jueves, abril 06, 2006

Materialismo lúdico: Índice de Poder de Banzhaf

Comprometidos en la causa de crear un sustrato ideológico que sustente la toma de conciencia de clase en el mundo Geek y guíe la próxima gran revolución social, les traigo un ejemplo de teoría de juegos aplicada a la política. La teoría de juegos no solo es mucho más divertida que la dialéctica hegeliana, también es más seria. Por eso el materialismo lúdico está llamado a vencer de una vez por todas al marxismo.

Muchas veces nos sorprendemos del peso que un grupo pequeño puede llegar a tener en el parlamento. Nuestra intuición tiende a extrapolar de forma lineal cuando trata con números y cuando estas extrapolaciones fallan, nos inquietamos. Si una cerveza cuesta un euro, seis cervezas costarán 6 euros ¿No?. Pues no, el six-pack suele tener descuento en muchos sitios. Con los escaños pasa igual, el doble de escaños no significa el doble de poder. Tener, por ejemplo el 51% de los escaños te da TODO el poder, y si el rival tiene el 49% no tiene NADA de poder. ¿No sería fantástico poder medir el poder? ¿Puede hacer eso la dialéctica hegeliana?

Pues la teoría de juegos SI QUE PUEDE y Hegel se chincha. El Índice de Poder de Banzhaf, por ejemplo, mide el poder de una coalición según el número de situaciones en que resulta decisiva. Es decir, con que frecuencia el voto de dicha coalición convierte a la formación perdedora en ganadora o viceversa. John Allen Poulos lo explica mucho mejor que yo, y a su libro les remito.

Lo interesante del índice de poder es que no solo depende de los de votos que uno tiene sino de como se distribuyen los votos entre los demás. Aunque calcular los índices de poder es un pelín pesado (¡combinatoria mala! ¡Cálculo bueeeno! ¡Gollum, Gollum!) existe esta bonita página que resuelve el problema por nosotros (aunque con ciertas limitaciones).

¿Que pasa si calculamos los índices de poder en el parlamento? Como la página anterior nos exige una cuota, vamos a calcular los índices para una votación que requiera mayoría absoluta:
partidoEscañospoder
PSOE16451.52 %
PP14810.55 %
CIU1010.12 %
ERC87.94 %
PNV76.67 %
IU54.12 %
CC33.64 %
OTROS11.09 %

Impresionante testimonio ¿verdad?. Al grupo mayoritario le da igual sumar los 148 escaños del segundo o los 10 del tercero porque en ambos casos rebasa la mitad de los votos. Seguro que la comparación CIU-PP encantará a unos y aterrará a otros, pero nadie quedará indiferente.

De propina les enlazo este paper sobre IPB en la UE

Demóstoles

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