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Ah, I was wrong. Social Security runs at 99.61% efficiency on a dollar in vs. benefits paid basis. (Due mainly to being highly automated)

http://www.cato.org/pubs/ssps/ssp15.pdf

In several important ways, the present Social
Security Administration does a highly efficient
job in administering the retirement program.
Overall administration costs are currently close
to $10 per worker. Those costs amount to 0.42
percent of contributions and 0.57 percent of
benefits paid. As a percentage of assets, the
administration costs are 0.39 percent.

Depending on who you ask, Medicare runs at 99.51% efficiency... or as this conservative think tank states:

http://www.cahi.org/cahi_contents/resources/pdf/CAHI_Medicare_Admin_Final_Publication.pdf


One of the most common, and least challenged, assertions in the debate over U.S. health
care policy is that Medicare administrative costs are about 2 percent of claims costs,
while private insurance companies’ administrative costs are in the 20 to 25 percent
range.
It is very difficult to do a real apples-to-apples comparison of Medicare’s true costs
with those of the insurance industry. The primary problem is that private sector
insurers must track and divulge their administrative costs, while most of Medicare’s
administrative costs are hidden or completely ignored by the complex and bureaucratic
reporting and tracking systems used by the government.
This study, based in part on a technical paper by Mark Litow of Milliman, Inc., finds
that Medicare’s actual administrative costs are 5.2 percent, when the hidden costs are
included.
In addition, the technical paper shows that average private sector administrative costs,
about 8.9 percent – and 16.7 percent when commission, premium tax, and profit are
included – are significantly lower than the numbers frequently cited.

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Either way, the Govt system is much more efficient.