On page 99 of Hidden Order, David Friedman writes:
Social Security taxes are paid half by the employer and half by the worker. How would the effect of the tax change if it were collected entirely from the worker or entirely from the employer? Why do you think Social Security is set up this way?
Earlier in the book, Friedman proved that who actually pays a tax - that is, whether the money comes out of the profits of the producers or is paid by the consumers in the form of higher prices - is not determined by who hands over the money to the government, but whose supply/demand curve is more elastic. That is to say, asking the producer to pay some tax per widget sold is equivalent to asking a consumer to pay the same tax per widget bought. If the demand for the widget is inelastic, much of the tax burden would fall on the consumer and not if the widget has a fairly elastic demand curve.
In light of this fact, it shouldn't matter which way the tax burden of Social Security is split. If the employer had to pay the entirety of the tax, she would pay a proportionately lower salary to the employee; if the tax burden fell solely on the employee, his salary would be higher.
One possible explanation of the present setup of Social Security is that voters don't understand economics. Although this answer works remarkably well as a justification for other inefficient government practices like trade barriers and rent controls, it flies in the face of the "don't attribute to incompetence what can be explained by rationality" principle that Friedman has adhered to throughout the book.
I am not from the US so I could be missing something obvious here, but given what I know I can come up with no better explanation. Any help would be appreciated.