What is the story's main message or theme & what does the story reveal about popularity?
Katherine Mansfield's short story "The Doll's House" shows that people will always gravitate toward those who are considered social or financial "betters". The Burnell girls, who are rich and come from a high social status, receive their new doll's house as a gift from someone equally wealthy. The gift befits the status of the girls: it is expensive, sophisticated, rich in detail, and entirely ornamental.
Having access to such a richly detailed gift made the girls popular at school.
Playtime came and Isabel was surrounded. The girls of her class nearly fought to put their arms round her, to walk away with her, to beam flatteringly, to be her special friend. She held quite a court under the huge pine trees at the side of the playground
In complete contrast, the only two people who never get to be around the Burnells were their complete opposites, the Kelvey girls--the daughters of a washerwoman and an unknown man. Therefore, money and privilege are unfortunate and superficial binds that temporarily bring people together, until those binds disappear.
That being said, the overall theme of the story is social injustice and the lack of opportunity of the poor to go near the same rights and privileges of the rich. Notice that the Kelvey girls were happy enough to have seen the lamp of the dollhouse: the main feature of the wonderful thing. Having seen it means that, for once, they had laid eyes on the same thing as the Burnells. For the first time, they were all "alike". That is an opportunity that would never present itself to the Kelveys again, so it is all the more cherished for that very reason.