Satire( the use of humor to make fun of another work, institution, or society with

The three words that share the same word root are:

All three words come from the Latin root mandare wchich means "to commit, to entrust". Mandate comes directly from this root which is composed by two roots man (Indo-European root with the second meanign "hand") and dare  "to give".

In general, all the words have the similar meaning "to give orders, give permits, to have the power to have the authority over something or someone" or literally "to give into one`s hand".