An angel-daemon approach to assess the uncertainty in the power of a collectivity to act

The final publication is available at link.springer.comWe propose the use of the angel-daemon framework to assess the Coleman's power of a collectivity to act under uncertainty in weighted voting games. In this framework uncertainty profiles describe the potential changes in the weights of a weighted game and fixes the spread of the weights' change. For each uncertainty profile a strategic angel-daemon game can be considered. This game has two selfish players, the angel and the daemon, the angel selects its action as to maximize the effect on the measure under consideration while daemon acts oppositely. Players angel and daemon give a balance between the best and the worst. The angel-daemon games associated to the Coleman's power are zero-sum games and therefore the expected utilities of all the Nash equilibria are the same. In this way we can asses the Coleman's power under uncertainty. Besides introducing the framework for this particular setting we analyse basic properties and make some computational complexity considerations. We provide several examples based in the evolution of the voting rules of the EU Council of Ministers.Peer ReviewedPostprint (author's final draft