# A reverse engineering problem

I want to try and work out what the relative voting strength of each union was in Labour’s leadership primary. My maths is too rusty to calculate it myself, but hoping some readers can help.

The voting breakdown for each union was:

- DWU – Cunliffe 33, Robertson 0, Jones 6
- EPMU – Cunliffe 25, Robertson 8, Jones 2
- Maritime – Cunliffe 18, Robertson 3, Jones 2
- MWU – Cunliffe 22, Robertson 1, Jones 6
- Rail – Cunliffe 18, Robertson 3, Jones 2
- SFWU – Cunliffe 254, Robertson 177, Jones 66

We know that the overall result was Cunliffe 70.77%, Robertson 17.3% and Jones 11.9%. So the question is what weighting is given to each union, to get that result?

Based on registered members, the DWU should be around 8%, EPMU around 40%, Maritime 3%, MWU 17%, Rail 7% and SWFU 25%. But the voting strength is based on affiliated members, not weighted members. The percentages above could vary by several per cent.

If someone can work out a formula to calculate voting strengths, that would be great. Why I want that, is to calculate the relative strength of a delegate in each union.