HERE IS THE OVERRIDING RULE OF DOWNSIZING ------THE FIRST OFFER IN THE DOWNSIZING WILL BE THE BEST IN MOST INSTANCES

1) That they have offered at all means they have sized it up and the management thinks they can do without you. <------EMPHASIS
2) Assuming you are senior staff the company paints a good picture on it if you voluntarily leave on your timetable, so to speak. It helps to keep appearances up and rumors down. It helps to avoid that office talk of .........."firings will continue until morale improves."
3) The highest paid are the first to go IF someone from above or below can take over the dutires. Sad but true. Forget the loyalty. In the managerial accounting group everyone is a line item in the overhead.
4) As I said above.........the first offer you receive to take early retirement/firing/severance is almost always the best.

I was the COO for a small but publicly traded company for quite a few years. I had to plan and implement overhead reductions on two occasions. FYI. This is sort of how it always worked, for good or bad.