Social security is not just an investment vehicle, it is also an insurance scheme. The insurance portion is that annuity is paid until beneficiary's death, but not a month more. So people who die early subsidize those who live a long life. The law of large number says when the participant of an insurance scheme increases its variance will be reduced, so there is efficiency to be gained from mandatory participation – a smaller variance implies smaller surplus to absorb negative shock. With government as the sole administrator there is also savings compare to private insurers building multiple administrative system and staff for just a portion of the population. Since safety is at the heart of social insurance, pursuing superior investment outcome isn't desirable as it inevitably involves risk taking and will have winners and losers. The goal of all social security is to provide a basic safety net, not a luxury retirement, hence there is a cap on pay that is subject to payroll tax. There is also a small degree of wealth transfer – lower income people will see social security replace a higher proportion of their pre-retirement income, but higher income people will also see a larger check. The bottom line is that society will always have losers, who don't save enough when they are young, squandered their money in bad investments, or become victims of a crime. Social security system is to provide that basic safety net so as to eliminate the need for charity helping senior citizens struggling financially perhaps in the street. Without government mandate individuals cannot by themselves form such an insurance pool, especially considering the ones who need it most is likely the ones refuse to buy in the first place.