Kempten Autumn Talks

Title of the lecture

“Ordinal measures of influence in social structures”

Abstract

In the literature of cooperative games, the notion of “power index” has been widely used to evaluate the “influence” of individual players (e.g., voters, political parties, nations, stockholders, etc.) involved in a collective decision process, i.e. their ability to force a decision in situations like an electoral system, parliament, governing council, management board, etc. In practical situations, however, the information concerning the strength of coalitions and their effective possibilities of cooperation is not easily accessible due to heterogeneous and hardly quantifiable factors about the performance of groups, their bargaining abilities, or other “psychological” attributes (e.g., the power obtained by threatening not to cooperate with other players). So, any attempt to numerically represent the influence of groups and individuals conflicts with the complex and multi-attribute qualitative nature of the problem. For these reasons, we introduced new solutions to provide a more flexible theory of cooperative interaction situations and power indices based on the evidence that the nature of available information about the interaction of individuals and groups is mostly ordinal.

In the paper [5] a particular social ranking (i.e., a map assigning to each “ordinal power relation” over the coalitions a ranking over the single players) is provided in terms of a classical solution concept for cooperative games that is also invariant to the choice of the characteristic function representing the ranking over the coalitions.
A similar problem has been studied in the paper [2], where the authors axiomatically characterize a different solution based on the idea that the most influential individuals are those appearing more frequently in the highest positions in the ranking of coalitions. Another social ranking solution has been proposed and studied in paper [3], where two individuals are ranked using information from ceteris paribus (i.e., everything else being equal) comparisons over all coalitions.
A still different social ranking solution based on the idea of ordinal marginal solution was more recently introduced in paper [4]. The resistance of social ranking solutions to a malicious behaviour
of individuals, and the related computational complexity of manipulations, has been also studied in paper [1].

The goal of this talk is therefore to provide a general introduction to basic notions and some main results related to social ranking solutions and their properties from the recent literature.

References

[1] T. Allouche, B. Escoer, S. Moretti, and M.Ozturk, “Social ranking manipulability for the cp-majority, banzhaf and lexicographic excellence solutions”, in Proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI-PRICAI 2020), p. accepted, 2020.
https://www.ijcai.org/Proceedings/2020/3

[2] G. Bernardi, R. Lucchetti, and S. Moretti, “Ranking objects from a preference relation over their subsets”, Social Choice and Welfare, pp. 1-18, 2017.
https://link.springer.com/article/10.1007/s00355-018-1161-1

[3] A. Haret, H. Khani, S. Moretti, and M.Ozturk, “Ceteris paribus majority for social ranking”, in Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI 2018), pp. 303{309, 2018.
https://www.ijcai.org/Proceedings/2018/0042.pdf

[4] H. Khani, S. Moretti, and M.Ozturk, “An ordinal banzhaf index for social ranking”, in Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI 2019), pp. 378{384, 2019.
https://www.ijcai.org/Proceedings/2019/0054.pdf

[5] S. Moretti, “An axiomatic approach to social ranking under coalitional power relations”, Homo Oeconomicus, vol. 32, no. 2, pp. 183-208, 2015.

Slides of the lecture