Suppose we are trying to get a board of six directors to agree on something. In this case, the board is has six members. Faction A has three directors that act in tandem. Faction B has two directors that vote together. Faction C has only one director.

Suppose to pass a resolution, 4 votes are required.

Suppose you are trying to influence the board and they slowly come round to agreeing with you, the Shapeley-Shubik index of power can be used to measure the influence of each faction.

If you convince Faction A first, you will have three votes. This is insufficient to get your resolution passed. But if you can get Faction B next, the resolution will pass, then Shapely-Shubik index for Faction B increases by 1 because they are pivotal for the resolution to be passed. In game parlance, B scores one point.

( For the folks who actually know this Shapely-Shubik