modelling for empirical estimations. In case of computer modelling, only small numbers of voters are considered in the literature, usually up to 10, 30 or 100 agents. We use computer modelling to obtain the values of manipulability indices for the case of large numbers of voters, for example, for the cases of 100-10000 voters. The obtained results allow to make empirical approximations of the manipulability of aggregation procedures and to find out the least manipulable ones.
Publication based on the results of:
N. L. Polyakov, Shamolin M. V., Journal of Mathematical Sciences 2025 Vol. 292 No. 6 P. 793–803
The paper proves a number of properties of a class of non-local aggregation rules that simulate
dynamic aggregation. The work is based on the clan approach in the theory of collective choice, which was
proposed by S. Shelah and developed by the authors. ...
Added: October 8, 2025
Karabekyan D., Yakuba V. I., , in: Human-Centric Decision and Negotiation Support for Societal Transitions: 24th International Conference on Group Decision and Negotiation, GDN 2024, Porto, Portugal, June 3–5, 2024, Proceedings.: Cham: Springer, 2024. P. 102–113.
The degree of individual manipulability of positional aggregation procedures is evaluated for the dynamic voting model within the framework of the two-dimensional Downsian model. In the dynamic voting model, alternatives move in steps toward a central point while agents attempt to manipulate at each step. The share of manipulable profiles, i.e., the Nitzan-Kelly index, is ...
Added: September 9, 2024
Cham: Springer, 2024.
This book constitutes the refereed proceedings of the 24th International Conference on Group Decision and Negotiation, GDN 2024, which took place in Porto, Portugal, during June 2–5, 2024.
The field of Group Decision and Negotiation focuses on decision processes with at least two participants and a common goal but conflicting individual goals. Research areas of Group ...
Added: September 9, 2024
Nesterov A. S., Rospuskova O., Rubtsova S., Social Choice and Welfare 2024 P. 519–548
We study the school choice problem and propose a new criterion for comparing non-strategy-proof mechanisms: robustness to manipulations. Mechanism A is more robust than mechanism B if each student (given any preferences of this student and any profile of schools’ priorities) can potentially access a smaller set of schools via a profitable manipulation under mechanism A than under mechanism B. This criterion strengthens the two ...
Added: March 10, 2024
Ivanov A., Журнал Новой экономической ассоциации 2022 № 5(57) С. 14–23
Abstract. Manipulation is a phenomenon when an agent or a group of agents misrepresent her/their preferences in the ballots in order to obtain a better outcome of the social choice. It has been proven that there is no not-dictatorial social choice rule which is nonmanipulable. There are two approaches to fi nd the least manipulable ...
Added: January 26, 2024
Artemii Lomakin, Kamil Minibaev, Alexander Nesterov, Economics Letters 2024 Vol. 237 Article 111647
We examine incentive compatibility of various school choice mechanisms as measured by the number of manipulating students. We find that Boston with Skips Mechanism, Secure Boston Mechanism, and Chinese Mechanism may have more manipulating students than Boston Mechanism. Similarly, Taiwan Mechanism with smaller deductions may induce more manipulating students than Taiwan Mechanism with larger deductions. ...
Added: October 6, 2023
Aleskerov F. T., Ivanov A., Karabekyan D. et al., , in: Advances in Collective Decision Making: Interdisciplinary Perspectives for the 21st Century.: Springer, 2023. P. 95–111.
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 ...
Added: June 1, 2023
Karabekyan D., Журнал Новой экономической ассоциации 2022 № 5(57) С. 24–37
Some distortions are possible in the process of preference aggregation. For example, one voter who is pivotal for some preference profi le may not read instructions properly and accidently submit wrong preference. We study how different voting rules react to these distortions for three, four and fi ve alternatives with computer modelling. One of the ...
