There have been many proposals to privatize social security retirement
funds.  How much of the contributions could be used for this purpose
while still funding other social security benefits such as disability
etc and those that outlive their contributions.  Is that remainder
sufficient to fund the current benefits rate to a typical retiree if
they don't live too long.  How does this change if the survivors keep
the benefits like almost all pro-privatization plans consider instead
of the excess funding those who "live too long"?  I am looking for
realistic scientific analysis of these factors (pro, con, or neutral),
not a politic position paper.  I am puzzled why I can't find this
information easily!

I am most intrigued by this issue myself and have done some math you
might find interesting:

A moderately poor person ($25,000 per year income) works from ages
26-67 then collects SS... he will get $1,244 according to www.ssa.gov
(they have a calculator to figure this out).
Right now SS collects a total of 14% from income (7% from the employee
and 7% from the employer).  If this person was allowed to invest 4%
and paid only 10% into SS, here are some possible results for various
interest rates he could receive:
6% interest (very conservative): He can collect $1,000 per month from
age 67-100 just from his investments.
8% interest (moderate): He can collect $2,000 per month from age 67-100
10% interest (aggressive but still less than the market has averaged
over the last 80 years): He can collect $4,000 per month from age
67-100.
**these are all inflation adjusted at 2.7% per year from age 67-100

And that is only from his investments.  Let's say now that the
government can aafford to pay him half the old benefit (remember he
paid in 10% of the normal 14% or 71% of the normal amount)...  that
means SS will pay him $622 per month on top of what his investment
gives him.
So it is completely obvious that the retiree will benefit (possibly
benefit greatly) from this option.

Now let's consider how the SS program (ie the government) fairs in this situation:
The government collect 71% of their normal SS income.  The current
payout would be $1,244 and the new payout (with the 10% collected/4%
invested idea) is $622 (half the old payout).  Until this person
retires (and government SS expenses decrease by half), the government
must borrow that additional 29% that is uncollected in the meantime. 
Government bonds have averaged around 5% over a couple decades so
we'll use this figure:
So this poorer employee now pays 10% of his income into SS (rather
than 14% as before) so the government must borrow 4% of $25,000 per
year to make up for the rest.  This is $1,000.  The employee works for
42 years (age 26-67)... the total debt (including the 5% interest)
that the government rakes up is $135,000 for this person.  But now the
government starts paying out $622 less per month because the employee
can rely mostly on his retirement account.
At the employees age of 91, the government makes up it's loss
(including interest before and during retirement) and at age 100, the
government is ahead $165,000 from the position that it would have been
in under the old system.

There are some assumptions in this math, but accounts can clearly be
beneficial for both the government and the employee in the long run if
done even with reasonable intelligence.  The only concern is that in
the short run, the SS system will be less funded and will require the
government to borrow more.  But as you can see above, in the long run,
the government can pay off this debt (and the interest accrued) with
no problem and even come out way ahead.