'Idiocy' carries a strong negative feeling; use it to express clear disapproval of someone's actions or ideas. Calling that idea idiocy really showed his disapproval.
Pro Tip 2/3
Context Matters
Use 'idiocy' when discussing topics where intelligence or good judgement are expected, to highlight a failure in these areas. In the context of strategic games, his move was pure idiocy.
Pro Tip 3/3
Often Hyperbolic
'Idiocy' can be used for emphasis or exaggeration; not always meant literally. He laughed off his late-night shopping as a moment of idiocy.