The strongly stable core in weighted voting games

Abstract

The problems associated with the concept of the core in spatial voting games such as non-existence and instability are well documented. The structurally stable core, presented by Schofield, attempts to resolve these problems by looking at the subset of the core which is still nonempty after a small change in voter preferences. Although this concept, combined with the adoption of supramajoritarian voting rules and weighted voting games, may very well explain the observed stability in reality, it may not be suitable for certain coalition situations. This article proposes a new solution concept, the strongly stable core. The conditions for the existence and the potential location of the strongly stable core are then explored and compared with those of the structurally stable core.