Well, aside from discounting, that would make sense. Then, the govt can be indifferent as to when you start taking benefits. Of course, there should be some adverse selection, i.e. those that take at 62 are less confident in their longevity (as a whole), so age at which one starts is likely not independent of age of death.
A starting point, albeit a stringent alternative, would be to give the full benefit at the average life expectancy in a single payment. You die before then, you get nothing, you live past that you get a lump sum X. There would be high confidence on the cost of that, but it is not very useful for retirement, so actuaries look at the actual life expectancy data by age/gender (and other variables) and create dollar amounts by age at which benefit starts that have the same cost as the stringent case......less some amount to account for risk and adverse selection.
But, good point. And, perhaps discounting is included in those break-evens. It certainly would be in the actuarial calcs.
