An individual manipulability of positional voting rules

Aleskerov, Fuad; Karabekyan, Daniel; Sanver, M. Remzi; Yakuba, Vyacheslav

doi:10.1007/s13209-011-0050-y

Cited by 17 publications

(9 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different versions of the k-stable set were introduced in [3]. In [1], extended preferences were introduced, in which many alternatives are ordered based on the singlevalued preferences of the agents. To evaluate the degree of manipulability of aggregation procedures, the Nitzan -Kelly index is used, which was introduced in [7,8].…”

Section: In This Matrix Inmentioning

confidence: 99%

“…For the case of multiple choice, the sets of alternatives also should be compared as an extension to the agents' preferences. In total, as introduced and discussed in [1], there are 4 extensions for 3 alternatives, 10 extensions for 4 alternatives, and 12 extensions for 5 alternatives. In the following formulae the extensions differ in underlined parts.…”

Section: Extended Preferencesmentioning

confidence: 99%

“…For 3 alternatives, the extended preferences look as follows, (agent's single-valued ordering is assumed to be a > b > c): PWorst (4 alts): The preference extensions are defined axiomatically. Formal definitions of all extended preferences and detailed discussion is presented in [1].…”

Section: Extended Preferencesmentioning

confidence: 99%

“…There are m alternatives (m = 3, 4, 5) and n agents (n = 4-20), even number, generated randomly with X coordinates from 0 to 1 and Y from −1 to 1. Without loss of generality we can assume that in any profile there are two alternatives that are farthest from each other, for example, a and e in the case of 5 alternatives, are placed in fixed positions: a in [0,0], and e in [1,0] and all alternatives are sorted alphabetically along the X axe. For each agent, the ordering of sincere preferences is constructed according to the distance from the agent's ideal point to alternatives.…”

Section: The Scheme Of Calculationmentioning

confidence: 99%

See 3 more Smart Citations

Manipulability of Majoritarian Procedures in Two-Dimensional Downsian Model

Karabekyan

Yakuba

2020

Lecture Notes in Business Information Processing

Self Cite

View full text Add to dashboard Cite

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 range of possible manipulating positions of the agents is restricted to some rectangle on the two-dimensional coordinate space, within the feasible area of positions of alternatives and agents. The preferences of agents are assumed to be linear orders, constructed by the proximity of the alternatives to the agents, ordered according to Euclidean distance. The computer calculations, using Monte-Carlo simulations has been performed for 3, 4, and 5 alternatives and for even number of agents from 4 to 20. 100 thousands profiles were generated for each number of alternativesnumber of agents case. The results of the simulations show that there are groups of procedures with relatively low degree of manipulability for all of the considered multiple-choice extensions.

show abstract

Section: In This Matrix Inmentioning

confidence: 99%

Section: Extended Preferencesmentioning

confidence: 99%

Section: Extended Preferencesmentioning

confidence: 99%

Section: The Scheme Of Calculationmentioning

confidence: 99%

See 2 more Smart Citations

Manipulability of Majoritarian Procedures in Two-Dimensional Downsian Model

Karabekyan

Yakuba

2020

Lecture Notes in Business Information Processing

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this case 12 votes were needed for a simple majority. This rule is very similar to Hare's rule or the Instant run-off rule, which is considered one of the least manipulable rules (Aleskerov et al 2011(Aleskerov et al , 2012. The main difference is that in the Instant run-off rule all the information about the preferences is provided at the beginning and voters rank all the alternatives in advance, while for exhaustive ballot system voter can vote 4 differently at each stage.…”

Section: Main Notions and Assumptions Of The Analysismentioning

confidence: 99%

Strategic Behavior in Exhaustive Ballot Voting: What Can We Learn from the FIFA World Cup 2018 and 2022 Host Elections?

Karabekyan

2016

SSRN Journal

Self Cite

View full text Add to dashboard Cite

There are many allegations about whether FIFA world cup host countries were chosen honestly or not. We analyse the results of the FIFA Executive Committee voting and reconstruct the set of possible voting situations compatible with the results of each stage. In both elections, we identify strategic behaviour and then analyse the results for honest voting under all compatible voting situations. For the 2018 FIFA world cup election Russia is chosen for all profiles. For the 2022 elections the result depends on the preferences of the FIFA president Sepp Blatter who served as a tie-breaker. If Sepp Blatter prefers Qatar over South Korea and Japan, then Qatar would have been chosen for all profiles. Otherwise there are the possibility that South Korea or Japan would have been chosen as the 2022 host country. Another fact is that if we consider possible vote buying, then it is shown, that the bribery of at least 2 committee members would have been required to guarantee winning of Russia bid and at least 1 member for Qatar.

show abstract