Sometimes, we need to have a contradiction between what we need to say and the way we say it. While essentially the message might have funny connotations, we need to deliver it in a completely serious tone. That is where a deadpan voice comes in.
Deadpan, is defined as dry humour, or dry-wit humour is the deliberate display of emotional neutrality or no emotion, commonly as a form of comedic delivery to contrast with the ridiculousness of the subject matter. Any listener or viewer who has heard or saw the excellent stand up comedian Steven Wright or seen the silent films of Buster Keaton would know exactly what deadpan means.
Any audience that has a funny bone is certain to appreciate a delivery of a deadpan voice. The bigger the difference between how humorous the content is and how serious the voice sounds, the more will such audience appreciate. This is particularly true if there is an underlying serious point to be made, when it is necessary to show the aburdity or contradictions of a certain situation or situations. This is often the case in political or social situations, where it is essential that after it laughs, the audience starts thinking about what has been said.
A deadpan voice has a flat delivery, as if the speaker doesn't care much about what is and how it is being said. It is understated and the voice expresses no emotions of its own. At no poin during the delivery does the voice change its tone or pitch.