clapometer http://www.EnglishForward.com/English/define.asp?dict=CALD&key=13862&ph=on noun [C or U] a device used to measure the popularity of someone or something by the amount that people clap, especially on television programmes: The audience lo
Winner will be determined by applause sounds perfectly natural to me, without an article. It would an article if modified: the applause of the audience, the reading of a clapometer.
Is there really such a device, or is it, as I suspect, just a humorous way of saying that the show's host will listen to the applause and decide who receives the most?