... instead of "What do you say?"
I am not sure if "What say you?" is even grammatically correct.
According to Urban dictionary it's a variation of what do you think. Here is the full description.
And here is what Learners dictionary has to say:
The way modern English formulates questions by using "do" as an auxiliary is rather recent in the story of English (~1400-1500).
In Modern German for instance you would say:
In Old English (before the Norman invasion) you would say something very similar.
The UK legal and judicial system is deeply rooted in the Anglo Norman historical period (1066-1485) and therefore predates the "periphrastic do" evolution (~1400-1500).
Just because it's archaic, doesn't make What say you ungrammatical.
And it's not just a stock phrase used in court, either. Here's What think you, which wouldn't often be said in a courtroom. But as the chart clearly shows, definitely an expression from yesteryear...
Over at the "Phrase of the Week" website, there's a question about the origin: http://www.phrases.org.uk/bulletin_board/58/messages/1572.html
With that in mind, for an exchange of information as critical as asking for a plea in court, the language should be formalized. If the question "what say you" evolved into "what is your plea?" or maybe "what would you like to plead?"... then maybe later the defendant might say "well you asked me what I would like to plead, not what I actually do plead." and then an unnecessary argument follows.
So for an important exchange, formal language helps with clarity.
As for why it hasn't been formalized as "what do you say" ... well, I think it's human nature to want assurances of structure. The awkward phrases sounds more formal, so helps us trust that the court proceedings are structured and formal.
Thank you for your interest in this question.
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