Social Democratic economic theory is that unions and collective bargaining can dramatically improve the earnings of the working class relative to owners of capital.
Neoclassical economic theory in contrast predicts that unions are not needed. Competition among firms for workers ensures that labor get's its marginal product. Social Democrats believe this is naive.
There is simple and powerful evidence that the Social Democratic theory is wrong and the neoclassical theory is correct.
I have plotted the share of workers that are covered by collective bargaining agreements. This is better than the share of workers that are members of unions. In some countries, such as France, few workers are actually members of unions, but unions have the power to determine contracts for workers that are not members. There are huge differences across countries. In Sweden and France 90% of workers are covered by collective union agreements. In the U.S and Japan only 15% of workers have their wages determined by unions.
I also plot the share of national factor costs that goes to labor (as wages and compensations). What you will notice is that this does not vary systematic across countries.
The way the economy gets divided between capitalists and workers is virtually identical in weak union countries such as the U.S as it is in countries with powerful unions, such as France and Sweden.
If anything, American workers with weak unions get a bigger share of the cake compared to European workers with strong unions. Due to high labor costs, European workers have to some extent been replaced by machines.
Italian workers get slightly less than other countries. The reason I believe is that they have a high share of self-employed, which does not fit nice in the capital-labor divide.
So are unions useless? Not entirely. Unions can raise the wage of some workers, but not at the expense of capital, but at the expense of consumers (mainly other workers), or perhaps single "rent" earning industries (such as mining or years ago American auto). This is good and well for those few workers, but does not work as a large scale redistribution program, since workers are just transferring resources from other workers.
Second, Unions seem to be better able to extract rent within the class of workers, from high skilled to low skilled workers, than they can do with capital, which is very responsive to returns. If capital earnings go down, investments in capital goes down, or is perhaps re-located to other countries. In contrast I.Q. and education seem less elastic in supply, so they can be taxed more by unions.
This simple graph can tell us a lot about the economy, and is a powerful argument against the world-view of the left.