A Core-Partition Ranking Solution to Coalitional Ranking Problems

Social Ranking Problems at the Interplay between Social Choice Theory and Coalitional Games

“…As remarked in [16], the non-emptiness of the core-partition social ranking can be directly proved as a consequence of some results shown in [29]. A simple procedure has been proposed in [16] to compute an element of a core-partition social rankings. We introduce the procedure as the following pseudo-code (Algorithm 1).…”

“…A social ranking that is strongly based on models of coalition formation has been introduced in [16]. More precisely, in [16] the authors study a notion of set-valued social ranking that is defined as a set-valued function R : R(P (N)) ⇒ R(N) associating to each power relation a subset of rankings over the individuals R≿ ⊆ R(N).…”

“…A social ranking that is strongly based on models of coalition formation has been introduced in [16]. More precisely, in [16] the authors study a notion of set-valued social ranking that is defined as a set-valued function R : R(P (N)) ⇒ R(N) associating to each power relation a subset of rankings over the individuals R≿ ⊆ R(N). In particular, core stability, a widely studied notion in the field of coalition formation games [27,28], is a central notion for the set-valued social ranking studied in [16].…”

“…Based on the fact that the set of core-stable partitions is always non-empty, in [16] the authors introduce the notion of core-partition social ranking as the set-valued social ranking associating to each power ranking ≿∈ R(P (N)) the set of rankings "induced" by partitions Π, as follows: Definition 14 (Core-partition social ranking [16]). The core-partition social ranking is the map set-valued social ranking RC : R(P (N)) ⇒ R(N) associating to each power ranking ≿∈ R(P (N)) the set of rankings…”

“…Game theory-inspired social rankings: These rankings are grounded in the principles of cooperative game theory. They leverage established solution concepts from this field to formulate rankings, providing a theoretical and strategic framework for understanding social rankings [15][16][17][18].…”