Simple Majority Achievable Hierarchies

Abstract

hierarchy, ordinal equivalence, power indices, simple majority, voting games,

The influence relation for ternary voting games

“…The number of players in the ordered list of equivalence classes is called a hierarchy. Many papers in the literature deal with the concept of hierarchies in the context simple games (Carreras and Freixas, 1996;Friedman et al, 2006;Bean et al, 2008;Freixas and Pons, 2008). In Section 7 this concept is extended to TVGs.…”

Achievable hierarchies in voting games with abstention

“…The study of hierarchies within the class of simple games can be traced back to Friedman et al [20] and continued by Bean et al [3], even though it is also an implicit study in Carreras and Freixas [5]. Indeed, in Friedman et al [20] it is proved that complete simple games and, particularly, weighted simple games show many di¤erent hierarchies, although two sequences of hierarchies are never achievable.…”

Characterization of Threshold Functions: State of the Art, Some New Contributions and Open Problems

“…This ordering entails a hierarchy among voters. Some studies on allowable hierarchies can be found in [2,20,24]. As before, we denote by N 1 > · · · > N t the equivalence classes which form the unique partition of N where a ≻ b for all a ∈ N i and b ∈ N j with i < j.…”

“…1, 1, 1, 1, 1, 1, 1, 1], i.e., there are only two types of provinces -the large ones, Ontario and Quebec, and the small ones, see [19]. Indeed the game is complete and the minimal winning vectors are given by (2,5) and (1,6). The maximal losing vectors are given by (2,4), (1,5), and (0, 8), so that we have M = 1 2 and P = 3.…”