Why does Judge Ford host a party at her apartment in The Westing Game?

The purpose of the party is to spy on the residents of Sunset Towers to see who is suspicious and find clues.

Judge Ford decides to host an “informal party” in her apartment so that she can get to know the heirs.  When people start using the elevator as a bulletin board, she puts a notice up saying everyone is invited.  She makes sure Mr. Hoo stays even after delivering food.

Grace Wexler coos over the idea of having a party, and offers the judge decorating tips.  None of the guests seem to be having much fun though.  Tensions are too high with the murder and the game on everyone’s minds.

The party went on and on. No one dared be first to leave. (Safety in numbers, especially with a judge there.) So the guests ate and drank and jabbered; and they watched the other guests eat and drink and jabber. No one laughed. (Ch. 10) 

Judge Taylor is not the only one who is watching people and trying to learn things from them. They are all participating in the same contest, after all.  Every word seems to be evaluated. 

 “I’m not having any luck at all, Angela,” Sydelle whined. “If only your mother hadn’t made you change clothes someone surely would have mentioned ‘twin.’ It’s much harder to judge reactions when I have to bring up the subject myself. (Ch. 10) 

Sydelle continually says the word “twins” hoping that someone will react to the clue.  Judge Ford wants in particular to talk to James Hoo, because he seems to have a motive.  He claims that Mr. Westing stole his idea for an invention of paper diapers. 

The guests take a poll as to where “May God thy gold refine?” comes from.  No one gets any conclusive information or clues from the party.  No one says or does anything suspicious, and they never figure out what the mysterious phrase is from.