An Angel-Daemon Approach to Assess the Uncertainty in the Power of a Collectivity to Act

  • Giulia Fragnito
  • Joaquim Gabarro
  • Maria Serna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)


We propose the use of the angel-daemon (\(\mathfrak {a}/\mathfrak {d}\)) 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 \(\mathfrak {a}/\mathfrak {d}\) game can be considered. This game has two selfish players, the angel \(\mathfrak {a}\) and the daemon \(\mathfrak {d}\), \(\mathfrak {a}\) selects its action as to maximize the effect on the measure under consideration while \(\mathfrak {d}\) acts oppositely. Players \(\mathfrak {a}\) and \(\mathfrak {d}\) give a balance between the best and the worst. The \(\mathfrak {a}/\mathfrak {d}\) 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.


Weighted voting games Coleman’s power of a collectivity to act Uncertainty profiles Strategic games Zero-sum games EU Council of Ministers 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.ALBCOM CS DepartmentUniversitat Politècnica de CatalunyaBarcelonaSpain

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