Added: January 17, 2023
Bonkoungou S., Alexander Nesterov, Theoretical Economics 2023 Vol. 18 No. 3 P. 965–991
Manipulability is a threat to the successful design of centralized matching markets. However, in many applications some manipulation is inevitable and the designer wants to compare manipulable mechanisms. We count the number of agents with an incentive to manipulate and rank mechanisms by their level of manipulability. This ranking sheds a new light on practical ...
Added: December 9, 2022
Bonkoungou S., Nesterov A. S., / Series WP BRP "Basic research program". 2021. No. 249.
Vulnerability to manipulation is a threat to successful matching market design. However, some manipulation is often inevitable and the mechanism designer wants to compare manipulable mechanisms and pick the best. Real-life examples include reforms in the entry-level medical labor market in the US (1998), school admissions systems in New York (2004), Chicago (2009-2010), Denver (2012), some cities in ...
Added: September 6, 2021
Bonkoungou S., Nesterov A. S., Theoretical Economics 2021 No. 16(3) P. 881–909
Dozens of school districts and college admissions systems around the world have reformed their admissions rules in recent years. As the main motivation for these reforms, the policymakers cited the strategic flaws of the rules in place: students had incentives to game the system. However, after the reforms, almost none of the new rules became strategy-proof. We explain ...
Added: September 6, 2021
Fuad Aleskerov, Karabekyan D., Ivanov A. et al., , in: Evaluating Voting Systems with Probability Models.: Cham: Springer, 2021. P. 231–249.
Added: April 14, 2021
Karabekyan D., Yakuba V. I., , in: Proceedings of the 20th International Conference on Group Decision and Negotiation.: Ryerson University, 2020. P. 120–132.
For the two-dimensional Downsian model the degree of manipulability of 16 known aggregation procedures, based on the majority relation, is evaluated using the Nitzan-Kelly index. Extended preferences for multi-valued choices are used to evaluate the fact of manipulation. Individual manipulability of agents is considered, when manipulating agent moves its ideal point over the plane. The ...
Added: September 3, 2020
Shvydun S., , in: Procedia Computer ScienceVol. 139: 6th International Conference on Information Technology and Quantitative Management.: Elsevier, 2018. P. 182–189.
Nowadays, we have seen a growing number of networks where nodes are connected to each other through different types of relationships. This makes identification of their topological structure and key elements both important and problematic. In this paper we propose a novel model for influence assessment in such networks using social choice rules. We evaluate ...
Added: October 20, 2018
Aleskerov F. T., Karabekyan D., Ivanov A. et al., , in: Procedia Computer ScienceVol. 122: 5th International Conference on Information Technology and Quantitative Management, ITQM 2017.: Elsevier, 2017. P. 993–1000.
The coalitional manipulability of 13 majoritarian aggregation schemes (voting rules) is studied by computational experiments. We consider a special case of coalition formation in which all agents of manipulating coalition report the same first-ranked alternative upon manipulation, i.e. a group of agents misrepresents their preferences and they agree that the same alternative will be on ...
Added: July 16, 2018
Nesterov A. S., Journal of Economic Theory 2017 No. 170 P. 145–168
I consider the problem of allocating N indivisible objects among N agents according to their preferences when transfers are absent and an outside option may exist. I study the tradeoff between fairness and efficiency in the class of strategy-proof mechanisms. The main finding is that for strategy-proof mechanisms the following efficiency and fairness criteria are mutually incompatible: (1) ex-post efficiency and envy-freeness, (2) ordinal efficiency and weak envy-freeness, and (3) ordinal ...
Added: May 30, 2017
Aleskerov F. T., Иванов А. А., Karabekyan D. et al., , in: VIII Moscow International Conference on Operations Research (ORM2016) Moscow, October 17–22, 2016.: [б.и.], 2016. P. 193–194.
The coalitional manipulability of voting rules for special case of coalition formation is studied by computer experiment. For the considered case, the coalition, upon manipulation, consists of agents with the same alternative on the first place in their orderings. Not necessary all agents of the manipulating coalition should report insincere preferences, i.e. manipulating agents can ...
Added: October 21, 2016