To appoint someone as a deputy or representative, or to assign a task to someone on your behalf.
From Latin 'deputare' (to assign, allot, appoint), from 'de-' (thoroughly) plus 'putare' (to reckon, think, prune).
Shakespeare used this verb—to 'depute' someone meant giving them your authority in a way that was formal and official, contrasting with just asking a favor.
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