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Now if Sandy happens to die before retirement, this is quite true. But if Sandy makes it to retirement age, she's going to be faced with a problem under the Social Security abolition system. Let's say the market continues to grow nicely between now and then (in which case there would have been no need to change anything in the first place) so Sandy has a decent-sized nest egg. The problem is that Sandy doesn't know how long she's going to live, and if she lives a long time (as people increasingly do nowadays) may wind up outliving her investment. Under the current system, that's not a big problem -- she would have been guaranteed Social Security benefits proportional to the wages she used to earn for the rest of her life.
Abolition advocates say Sandy can solve this problem by buying an annuity from an insurance company. This is a sort of reverse life insurance that lets you hedge against longevity by converting your lump sum of savings into a guaranteed monthly benefit (just like today's Social Security). But if Sandy does this she won't have anything to pass on to Wynter after all, though Wynter will spend her working life paying taxes to repay the $2 trillion (plus interest) that Bush borrowed in order to finance the transition. Another major problem with the annuity proposal is that even if the market does perform well over the long run (it has in the past -- I should emphasize again that if it does in the future Social Security doesn't need any fixing), if Sandy happens to retire during a down year (and these happen pretty frequently, even in the context of long-term growth) then she'll be stuck with lower monthly benefits for the rest of her life.
I want to add that while any mandatory private savings plan is, to me, an abominably bad idea, whether it's just "abominable" or "super nuclear fuck abominable" will depend a great deal on the details of said plan. It's difficult of course to write about these details when the plan does not exactly exist. But, I'm not very optimistic that our media will be very up to the job once the magic plan is unveiled. They've been doing an admirable job screwing up the reporting on the details of a plan which has been around for quite some time now, so I don't expect them to get much beyond the press releases whenever the new plan is unveiled.