What is the Link between Unionization and Inequality?

Stephen Gordon asks:

What is the link between unionisation and inequality?

After looking at the data he concludes:

Increases in inequality were accompanied by declines in union coverage in Canada, the US, the UK and some other countries. But similar increases in inequality were accompanied by increased union coverage in Sweden, Norway and Finland.

I don't really see much of a link - either in theory or in the data - between unionisation rates and increases in inequality across occupations. (Inequality within an occupation is a different story.)