What was the proposal to privatize Social Security?

The most recent proposal to privatize Social Security was
put forward by Pres. Bush in 2004 during his campaign for reelection.  After being
reelected, he put some effort into pushing his plan, but was unable to get it passed by
Congress.

Bush's plan was, basically speaking, to allow
people to pay into private accounts instead of Social Security.  In such a plan, a
person's savings would actually belong to them rather than going into the general Social
Security pool.  This money would have been invested in one of a variety of plans
(various mixes of stocks and such).  The person who put the money in would get back
whatever they put in plus however much money it made through dividends and having the
prices of stocks and such go up.  This would have been in contrast to the current system
where all the money that people put into Social Security goes into a big pool that is
paid out to retirees based on formulas set up by the
government.

It is hard to know whether this would have been
good or bad for investors.  In the aftermath of the financial crash of 2008, it does not
look good because of how much the stock market fell.  This kind of volatility in the
stock market scares people and makes them want to have the more "guaranteed" return of
Social Security rather than gambling on stocks.