Shapley-Shubik Index Calculator

About this calculator

The Shapley-Shubik power index measures how much real influence each voter has in a weighted voting game, not just their nominal vote share. It considers every possible ordering of voters (all n! permutations), finds the pivotal voter in each ordering — the one whose vote pushes a growing coalition from below the quota to meeting it — and gives each voter the fraction of orderings in which they were pivotal.

Political scientists and legal scholars use this index to analyze bodies with weighted votes, such as the EU Council of Ministers or corporate shareholder meetings, showing that a voter's actual power often differs sharply from their raw vote weight — a large bloc can sometimes have zero power if it can never be pivotal, while a small one can be decisive.