Republicans try to appeal to younger voters by painting SS and Medicare as "entitlements" that were not earned, but given to them by currently-employed workers. There is just enough truth in that to appeal to the stupider ones.
The problem with turning SS into a 401(k) type scheme is the vagaries of the markets. What happens if the markets -- and all that money the government invested for you -- are down at the time you decide to retire? Either you accept less pay-out, or you continue working. The current scheme has concrete payouts which allows employees more freedom in deciding when to hang it up. There is no risk-taking. And you don't end up having to move in with one of your kids.
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