In the Fellowship of the Rings movie, the Middle Earth Council('Elrond's Council') were arguing about who was to bear the Ring. The scene was fierce because of the differences between races (conflicts between Dwarves and Elves, Human's desire, etc.) and they couldn't get to a consensus. But then when Frodo spoke, suddenly all of them agreed to let Frodo be the Ring-bearer.

I knew that there was record for a Hobbit not being tempted by The One Ring (Bilbo), but why did all of them agree, all of a sudden?