The Banzhaf index

Many political assemblies are divided along party lines where 
each party usually vote as an unit. It is widely recognized 
that the power a party then can veld is not proportional to its 
number of representatives but rather to the number of winning 
coalitions it can create, the Banzhaf index. The index for a 
party is thus a count of the situations in which the party can 
tip the balance one way or the other.  

Usually the majority decides if a motion is accepted but in some 
situations such as for constitutional changes a greater majority 
may be required. A slightly different situation where the index 
can be applied is the EC's council of ministers. Here each 
countries has multiple votes but only a single representative, 
a motion also requires more than a simple majority to be approved.

The Banzhaf function converts a list of parliamentary seats into a
list of index values.  If different from a simple majority the
required number of votes to gain acceptance can be sent along as a
parameter.

Let the German election in 1994 serve as example. There is a 
remarkable difference between the number of representatives and 
the voting power:

                                    Banzhaf voting
party             representatives   power index
------------------------------------------------
CDU/CSU              294               12           
SPD                  252                4
Die Grynen            49                4
Free Democrats        47                4
PDS                   30                0
   

Reference:  For all Practical Purposes, Editor Lynn Stein


If you have any comments please write to:

Mats Liljedahl
Hemmansv 37
S-433 46 Partille
Sweden