Distinct Random select
Assuming a not very old version of SQL-Server, you can use ROW_NUMBER() to find one row per submitter:

; with r as
  ( select id, submitter, answer, 
           rnd = row_number() over (partition by submitter order by newid())
    from #tmpData 
  )
select id, submitter, answer
from r
where rnd = 1 ;


Test at: SQLfiddle