noun
disorder; chaos; inversion of the natural order
A rare yojijukugo literally meaning 'caps and shoes are reversed', used to describe a situation where the proper order of things is turned upside down, such as social hierarchy or logical precedence.
彼の提案は冠履転倒も甚だしい。
His proposal is a complete inversion of the proper order.
この組織では冠履転倒の人事がまかり通っている。
In this organization, personnel decisions that turn the natural order upside down are accepted.