Deegan-Packel & Johnston spatial power indices and characterizations

In this paper, we propose two spatial power indices in political games, taking into account ideological preferences of players. To do this, we develop an explanatory spatial model linked to the asymmetry Deegan-Pakel index introduced by Rapoport & Golan [Rapoport, A., Golan, E., 1985. Assessment of political power in the israeli knesset. American Political Science Review 79 (3), 673-692], which is the original Deegan-Packel index readjusted for measuring power according to the spatial preferences of players in real political games. In addition to extending such a readjustment for the original John- ston index | transforming it concomitantly into the Johnston spatial power index | this paper presents both the general versions of these two spatial indices, and their axiomatic characterizations through new axioms such as the vetoer property and others mainly in- spired from Lorenzo-Freire et al. [Lorenzo-Freire, S., Alonso-Meijide, J. M., Casas-Mendez, B., Fiestras-Janeiro, M. G., 2007. Characterizations of the Deegan-Packel and johnston power indices. European Journal of Operational Research 177 (1), 431-444].