If the layoff criteria was based on a formula such as "manager with no or few direct reports" = higher salary = efficient savings, why not disclose that? One reason is that it may eliminate good people because of where they fit in a demographic.
The other way is to have dept. heads choose but, that leaves it open to politics so you can terminate those that you don't like based on any ole prejudice. This would likely lead to illegal terminations which is why, my friends, there was a need for secrecy.