Annexations and alliances: When are blocs advantageous a priori?

For any simple voting game (SVG), we consider the question posed in the title from two different points of view as to what voting power means. We also distinguish between blocs imposed by annexation and those formed voluntarily, and present some general theoretical results concerning these notions. We illustrate our theoretical findings with examples using both toy SVGs and the Qualified Majority Voting rule of the Council of Ministers of the European Community (CMEC). We show that when voting power is understood as influence (I-power), forming a voluntary bloc may be advantageous even if its voting power is smaller than the sum of the original powers of its members; and it may be disadvantageous even if its voting power is greater than that sum. Received: 9 February 2000/Accepted: 19 October 2000