The most common and most likely answer to this crossword clue is the 8 letter word UNREASON
I've seen this crossword clue in The Times
U
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A
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More clues leading to the result UNREASON
Buddy explains!

The straight part
We know that "Madness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case madness = unreason.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does UNREASON mean?
UNREASON noun- Lack of reason or rationality; unreasonableness; irrationality.
- Nonsense; folly; absurdity.
- To prove to be unreasonable; disprove by argument.
- To apply false logic or think without logic.
- To make unreasonable; to deprive of reason.