|A separating family|
Carreras (2009) divides coalitions into four groups: decisive winning coalitions, conflicting winning coalitions, blocking coalitions and strictly losing coalitions depending on whether a coalition or its complement is winning or losing. The focus is then on blocking coalitions that can prevent, although themselves cannot make changes. A separating family of coalitions is a set of coalitions, such that for each maximal inclusive chain of coalitions contains an element.
While it is common to define voting games in terms of winning coalitions, Carreras studies games defined in terms of blocking coalitions. The blocking coalitions
The ability to block is just another manifestation of power and it is therefore natural to apply power measures to blocking. Several blocking indices are introduced analogously to power indices. While these give additional information to power indices, interestingly in games with many blocking coalitions the Banzhaf strict protectionism index will be close to the Banzhaf value. Some additional properties are discussed, but an axiomatic characterisations of the newly introduced indices is not presented.
The review will be published in Mathematical Reviews.
Carreras F. (2009) Protectionism and blocking power indices, Top 17: 70-84