tail

the tail wags the dog the less important or subsidiary factor or thing dominates a situation; the usual roles are reversed.

2012Washington Post He said that primary challenges from the ideological fringe allow a relatively small minority to exert undue influence on electoral outcomes.…'We've set up a system that allows the tail to wag the dog,' Edwards said.

turn tail turn round and run away. informal

with your tail between your legs in a state of dejection or humiliation. informal

with your tail up in a confident or cheerful mood. informal

☞ For other idioms containing tail, see the entry for the main word in the idiom (for example, make head or tail of at head).