I think doubt is a negative emotion, so I find it difficult to know what is meant by "benefit of the doubt". How does this phrase work, and how did it arise?
closed as general reference by Matt E. Эллен♦, aedia λ, user2683, kiamlaluno, Daniel Mar 7 '12 at 14:20
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It means that when a speaker has explained something, the listener doesn't entirely believe them, but accepts their argument as they have no contrasting arguments.
"The doubt" refers to the the doubt that the listener has as to the veracity of the speakers version of events. It is negative, in that it does imply that the listener does not entirely believe the listener, but that their version of events is at least plausible.
"The benefit" refers to the fact that the listener is not entirely convinced either way, and so gives the speaker the benefit or the most positive outcome that they can, and believes them.
So the speaker gets the benefit or positive results of there being doubt as to whether the account is correct.
Giving someone (or something) the benefit of the doubt is an idiom, so normal senses don't apply. Note that this idiom requires the before doubt, unlike (for instance) the idiom without a doubt, which requires a.
Jez and Barrie have defined the sense closely enough; the idea is that, when there is some doubt about something, then one's opinion could go either way, and that could benefit someone. Or not. If we give a person the benefit of that doubt, then we decide in their favor, pending further information.
It's always a provisional decision, and usually used as the object of the verb give.