doormat vs willow in the wind

doormat

noun
  • Someone who is overly submissive to others' wishes. 

  • A coarse mat at the entrance to a house, upon which one wipes one's shoes. 

willow in the wind

noun
  • One whose views are easily and regularly changed by the persuasion or influence of others. 

How often have the words doormat and willow in the wind occurred in a corpus of books? (source: Google Ngram Viewer )