This continues on from the previous post, trying to make some sense of the voting in my electorate of Wills and the neighbouring electorate of Cooper. Both these electorates (or more formally "Divisions"), as I mentioned in the previous post, are very similar in their geography, demography, and history.

Last …

As we have seen previously, it's possible to compute power indices by means of polynomial generating functions. We shall extend previous examples to include the Deegan-Packel index, in a way somewhat different to that of Alonso-Meijide et al (see previous post for reference).

Again, suppose we consider the voting game …

We have explored the Banzhaf and Shapley-Shubik power indices, which both consider the ways in which any voter can be pivotal, or critical, or necessary, to a winning coalition.

A more recent power index, which takes a different approach, was defined by Deegan and Packel in 1976, and considers only minimal winning …

Introduction and recapitulation

Recall from previous posts that we have considered two power indices for computing the power of a voter in a weighted system; that is, the ability of a voter to influence the outcome of a vote. Such systems occur when the voting body is made up of a number of "blocs": these …

Naive implementation of Banzhaf power indices

As we saw in the previous post, computation of the power indices can become unwieldy as the number of voters increases. However, we can very simply write a program to compute the Banzhaf power indices simply by looping over all subsets of the weights:

def banzhaf1(q,w): …