David is the son of the 1972 Nobel Laureate in Economics Kenneth Arrow. His mother Selma is a psychotherapist. He became interested in acting at the age of 12 while attending The Carroll School for dyslexic children. His first role was Oliver in the musical Oliver performed at Tuffs University in Massachusetts. His first job in the professional theatre was at age 16 in a summer stock company in Concord MA. One of his fellow cast members was Steve Carell.

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