Similar proposals have proven highly successful in Chile and in a number of other countries. I have witnessed the success of the Chilean system first-hand. Under Chile's PSA system, neither the worker nor the employer pays social security tax to the state. Instead, during their working life they automatically have a percentage of their wages deposited into their own PSA account. A separate government agency provides oversight over this program to prevent theft and fraud.
Workers are free to change from one administrating company to another.
This provides competition among the companies to provide a higher return on investment, better services, or lower commissions. Each worker is given a PSA passbook so they can watch their savings grow. They receive quarterly statements informing them on how well their investment funds have performed. They use ATM-like machines that permit the workers to calculate the expected value of their future pension based upon their contributions, and the age at which they wish to retire. Conversely, a worker may type in how much money they want to receive when they retire, and at what age, and the computer will tell them how much they will need to contribute to achieve their desired outcome.