"Offers will be reviewed by senior management" is pretty vague.
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The method chosen (“name your price”) is fairly unorthodox, so 3rd party may have been chosen to simply avoid claims of bias
“Fred got 7 months and I only got 5, despite....”
“Sorry, we didn’t ultimately handle those decisions”
They are reviewed by management and a 3rd party HR law firm. Couldn’t even do this in house. Had to outsource and waste more money!