under protest vs willy-nilly

under protest

prep
  • of a payment made subject to dispute 

  • Without full agreement. 

  • while protesting 

willy-nilly

adj
  • That happens whether willingly or unwillingly. 

adv
  • Seemingly at random; haphazardly. 

  • Whether desired or not; without regard for the consequences or the wishes of those affected; whether willingly or unwillingly. 

How often have the words under protest and willy-nilly occurred in a corpus of books? (source: Google Ngram Viewer )