An individual in Parliament can belong to any party (of which there are hundreds) or can be independent of any party but in practice, around 48% belong to the Liberal Party and roughly 48% belong to the Labor Party. Members of these two parties generally vote the same way as all the other members of the same party so when the two parties are opposed to each other on a particular matter, the remaining roughly 4% of parliament hold the deciding votes.

At times, this has come down to a single person and at times a few people who were all from the same party (say, the Greens) who would all vote the same way.

Of course, if the two major parties agreed on a matter, the remaining 4% had no power to affect the vote at all.

Paul: Thanks for the questions. I have limited understanding of the reasons to use one index or the other, but here is what I could dig up.

The Shapley-Shubik is concerned specifically with sequential voting. Perhaps this is an assumption one might make with an open hearing such as a congressional approval.

There is another index used for simultaneous voting called the Penrose-Banzhaf power index, but it requires assuming that voter decisions are made like coin flips. Both SS and PB are commonly used.

I also thought about the conditional voting issue as you point out. In particular elections it is absolutely true that you must consider how people vote. The Shapley-Shubik is a theoretical measure of power–if voting were sequential, which vote is good enough to tip the scale. One might use the Shapley-Shubik index to analyze voters that do not show particular patterns.

Thanks for the suggestion on US voting. I came across a couple articles but didn’t understand them immediately, so I pushed them off. I’ll see if I can work those papers into another article